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Rummy is the most popular card game played where you have to match cards as per a sequences. If you're new to play real rummy online don't worry, here you will learn the basic of rummy and how to play online rummy. Once you understand the basic rules and strategies of rummy games, you will be rocking the rummy world.
The objective of the Indian rummy game or 13 card rummy game is to place all the 13 cards to be formed into a group of sequences or sets.
The cards game is played either with one set of 52 cards or multiple set of 52 cards. Each set of cards also have two jokers which can be used to form a sequence of set. The cards are ranked low to high from 2,3,4,5,6,7,8,9,10 and points are awarded to the respective number. This a card with number 2 has 2 points and card with number 5 has 5 points. Cards J, Q, K, A have 10 points each.
A sequence in rummy is formed by arranging 3 or 4 cards in sequence. Arranging cards in sequence of a number create a set. A three set can have 3 cards of the sme suits in a sequence 3,4,5 or A,2,3 or four cards in sequence of 10,J,Q,K,A.
A pure sequence is formed when three or four cards of the same suits are placed in an order without the use of Joker or wild card.
A set of card is formed when three or Four cards of the same value but different suits are grouped together.
Not a valid Set in Rummy: Please note if more than one suit of card of the same value is formed within the same group it is not considered as a valid set.
In a single regular deck pack, there are 52 cards and 2 printed jokers or wild card. Usually, we use 2 decks for Point Rummy and the Pool Rummy, it does not depend upon the no. of players.
The opening of all games you will receive 13 cards.
The undealt set of cards is positioned face down, assemble the closed deck. The subsequent card in the set is positioned face up arranging a new discard pile.
At the start of every game, players receive 13 cards and the last opened up card in the deck is called Joker or Wild Card. The rest of the other cards are faced down and turn into the common closed deck or stack of cards.
In the deck, all cards as the same number are considered as Jokers and also called as Cut Joker.
For Example: Opened up Joker card is 5 means all the set of 5 like 5♠ 5♥ 5♣ 5♦ as Joker. So that number of Joker cards in a deck is 4.
In each deck, printed jokers of 2 cards also added. These cards have the image of a real clown drawn on them. These cards don't have any point value, simply it's considered as the Joker or wild card. These cards can be used as a alternate for all cards to form a sequence of sets.
Using 13 cards rummy in your hand, you need to match at least one original or pure sequence. Pure Sequence means you form a set without using any joker card. It is a set of cards of the same suit.
Using of 13 cards in your hand, you have to match another set sequence called impure sequence. If you're used to forming a set with a joker card known as an impure sequence.
The resting cards of 13 can be formed into valid sequences. It may be pure sequence or an impure sequence of the same point value cards.
As per the above explanation the below set is not permitted in the rummy game.
Playing online rummy free or cash both are simple and easy. The player has to start the game by picking the first card from the closed deck or pick the discarded card from the Discard Pile, which the card discarded from the previous player.
Now, the player has 14 cards in his/her hand, player must discard one card to the discard pile. Then the chance goes to the next player. The game is forwarded in a turn wise mode to anyone completes his/her 4 sets and declares. The player's points are considered on the basis of their non-set cards.
Once the player has arranged the 4 correct sequences of the 13 cards, he/ she should show/declare the game.
Before the declaration, player must recheck the set of sequences, it is correctly matched and grouped or not.
If cards are correctly matched and grouped, according to the above validation rules,the first player will win the game.
If the cards are incorrectly matched or grouped, you get a full point that is 80 points for invalid declaration.
Another set is an impure sequence, with or without using a Joker or wild card.
And the remaining 2 sets could be the sequence of the same value points.
You want to save your points always you can drop out the game.
Drop out is the better strategy for a rummy player, if your cards are really bad.
The drop out points is differing according to the time of the drop. Compared to middle drop out, the game beginning drop points is lesser.
If you're declared in the first round of the game, you will not get the full points of other players; the value is calculated as the middle drop of deduction points.
After the card distribution, you exit the table by dropping your cards, it's considered as a full point that is 80.
You can arrange the set consist of minimum 3 and above 4 cards of different suits.
Hope you become master in the rules of rummy game, are ready to play rummy online for cash?


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Category Archives: prisons / criminal justice
What the War on Terror Owes to the War on Crime
Posted on September 10, 2011 by James Ridgeway and Jean Casella | 1 comment
Long before the War on Terror, there was the War on Crime. And as much as 9/11 was a watershed event, many aspects of the nation's response to the terrorist attacks find longstanding precedent in the American criminal justice system.
In his article "Exporting Harshness: How the War on Crime Helped Make the War on Terror Possible," Georgetown Law professor and former public defender James Forman Jr. argues against the widely accepted notion that "the war on terror represents a sharp break from the past, with American values and ideals 'betrayed,' American law 'remade.'" Forman continues: "While I share much of the criticism of how we have waged the war on terror, I suspect it is both too simple and ultimately too comforting to assert that the Bush administration alone remade our justice system and betrayed our values." Instead, he believes, "our approach to the war on terror is an extension–sometimes a grotesque one–of what we do in the name of the war on crime":
By pursuing certain policies and using particular rhetoric domestically, I suggest, we have rendered thinkable what would otherwise have been unthinkable. Moreover, as the world's largest jailer, we are increasingly desensitized to the harsh treatment of criminals. We have come to accept such excesses as casualties of war—whether on crime, drugs, or terror. Indeed, more than that, we no longer see what we do as special, different, or harsh. Certain practices have become what David Garland calls "the taken-for-granted features of contemporary crime policy." In part for this reason, despite the mounting evidence regarding secret memos, inhumane prison conditions, coercive interrogations, and interference with defense lawyers, the Bush administration's approach to the war on terror went largely unchecked and unchanged. (H/T Prison Law Blog)
Berkeley professor Jonathan Simons, in his 2007 book Governing Through Crime: How the War on Crime Transformed American Democracy, also looks for the roots of these "excesses," and locates them decades prior to the terrorist attacks. "Fear of sudden and terrible violence was a major feature of American life long before September 11, 2001. The collapsing towers were only the latest–and most lethal–of a series of spectacular scenes of violence that have unfolded at the centers of our large cities since President Kennedy was shot to death in Dallas with a mail-order rifle in 1963." In the subsequent decades, Simon writes, "American have built a new civil and political order, values like freedom and equality have been revised in way that would have been shocking…in the late 1960s, and new forms of power institutionalized and embraced–all in the name of repressing seemingly endless waves of violent crime." Simon continues:
The terror attacks of 9/11 have created a kind of amnesia wherein a quarter-century of fearing crime and securing social spaces has been suddenly recognized, but misidentified as a response to an astounding act of terrorism, rather than a generation-long pattern of political and social change. Just as we now see the war on terrorism as requiring a fundamental recasting of American governance, the war on crime has already wrought such a transformation–one which may now be relegitimized as a "tough" response to terrorism.
Many historians trace the birth of the War in Crime to the mid-1960s–specifically, to Barry Goldwater's 1964 presidential campaign, with and his rhetoric of "crime in the streets" and the need for "law and order." Since that time, politicians have increasingly exploited the fear of violent crime and its perpetrators to institute ever more draconian laws and policies. The War on Crime was soon joined by its partner the War on Drugs, which was launched by Richard Nixon and gained traction during the Reagan Administration. One crime bill after another was passed with broad bipartisan support, and more and more federal and state monies were poured into expanding law enforcement and building and maintaining prisons. Between 1970 and 2005, the U.S. prison population grew by 700 percent.
Even as crime rates declined sharply in the 1990s, a Democratic president, Bill Clinton, championed two of the harshest pieces of criminal justice legislation ever passed: The Anti-Terrorism and Effective Death Penalty Act of 1996 (AEDPA), passed after the Oklahoma City bombing with broad bipartisan support, undermined habeas the corpus rights of U.S. prisoners long before the Bush Administration sought to withhold them from "enemy combatants." AEDPA placed severe limitations on prisoners' ability to challenge death sentences–or life sentences, or any unjust convictions–in federal courts, even when they had new evidence of their innocence. The Prison Litigation Reform Act (PLRA) also passed in 1996, was intended "to deter inmates from bringing frivolous lawsuits," said the New York Times in a 2009 editorial. "What the law has done instead is insulate prisons from a large number of very worthy lawsuits, and allow abusive and cruel mistreatment of inmates to go unpunished" long before the advent of Guantanamo Bay, Abu Ghraib, Bagram, and the black sites spawned by the War on Terror.
Anne-Marie Cusac, who spent the decade prior to 9/11 reporting on prison abuses on American soil, wrote in The Progressive after the Abu Ghraib scandal broke, "Reporters and commentators keep asking, how could this happen? My question is, why are we surprised when many of these same practices are occurring at home?" Cusac continues:
In February 1999, the Sacramento Sheriff's Department settled a class-action lawsuit alleging numerous acts of torture, including mock executions, where guards strapped inmates into a restraint chair, covered their faces with masks, and told the inmates they were about to be electrocuted.
When I read a report in The Guardian of London of May 14 that it had "learned of ordinary soldiers who . . . were taught to perform mock executions," I couldn't help but remember the jail.
Then there's the training video used at the Brazoria County Detention Center in Texas. In addition to footage of beatings and stun gun use, the videotape included scenes of guards encouraging dogs to bite inmates.
The jail system in Maricopa County is well known for its practice of requiring inmates to wear pink underwear, and it is notorious for using stun guns and restraint chairs. In 1996, jail staff placed Scott Norberg in a restraint chair, shocked him twenty-one times with stun guns, and gagged him until he turned blue, according to news reports. Norberg died. His family filed a wrongful lawsuit against the jails and subsequently received an $8 million settlement, one of the largest in Arizona history. However, the settlement included no admission of wrongdoing on the part of the jail.
The Red Cross also says that inmates at the Abu Ghraib jail suffer "prolonged exposure while hooded to the sun over several hours, including during the hottest time of the day when temperatures could reach 50 degrees Celsius (122 degrees Fahrenheit) or higher." Many of the Maricopa County Jail system inmates live outdoors in tent cities, even on days that reach 120 degrees in the shade. During last year's heat wave, the Associated Press reported that temperatures inside the jail tents reached 138 degrees.
Cusac goes on to document other abuses familiar to U.S. prisoners as well as foreign detainees, including stress positions, torturous restraints, rape by guards, and long-term solitary confinement. It is no accident that Army Specialist Charles Graner, convicted as the ringleader in the Abu Ghraib prison abuse scandal (and recently released from a military jail at Fort Leavenworth) honed his sadistic skills at Pennsylvania's state prisons, where guards admitted to beating prisoners and were accused of placing a razor blade in one inmate's food.
It is no accident, either, that laws passed in the name of terrorism–both the AEDPA and the USA-PATRIOT Act–have been used to trample on the rights of the accused and prosecute ordinary American lawbreakers, including drug offenders and undocumented immigrants, far more than to round up actual terrorists. If the War on Crime fed the War on Terror, the War on Terror has also expanded and relegitimized the War on Crime. All this has happened with the approval of both political parties, virtually guaranteeing that the legacy of 9/11 will be an endless war at home, as well as abroad.
Posted in civil liberties, legal issues, prisons / criminal justice
Tagged 9/11, War on Crime, War on Drugs, War on Terror
Green Is the New Red: The Crackdown on Environmental Activists
Posted on May 11, 2011 by James Ridgeway | Leave a comment
One morning back in 2002, Will Potter, a young newspaper reporter on the metro desk at the Chicago Tribune, heard three heavy knocks on his apartment door. When he opened it, two FBI agents flashed their badges. They told Potter he could either come outside and talk with them, or they would visit him at work.
Downstairs in the alley, the agents brought up a demonstration that Potter and his girlfriend, Kamber Sherrod, had participated in a month earlier. They had joined in an animal rights leafleting campaign in the high-class suburb of Lake Forest, dropping flyers on the doorsteps of houses around the home of an executive in an insurance company that covered an animal testing laboratory. Both were arrested, along with numerous others, and charged by the local police with misdemeanor disorderly conduct. The charges weren't serious, but the agents warned Potter of other possible consequences if he didn't cooperate with them.
"He told me I could help them by providing more information about the other defendants and other animal rights groups," Potter told me in an interview in Washington. "I had two days to decide." Potter has described in writing what happened next: "He gave me a scrap of paper with his phone number, written on it underneath his name, Chris. 'If we don't hear from you by the first trial date,' he said, 'I'll put you on the domestic terrorist list.'"
Potter was stunned. "I felt as if I was staring blankly ahead," he said, "but my eyes must have shown fear. 'Now I have your attention, huh?,'" Chris said. The agent went on to tell him, "'after 9/11, we have a lot more authority now to get things done and get down to business. We can make your life very difficult for you. You work at newspapers? I can make it so you never work at a newspaper again.'"
Potter left, and threw away the FBI's number. The charges against him and the other demonstrators were dropped—but for years afterwards, small incidents recalled the FBI's threats. When Kamber Sherrod went to the DMV in another state to renew her drivers' license, "I was detained by several police officers as I was trying to leave the building, because, according to them, my name was 'flagged' in the system," she told me. Before they finally let her go, they asked, "What happened in Chicago,?" and "I overheard one cop mention a 't-list.'" When J. Johnson's car broke down years later in Arkansas and a cop idly ran his license plates, "flashing letters burst forth in bold: 'member of terrorist organization, animal rights extremists, approach with caution." And Kim Berardi, also arrested along with Potter, was blocked from boarding a flight at the Seattle airport, handcuffed, and questioned by "two SEATAC security officers, two FBI agents, two Homeland Security operatives, and two officers from the federal Joint Terrorism Task Force."
For Will Potter, the FBI's visit marked the beginning of what would become a career as an independent journalist, tracking the government's prosecutions—and persecutions—of environmental and animal rights activists, which one FBI deputy director, at the height of the war on terror in 2004, identified as "our highest domestic terrorism investigation priority." Because of this campaign's similarities to the anti-communist witch hunts of the 1940s and 1950s, Potter dubbed his blog on the subject, launched five years ago, "Green Is the New Red."
Potter's book, published last month and also titled Green Is the New Red, documents the scare tactics used by the government, often in concert with large corporations, against even patently non-violent activist groups, which they dub "animal rights extremists and eco-terrorists." Prime targets were the Animal Liberation Front (ALF), Earth Liberation Front (ELF) and especially Stop Huntingdon Animal Cruelty (SHAC). Far from targeting only their clandestine operations (which focused on corporate property damage), the FBI "argued that terrorism laws must be radically expanded to include the above-ground campaigns of groups like SHAC," Potter writes. In November 2006, George W. Bush signed into law the Animal Enterprise Terrorism Act.
Activists prosecuted under AETA have in several cases ended up in the "Communications Management Units" at two federal prisons. Created secretly during the Bush administration, these "experimental" units were supposedly designed to hold high-risk inmates, including terrorists, whose crimes warrant heightened monitoring of their external and internal communications. But the reality, as a current lawsuit by the Center for Constitutional Rights asserts, is that many prisoners end up in the CMUs "for their constitutionally protected religious beliefs, unpopular political views, or in retaliation for challenging poor treatment or other rights violations in the federal prison system."
Even attempting to communicate with those in a Communications Management Unit can subject a person to surveillance and harassment, as Potter learned early this year when he received some documents from Public Intelligence, a Wikileaks-style organization. The documents included what appeared to be a running report to law enforcement officials around the nation from the federal Bureau of Prison's Counter-Terrorism Unit, which monitors correspondence in and out of CMU's. (Sample reports appear here and here).
On his blog, Potter wrote about the reports' contents. Acknowledging that even "mundane" prisoner letters could include "coded threats," Potter argues "that's not what's going on with the reports on environmentalists labeled 'eco-terrorists.'" In these documents, "government officials make clear they are much more concerned about bad PR." In one instance, "The Counter-Terrorism Unit notes an August 7, 2009 email received by Daniel McGowan, an Earth Liberation Front prisoner, regarding a possible vigil to raise awareness" about the CMUs. McGowan is part of the Center for Constitutional Rights' lawsuit against the prison units. The report also describes an email to McGowan from CCR attorney Matthew Strugar, discussing efforts to raise awareness about the CMUs and challenge them. And here, Potter discovered his own name. According to the report:
Strugar described attending the animal rights conference in Los Angeles two weeks prior, in which an individual identified as Will spoke about inmate McGowan and his co-defendants' cases, as well as the Communications Management Units (CMU). Will is believed to be Will Potter, an independent journalist based in Washington, DC…
In his email, Strugar wrote to McGowan: "Will was on four panels, I think, and talked a bit about you and your co-defendants' cases and the situation with the CMUs. He's a good advocate on that issue. There is still a lot of organizing and discussion about the Green Scare generally, which is good, and I talked a bit about green scare speech repression and the like. It was interesting."
Potter writes that "It's unsettling to see my name in documents produced by the Counter-Terrorism Unit. What's even more disturbing, though, is the thought of scarce government resources being wasted on such reports…Lectures, public websites and First Amendment activity by journalists and attorneys should not be the purview of the Counter-Terrorism Unit. And even if you think that it should be, and even if you think I am some kind of potential terrorist, this "intelligence briefing" is absolutely useless. Any intern could have created the same report using Google."
When I phoned the Bureau of Prisons media relations office to ask about this report, a spokeswoman said I would have to request the documents under the Freedom of Information Act. "I know what you mean," she said, "but I can't comment on it."
Posted in Bush Administration, corporations, environment, legal issues, prisons / criminal justice
Tagged animal rights, eco-terrorists, environmental activists, FBI, Will Potter
"Three Old Farts"
Posted on March 26, 2011 by James Ridgeway | 1 comment
Guest Post by Lane Nelson
Editor's note: One of the fastest growing subcultures in American life is that of old people struggling through their last years in prison: The old lady who in her twenties shot and killed an abusive husband. The parapalegic bank robber who once tried to escape. The 78 year old, who can barely walk and seems a goner ever since the prison guards pulled his meds. The mentally ill man who hasn't seen sunlight in 10 years. All spend out their lives–20-40-60 year stretches–behind bars.
Their sole desire is to die in the free world, and though they are rendered utterly harmless by age, few states have program to release aging inmates. And so, at great financial cost to society, they must live out their lives in prison. If they are the lucky ones, the end may come in a prison hospice where they are carred for by fellow inmates, whose sole rehabilitation to society has been their education as gentle, caring nurses–behind bars.
As for the judges who banished them to their fate, they for the most part ignore them, as do the politicians who introduced their draconian sentences. Bills to let them out wander through the state legislatures, succeeding in one court, being thrown back in another, year after year.
All this by way of introducing the work of Lane Nelson. While serving time at the Louisiana State Penitentiary, Lane Nelson spent 18 years as a staff writer and later managing editor for the nation's most renowned prison magazine, The Angolite. He covered a wide range of subjects, including Angola's longtermer population and hepatitis-C behind bars, and he interviewed and profiled several men just days before their executions. Nelson himself spent two years on death row–at one point coming within five days of being executed–before a judge overturned his death sentence citing inadequate counsel.
Lane Nelson eventually received a pardon based on good behavior and his volunteer work at Angola. In January he rejoined the free world after 29 1/2 years behind bars. Nelson has opened his own business, Capital Punishment Consulting Agency (CPCA), offering services that extend outside the area of the death penalty to general matters concerning criminal justice and prison life, and he is available for speaking engagements.
He also writes fiction, much of it based on personal experiences from his years at Angola. The story that follows is one of the best depictions of the life of the old, inside prison or out, that I have ever read.
The orange ball inched over the Tunica Hills that border Mississippi and Louisiana, turning the expansive wheat fields into a glazing golden hue. Frency sat on a bent up plastic coke crate in back of the wood-framed clothing room, cup of black coffee in hand and a crimped hand-rolled cigarette hanging from his cracked lips. He wiped the sweat bead rolling down and aged crease in his cheek. Another dog-day of summer. Staring through the razor-wire topped chainlink fence separating him from the fields of wheat, Frenchy thought about the dazzling sparkle the sun gave the deadly razor wire; how it symbolized the external beauty of this 18,000-acre maximum-security prison set in the Mississippi River basin of east-central Louisiana, while depicting the despair among its 5,102 inhabitants. After 27 years chained to this beauty and unable to taste its pleasures, Frenchy was neither sad nor angry at the irony. He had long ago grown numb.
The sound of work whistle jarred Frenchy from his trance and signaled an end to the quiet morning and beginning of another monotonous work day. Nearly all the 150 trustee prisoners filed out of the three dormitories headed for their work assignment. He watch "Hog Head" bounce out of dorm 2, leading the other inmate tractor drivers on the half-mile walk to the tractor shed. Tractor drivers put in 10 hours of kidney-shaking work in the crop fields six days a week, while nearly 2,000 nontrustee convicts from the bigger camps within the prison picked vegetables and cotton under the careful eyes of rifle-totting guards on horseback.
"Dem Saints, theys ready this year, dog!" Hog Head's voice amplified over the conversations of other prisoners. "Ya heard what that white boy said on the news? My team, theys together. All you Saint haters bring your smokes to Hog Head, 'cause he's putting down on every game." For his 18 years in prison for aggravated rape, driving his tractor and sports consumed Hog Head's life. Every season he bet packs of cigarettes on the Saints. At the end of every season he was broke.
Frenchy flicked his butt at the guard's fence in front of him and pushed himself up from the coke crate. He eased his weight onto his right side before taking a step. The bullet he took in the hip while robbing his first bank in 1960 hurt him more now than when it happened. "Son of a bitch cop couldn't shoot straight enough to kill me and put me out of my misery," he often recited. He grabbed a small empty clothing cart and maneuvered it down a cement walkway, headed for Dormitory 3.
His 1960 bank heist sent him to Raiford Prison in Florida for his first adult jolst at the age of 18. The four years at Raiford started him on the road to the only successful skill he ever learned—professional convict. After Raiford it was Holman, Alabama, Tucker, Arkansas, Parchman in Mississippi, Huntsville, Texas, and his final destination Louisiana's infamous Angola to serve life-without-parole for a jewelry store heist in the Garden District of New Orleans (while on escape from Hunstville). The prosecution had no problem citing Frenchy as a habitual offender and the judge had no problem giving him life. "Mr. Mancini, you're through," said the judge in ending his lecture during the sentencing hearing. Frenchy being Frenchy had to have the last word, "So was your momma when she had your dumpy-headed self," and he grabbed his crouch as the guards yanked him out of the courtroom.
He parked the clothing cart in front of the dormitory and walked inside, where he found Whit hunkered over the edge of his bunk sucking air. "Hey ya old fart, said Whit. "Rough night?," replied Frenchy.
"Naw. Slept like a baby in a bank vault." Frenchy knew Whit was lying like a dog, but didn't press the issue. "Your carriage waits, Princess, so get your sexy ass up and lets go.
"Fuck you too early this morning," Whit said and started one of his coughing fits. Frenchy reached over and rubbed his back. "Wow old fart, relax. Be the Buddah." That only made it worse, with Whit laughing and coughing at the same time. It took several minutes before the heavy heaves and cough subsided. Having gained a little strength, Whit allowed Frenchy to help him across the dormitory and onto the cart. His serious emphysema and weak heart begged for a wheelchair, but Whit refused. He wanted to die without help.
By the time they rolled into the clothing room Cupid had another pot of strong coffee brewing, and black market bacon inside the 15-year-old microwave that sparked every time in use. "Happy, happy morning," sing-songed Cupid. "Bacon sandwiches and steaming coffee is on the menu. And for you ladies it's half price."
"Just make sure you put enough mayo on mine," said Whit. "Last time we had this crappy breakfast you almost choked me to death."
"Shut your pie hole and get in your chair," countered Cupid. Frenchy helped Whit out of the cart and into the ragged recliner. The chair had been in the Captain's office before it mysteriously disappeared two months ago and took on a rough reupholster job to change its appearance. Every time the captain paid the three old farts a visit he commented, "Just like my ole chair. If I ever catch the son of a bitches who stole it I'll hang them by his heels from the razor wire." The three old farts always grumbled how their chair cost them an arm and a leg from an unnamed prisoner who picked it out of the prison dump. A little game they played. Captain Fontenot knew his missing chair the first time he saw it, and they knew he knew it."
Cupid distributed the bacon sandwiches and turned on the small portable fan, leveling it in Whit's direction. The heat was already close to unbearable at 8 in the morning. Gonna be another hot one on the farm," commented Cupid. "I'd rather be fishing under a shade tree," added Whit, who struggled with each small bite of his sandwich. "I'd rather be drinking a cold brew in an air conditioned strip joint in Dallas," said Frenchy. They finished their breakfast in silence.
At 69, Whit was the oldest of the three, but only by a couple years. He also had the least criminal experience, with no prior brushes with the law before he was sent to prison 18 years ago for killing his cheating wife. Before that he had been a full bird Colonel. His terminal emphysema and bad ticker was a result of his hard drinking and chain smoking lifestyle in the Air Force. He found Frenchy and Cupid here and they showed him the ropes of being a standup convict. More important, they taught him how not to let his yearning for freedom drive him crazy. Walk slow and drink a lot of water was their edict for doing time.
Cupid was the trio's true gangster, serving life for a murder he didn't commit. The cops hooked him up to get him off the streets once and for all. Until he came to Angola for good in 1980, he was part of a loosely-fit criminal organization in North Louisiana that delved into gambling, enforcement, prostitution and gun smuggling. He didn't hate of the police for giving him a bum murder charge. Just part of the outlaw game, he would say, and just deserts. He had killed his share of like deviants over the years and either never got caught or beat the charge in court. Only once he couldn't finagle his way out of a criminal act—back in the mid-60s, when he used a baseball bat on a bar owner. That put him in Angola for five years, in the days when Angola was rough and tumble and Sears Catalogues carried their weight in gold (prisoners would tape them to their chests when they slept to protect against middle of the night knife attacks). Compared to that violent era, Angola is now a lamb. Elderly prisoners make up half the prisoner population, due to life meaning life in Louisiana since 1972, and the young guns coming to Angola are crack heads who think this is just an extension of the projects they left. So a balance of peace exists; one that is rarely thrown off kilter.
A soft knock on the closed wooden window interrupted the reflective silence. "Hey studs, open up."
The three old farts said in unison: "Read the sign, asshole." Today is Tuesday. No clothing handouts on Tuesday. Leave your request in the box. No bikini underwear in stock.
"Fuck your sign. And don't be calling me that dirty word. It's Precious." The size of all three farts put together, Precious had not an ounce of fat on his well-chiseled body. He also wore bikini underwear, tight shorts and low-cut tank tops. "Come on, hurry up or I'm a gone pecan."
The three looked at each other and said, "Yeast!" Cupid jumped from his chair to the window. As he pushed the wood flat opened Precious slipped his hand down the front of his shorts and pulled a half-filled baggie from inside his flowery underwear. He shoved it at Cupid as he looked nervously around the courtyard. "I gotta go. Pay me later. Remember pink. And it better be a thong and have a heart on the front like you promised, 'cause it's what my man wants." Precious's man was Needle Dick Slim—6' 2" and 135 pounds. How Needle Dick could order and slap Precious around was just one of many mysteries of prison life. "Yeah right," said Cupid. "I'll bring them to the dorm tomorrow." And he closed the window.
Turning around he held the bag of yeast in front of him like a diploma. Frenchy got up, took the yeast and walked to the back room. Seasoned convicts can get their hands on any anything from an x-rated video to an ounce of heroin, but yeast was one of the hardest contraband items to score. It came from the kitchen where it was kept under lock and key and inventoried on a daily basis. Security often overlooked a joint now and then, but when it came to making hooch they were serious. A group of prisoners drunk on home brew always meant trouble. Yet, for the most seasoned convicts, they always find a way.
In the back room, where their small, rusted refrigerator sat among stacked boxes of state-issued clothing, Frenchy knelt down and lifted a floor board. He tapped the yeast to the bottom of the board and snugged it back into place. Reserve stock. In the back corner of the room, under a barred window and behind a dilapidated shelf used to store rubber boots and brogans sat the covered bucket of fermenting wine. Frenchy opened the sealed top, took a quick sniff and hurriedly closed it back. Ready. He then reached his hand into a size 13 rubber boot and pulled out a woman's pink thong underwear, brought to him by a guard in exchange doing the guard's application for divorce. Tit for tat.
Frenchy heard the front door open and stuffed the thong back into its hiding place. Captain Fontenot walked in with his new Lieutenant trailing behind like a police dog. "How ya old fart doin' this morning?"
"Like shit, and you?" answered Cupid. "Want some coffee, Cap?" asked Frenchy as he stepped from the back room.
"Just had a cup. Wanted to stop by to see how were doing, Whit. How ya feeling?"
"Okay," wheezed Whit. Captain Fontenot smiled, but lines of concern etched his face. Cupid, let me see ya outside for a minute." The two walked out leaving the green Lieutenant to browse around the room. He didn't like what he saw. And old color TV with rabbit ears, a deck of cards with poker chips and a shelf underneath the still smoking microwave. "Ya'll are laying out on this farm," he said with stern sarcasm while bending over to look at a brand new VCR.
"Laying out?" responded Frenchy as he moved across the room and into the Lieutenant's face. "Were in for life. Gonna die in this stinking piss hole. How the fuck are we laying out!?" Frenchy's abruptness caught the Lieutenant off guard. He quickly regained his composure, moved closer to Frenchy with a scowl. Captain Fontenot walked back in and saw the two squaring off. "Let's go Smith. We need to make our rounds. From now on stay out of here. The clothing room is off limits to you. These old convicts, they know how to do time and they don't give us no trouble. So we don't give them none, understand?" Without saying a word, Lieutenant Smith turned on his heels and walked out, tail between his legs.
"He come from one of the non-trustee outercamps," Fontenot told the trio. "You know how they play it in those camps, everything by the book. He don't know no better about this camp, and I don't expect he'll make it here. Fontenot knelt in front of Whit. "You're not look so good, my man." Whit struggled to hold off a coughing spell as he told the Captain, "I'm okay, really. Fontenot stood up and headed to the door. "If you need anything let me know."
"Three whores and a case of beer," said Frenchy. Fontenot smiled and shut the door.
"What he want when he took you outside," asked Frenchy. Cupid looked at Whit. "He wants to send you to the infirmary. Says he's worried about you." Whit's eyes grew moist and big as silver dollars. "No way! I ain't going to that butcher shop! I don't want to leave you guys and have to die alone in a locked room." His anxiety caused him to miss every other breath. "Calm down ya old fart. I talked him out of it. Told him I'd let him know if you got any worse. So just be sure to die before you get any worse." Whit chuckled with relief.
The day drug on, like every day does in prison. They tried to play three-handed poker, but Whit kept fading out, and sweat kept dripping on the cards. So they turned on a baseball game. Whit's favorite team, Atlanta Braves, were playing.
An hour before supper, just as everyone returned from their job assignments, all hell broke loose. From inside the seclusion of the clothing room the three old farts were jarred by security radios blaring and hard shoes beating the pathway outside. Before Frenchy and Cupid could get to their feet and race to the window, Knucklehead, the yard orderly, came crashing through the door. "Bopeep just took out Hog Head! Busted his head wide open with a weight bar. Blood and brains everywhere on the walk! Hog Head laying dead as a doornail.
"What happened, man?" asked Frenchy.
"Heard they been beefing all day at the tractor shed over football," said Knucklehead. "Hog Head called Bopeep's mom a grizzly old linebacker. I heard Bopeep didn't say nothin' after that. Just walked away. Now this. Snuck ole Hog Head good."
Cupid looked at Frenchy and Whit. "Wow."
"That's his issue," said Frenchy. "You don't beef with a psycho like Bopeep, then go about your business like nothing' happened. I though Hog Head had more sense."
"Later," said Knucklehead. "I gotta get back over there. Gotta clean up the mess." Knucklehead seemed excited about that. Frenchy and Cupid opened the window. Across the courtyard Bopeep wore handcuffs and leg shackles as three guards led by Lieutenant Smith shuffled him into a prison SUV. The sound of the prison ambulance screeched in the distance. "Wow," repeated Cupid. "Thought he was smarter than that," repeated Frenchy. Whit was struggling to get out of the chair and to the window, but couldn't make it. Frenchy and Cupid helped him over. "I'm glad I'm not going out like that," Whit said.
Two hours later all was quiet in the camp. Hog Head's body had been hauled away to the prison's small morgue. Bopeep went to a lockdown cell where he would stay for at least a couple decades. Knucklehead had cleaned up the blood and grey matter on the walk. Shit happens in prison, then it's over and life moves on.
The sun set, making way for a harvest moon to rise over the wheat fields. Whit was in his chair half asleep and laboring with every breath. His thoughts were consumed with anxiety over the possibility of being transferred to the infirmary. Cupid and Frenchy were looking at Whit, willing him to breath. In the background the TV was on AMC, showing, "The Great Escape." "Too much excitement for me today," said Cupid. "Yep, me too. I think we need something to calm our nerves," grinned Frenchy. Whit looked up smiling. Frenchy got up and walked to the back. Cupid followed with three empty water bottles.
A few minutes later they pulled their folding chairs around Whit and handed him a half-full bottle of hooch. "To three old farts," said Frenchy. "To three old farts," agreed Cupid. They all took a swig. Whit's weak hand shook as he took a gulp. The home brew trickled down the corners of his mouth. "Frenchy my man, you've out done yourself this time," Cupid said as he readied himself for another swig. "I believe you're right. I have outdone myself. What ya say Whit? Does it hit the spot, or does it hit the spot?"
"Mighty good," wheezed Whit. "A drink with friends." He lifted his bottle for another drink, but before it reached his lips is slipped from his hand. Frenchy quickly bent over to pick it up from the floor before much spilled. "Ain't nothing but a thing, ya old fart. You didn't lose any." Whit's hand brushed the top of Frenchy's head as it swung loose over the side of the recliner. Rising, Frenchy noticed Cupid's stunned look. He turned to Whit, whose head lolled to the left side and he eyes drooped with a blank stare. "I think he just died" said Cupid. Frenchy set the two bottles of home brew on the floor and reached the back of his hand to Whit's neck. "Whit? Whit?" No answer, and no chest movement. Whit was indeed dead. The two sat there of several minutes staring at their friend.
Cupid broke he silence. "Is that it? Just like that?"
"I guess so," said Frenchy. "The old fart is free, and he died the way he wanted to—with us, on his terms." Cupid nodded, bowed his head and said, "We need to tell someone. I mean, we need to tell a guard."
"Later," said Frenchy. "He's not going anywhere." For the next hour , with Whit dead in his chair, Frenchy and Cupid went back and forth to the bucket of hooch. Somehow they ended up on the back porch, arms around one another's shoulders, facing the wheat field shinning under a full moon. "We still got those wire cutters underneath the floorboard?" asked Frenchy. Cupid turned and walked in to get them.
Taking the wire cutters, Frenchy asked, "You coming?" Naw, Wheat fucks up my sinus. You go, old fart. Have fun."
Frenchy walked unsteadily to the fence and cut a hole at the bottom. With his bad hip and drunken state, it took him a while to shimmy through the hole, but once on the other side he shed his clothes, leaving on his socks and brogans. Then he staggered across the 100-yard gravel perimeter between the camp and wheat fields.
The guard in the tower at the back corner of the camp spotted Frenchy with the searchlight and sounded the alarm. Frenchy walked faster, finally reaching the edge of the wheat field, where he ducked in and spun around while looking up at the shinning moon. He sucked in the smell of wheat, of freedom, tasting it with every fiber of his body.
Cupid stood on the back porch, tears running down his cheeks, listening to his friend holler with joy.
Flashlights bounced in the night as a dozen guards ran to the edge of the field. Leading the chase team was Lieutenant Smith, who volunteered to work overtime. Smith has his rifle in hand. "It's only Frenchy," hollered a longtime guard. "He must be drunk or something. He ain't no problem. I'll get him." Before the guard stepped into the wheat field, a rifle shot echoed through the night.
Feeling empty and alone, Cupid shut the back door and walked over to Whit to tell him what happened.
Posted in Aging Behind Bars, prisons / criminal justice
Tagged fiction, Lane Nelson, old prisoners
How to Put Wall Street CEOs in Jail
Posted on March 9, 2011 by James Ridgeway | 1 comment
"Forgive me,'' director Charles Ferguson said in receiving an Academy Award for his documentary Inside Job, "I must start by pointing out that three years after a horrific financial crisis caused by fraud, not a single financial executive has gone to jail — and that's wrong."
In New York, Tuesday marked the beginning of the long awaited trial of hedge fund manager Raj Rajaratnam–who ran the $7 billion Galleon Group and whose personal wealth is estimated at $1.3 billion. He is being prosecuted by the SEC for insider trade deals. Rajaratnam is said to have made $45 million in illegal profits. He has denied the charges and is free on $100 million bond. If he is convicted he could go to prison for as long as 20 years. The SEC historically has been such a handmaiden of the finance business that it's hard to imagine anything serious coming out of its prosecutions, but one never knows.
Whatever happens to Rajaratnam, it would be simple enough to prosecute many of the high rollers on first civil, then criminal charges, fining them millions of dollars and taking them out of circulation for up to 20 years.
"Contrary to prevailing propaganda, there is a fairly straightforward case that could be launched against the CEOs and CFOs of pretty much every US bank with major trading operation," writes Yves Smith in her popular Naked Capitalism blog. "I'll call them 'dealer banks' or 'Wall Street firms' to distinguish them from very big but largely traditional commercial banks.'' She proceeds to lay out the case, the key points of which I have excerpted below:
Since Sarbanes Oxley became law in 2002, Sections 302, 404, and 906 of that act have required these executives to establish and maintain adequate systems of internal control within their companies. In addition, they must regularly test such controls to see that they are adequate and report their findings to shareholders (through SEC reports on Form 10-Q and 10-K) and their independent accountants. "Knowingly" making false section 906 certifications is subject to fines of up to $1 million and imprisonment of up to ten years; "willful" violators face fines of up to $5 million and jail time of up to 20 years.
The responsible officers must certify that, among other things, they "are responsible for establishing and maintaining internal controls'" and making sure everyone concerned knows about them–and beyond that, for taking steps to have these controls evaluated and reported. Smith continues:
It's almost certain that you can't have an adequate system of internal controls if you all of a sudden drop multi-billion dollar loss bombs on investors out of nowhere. Banks are not supposed to gamble with depositors' and investors' money like an out-of-luck punter at a racetrack.
Readers may have better suggestions of where to start, but I'd target Lehman. First, it already has a smoking gun: a May 2008 letter written by former senior vice president Michael Lee to senior management, including the CFO Erin Callan. It describes numerous accounting shortcomings, none of which look to be new and many of which look to be Sarbanes Oxley violations. Second, its derivatives books were by all accounts an utter disaster at the time of its collapse: multiple non-intergrated systems, to the point where the bank did not even have a good tally of how many positions it had….
Naked Capitalism concludes:
Will any of this happen? Of course not. The decision was made at the time of the TARP, and reaffirmed early in the Obama administration when there was serious talk of resolving Citigroup and Bank of America, that no one at the helm of the senior banks would be subject to serious scrutiny, much the less actually expected to be held accountable for actions that wrecked the economy and have imposed serious costs on ordinary Americans. The case we described above is relatively simple to explain to a jury and has the advantage of being the sort where the plaintiffs could build on their experience in one action in subsequent cases.
But that sort of truth, that most, probably all, of the major Wall Street banks were engaged in the same sort of misconduct and the violations extended to the very top of the firms, would expose numerous other parties as complicit. So we'll permit the cancer in our society to metastasize rather than threaten the power structure. But at least we citizens can make it clear, even if we cannot change the outcome, that we are not buying the canard that nothing can be done to fight this disease.
In other words, the power structure forges ahead, while the poor and middle classes will pay for their own screwing with reduced social security, medical care, and social welfare services of all sorts. All this is being arranged by both Democrats and Republicans, in response to a recession that will only serve to deepen the already enormous divide between rich and poor in American society.
Posted in budget / tax policy, Congress, economy, financial crisis / recession, Obama Administration, prisons / criminal justice, Social Security, Wall Street / financial industry
Tagged banking industry, CEOs, Charles Ferguson, civil penalties, crime, criminal penalties, jail time, Naked Capitalism, SEC, Wall Street
"Geezer in the Hole": The Reality of Aging Behind Bars
Posted on September 19, 2010 by James Ridgeway | 2 comments
Over the past few years there has been a growing interest in the increasing numbers of older prisoners. At times this interest has been accompanied by some piddling gestures to alleviate their miserable situation–for example, theoretically granting them leave to die "in the free world," or perhaps showing sympathy for granny having to climb up three tiers of bunks to get a night's sleep, or gramps asking for a cane (denied because it is a possible weapon) so he can get to the toilet without crawling.
Nonetheless, the dominant view from the corrections industry and most of the public is that these people did the crimes and now they have to do the time–even if the time reflects absurdly the long sentences instituted in the 1980s and 90s, and creates a new cohort of septuagenarian prisoners. In fact, most of the new interest in aging inmates actually has to do with money. According to a recent AP article:
The ACLU estimates that it costs about $72,000 to house an elderly inmate for a year, compared to $24,000 for a younger prisoner.The federal Bureau of Justice Statistics reported that the number of men and women in state and federal prisons age 55 and older grew 76 percent between 1999 and 2008, the latest year available, from 43,300 to 76,400. The growth of the entire prison population grew only 18 percent in that period.
"We're reaping the fruits of bad public policy like Three Strikes laws and other mandatory minimum sentencing laws," said David C. Fathi, director of the ACLU National Prison Project in Washington, D.C. "One in 11 prisoners is serving a life sentence."
With prison costs escalating and states overwhelmed with deficits, letting granny and gramps out of the clink suddenly doesn't sound so bad to some state officials. Old prisoners are expensive, and if we must take care of them, then why should local and state government's foot the bill. Better to let the federal government pay instead, through Medicare and Medicaid. The leading predictor of criminal behavior is age (young), so there's little risk involved in letting the geezers go; all that's keeping most of them behind bars in the nation's insatiable taste for punishment.
With all this in mind, I am reprinting an article that just appeared on Solitary Watch, another blog where I am editor along with Jean Casella. It is the story of Robert Platshorn, leader of the "Black Tuna Gang" of marijuana smugglers in the late 1970s, an experience described in his book The Black Tuna Diaries. In 1980, he received what was then an unprecedented sentence of 64 years in federal prison.
When Platshorn was released on parole in 2008 at the age of 65, he was the longest-serving non-violent marijuana offender in America. But as he wrote in a blog post for High Times earlier this year, that distinction "won't be mine for long. Many sentenced after me will soon be able to claim my title. They are serving LIFE WITHOUT PAROLE and will never get to spend another minute as a free man." When Platshorn was convicted, he writes, "no one received a life sentence for marijuana. That changed in the early 80′s as Reagan stepped up this insane failure of a drug war." According to Platshorn, several other non-violent marijuana offenders, including Billy Deckle, are now in their sixties and seventies, and will likely never be released.
Here is what they have to look forward to: Surviving day to day in an environment so dangerous that a slip of the tongue often ends in death. Since the elimination of parole, federal prisons are populated mainly by young, uneducated, aggressive inmates serving absurdly long sentences. They have little hope and nothing to lose. Violence has become endemic in a system that has little or no reward for good behavior. Prison gangs find older non-violent inmates easy prey.
Inadequate medical care. It costs the taxpayers billions to provide even minimal health care for older inmates. Yet these are the people least likely to commit a crime after release. An older marijuana offender serving a long sentence is likely to die in prison for lack of medical care…
An extremely unhealthy diet. It becomes an obsession, trying find enough decent food to maintain good health. Even under the best of circumstances, it's no longer possible. When I entered prison in 1979, the budget to feed an inmate for three meals a day was $2.62. When I left prison in 2008 it had shrunk to $2.25…This has to pay, not only for food, it has to cover repairs and replacements for kitchen equipment, civilian salaries, and eating utensils…You don't have to be an economist to figure out, that since Bush decimated the prison food budget, the cost of inmate medical care has skyrocketed. Especially for older inmates, many of whom require a special or restricted diet…Now, the Bureau [of Prisons] will say that they provide special diets for those who require them. And it's true. Sort of! Those diet trays usually contain so little edible food that the starving sick geezer ends up eating a piece of deep fried breaded sewer trout or a hunk of fried breaded mystery meat, just to stave off the terrible never ending hunger pangs. The results, a sick geezer who now needs expensive medications and has little or no chance of surviving a long sentence. Most of those geezers would pose no threat to society if released. It's even worse when the geezer is serving forever for marijuana, a harmless substance, and an effective medication that is now legal in many states. How would you feel if that old pot smuggler was your Uncle Billy?
Geezer in the hole! "The Hole"! Segregation!…The Federal Bureau of Prisons thinks it sounds better if they call it the SHU (Special Housing Unit). Take my word for it, it ain't special in any way you'd like to experience. During my almost 30 years in 11 different federal prisons, about 3 ½ years were spent in segregation. They got it right in the old movies, "the hole". Now you might ask, why would a nice non-violent old dude wind up in the hole? Lots of reason! Someone "drops a note" saying the old dude's life is in danger. Result many months in the hole. He gets in a fight. Doesn't matter if it's self-defense. Into the hole! Uncle Billy gets caught coming out of the chow hall with an apple or a cookie in his pocket. The hole! The old pot smuggler has been forced to work in the prison factory because he owes a fine. A tool disappears from his work area. Everyone who works in that area is tossed in the hole. And so on and so on. Now what happens is: he has to eat whatever shows up on the meager tray that comes through the slot, or starve. Mostly he eats all the starchy crap because he's been flat on his back all day and night, and he's bored to death. Meals are the only break he looks forward to. Each time he leaves his cell his hands are cuffed behind his back. This is especially painful for an older inmate. He has to be cuffed while he crouches backwards with his hands pushed out through the lower food slot. This usually means Uncle Billy will forgo his three weekly showers and exercise periods. It's no big deal when your young and supple, but for a geezer it's a different story. The only way I can express it is, if you are over fifty, spend 90 days in the hole and you come out two years older. Fatter, slower, more depressed, and less likely to recover physically or mentally.
Its time for all the Uncle Billys to go home…
Posted in Aging Behind Bars, elder books / arts, financial crisis / recession, legal issues, Medicare, prisons / criminal justice, radical geezers
Tagged Black Tuna gang, criminal justice, older prisoners, sentencing
On Bastille Day, No Mercy for Prisoners from Sarkozy or Obama
Posted on July 14, 2010 by James Ridgeway | Leave a comment
Charles Thévenin, "La prise de la Bastille," 1793. Musée Carnavalet, Paris.
The following Bastille Day Post appeared this morning on Sara Mayeux's Prison Law Blog:
On this day 221 years ago, revolutionaries stormed a prison and, as they say in History 101, the modern world began…
Traditionally, the French president would grant a mass pardon every July 14, but President Sarkozy has discontinued the practice. In that respect, he is not dissimilar from his American counterpart. Although historically most U.S. presidents have used their executive clemency powers within 100 days of their inauguration, Obama recently reached his 536th day in office without granting a single pardon or commutation — surpassing John Adams and catapulting into third place on the list of presidents who have waited the longest. Nos. 1 and 2 are George W. Bush and Bill Clinton.
Sarkozy's motivations are a mystery to me (as they apparently are to many French people). But why has Obama been so reluctant to issue pardons–or even commutations to a few of the thousands of prisoners serving absurdly long sentences, as a result of national trends of the past 30 years? Is he simply following the lead of other recent presidents? Or, as the first African American president–and one who is constantly facing (absurd) charges of radicalism and reverse racism–is he afraid of appearing soft on crime?
If the latter is true, it's not excusable, but it is understandable. Conservative media figures are already bent upon depicting Eric Holder's Justice Department as having a pro-black bias; the phony "scandal" involving the Department of Justice's decision not to prosecute the New Black Panther Party has lately been called a "21st-Century Willie Horton" ploy. And this is only the latest and stickiest of countless accusations of favoritism toward African Americans. Last month, Iowa Congressman Steve King said that he "knew of no instance where Obama's racial favoritism wasn't a factor in his decision making." The right-wing National Legal and Policy Center even managed to find "racial favoritism" in the financial regulation bill passed by the House earlier this month. This kind of race-baiting would be sure to kick in big time if Obama pardoned or commuted the sentence of someone who happened to be black.
Nonetheless, for the thousands of people who may be undeservedly languishing in America's prisons, it will be small comfort to know that the president is once again allowing his actions to be shaped by a right-wing agenda.
Posted in Bush Administration, legal issues, media, Obama Administration, prisons / criminal justice, right wing
Tagged Bastille Day, executive clemency, Obama, pardons, Sarkozy, sentencing

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Statistical Inference in Markov Processes and Copula Models
Volume 5, 2022
https://doi.org/10.1051/fopen/2022022
Conditional independence
Definition 2.1
Example 2.1
Theorem 2.1
Corollary 2.1
Exchangeability
Remark 3.1
4open 2022, 5, 20
Conditional independence and predictive copula
V.A. González-López1 and Vinícius Litvinoff Justus2*
1 Department of Statistics, University of Campinas, Sergio Buarque de Holanda, 651, Campinas, S.P. CEP: 13083-859, Brazil
2 University of Campinas, Sergio Buarque de Holanda, 651, Campinas, S.P. CEP: 13083-859, Brazil
* Corresponding author: v245362@dac.unicamp.br
In this paper, we address the concept of conditional independence between two random variables X and Y given the entity Θ. We identify the impact of conditional independence on the analytic form of the predictive 2-copula between X and Y. We obtain a representation of the predictive 2-copula between X and Y in terms of functions associated with the copulas between X and Θ and between Y and Θ. Through the concept of infinite exchangeable sequences we amplify the validity of our results, obtaining the predictive 2-copula between two variables in terms of the copula between only one of these variables and the quantity Θ.
Key words: Dependence / Exchangeability / Representations of de Finetti
© V.A. González-López & V. Litvinoff Justus, Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this article, we address the notion of conditional independence and its impact on unconditional dependence. Here, unconditional dependence is being represented by a copula function and the impact of conditional independence on unconditional dependence is studied using the assumption of conditional independence in the copula function. Independence allows us to carry out the usual inferential process, for example, those obtained by calculating the likelihood function, and because of that is a relevant notion in statistical inference. Under the independence assumption is possible to carry out the classic techniques of point estimation, hypothesis testing, and all those procedures based on the likelihood function. As can then be verified, the concept of independence occupies a relevant space in statistics and for this reason, it is widely found in the literature. Several efforts have been done to promote its identification, see for instance García and González-López [1, 2]. In such papers are proposed statistics for independence detection, see also Genest and Rémillard [3] and Hollander et al. [4]. Such statistics work under certain conditions imposed on the nature of the underlying variables. Other authors are concerned with measuring dependence. For example, García et al. [5] proposes an index with such purpose. Despite its enormous use, independence is a very restrictive case within the diversity of types of dependencies that could occur. For example, if we consider the random vector (X, Y) with bivariate Normal distribution, and density function then, the independence only occurs when ρ = 0, which shows that independence is a restrictive assumption. The theory of copulas has been extensively used to investigate such diversity. Nelsen [6] and Joe [7] show the enormous diversity of possible dependencies, addressed from the notion of copulas.
This article explores conditional independence, seeking to preserve some inferential procedures, and we also seek to characterize the impact of conditional independence on dependence. Conditional independence requires the identification of the entity Θ under which we can declare conditional independence (conditional to Θ), that requirement can be a constraint in practice since there is no clear identification procedure of Θ. The first question we seek to answer is how conditional independence impacts unconditional dependence. For the characterization of unconditional dependence, we will rely on the notion of copula. Secondly, we approach the impact of the notion of infinite exchangeability on conditional independence, based on the fact that such a notion guarantees conditional independence [8, 9]. With such a notion in hand, we return to the investigation of the structure of the copula representing unconditional dependence. That is, in this paper, we investigate the impact of conditional independence on unconditional dependence and extend this question to a stronger notion as is the case of infinite exchangeability.
Independence is a very restrictive case within the diversity of types of dependencies, on the other hand, conditional independence (to Θ) is a much more flexible concept, and for this reason, it is the condition that we explore in this article. In our approach, we take the entity Θ as being a random variable since in this way we generalize the notion. In addition, we give space so that the reader can access the interpretation that de Finetti offers of such an entity.
Here we describe the content of this paper. In Section 2 we address the notion of conditional independence and we introduce a theorem that shows a representation of the dependence (copula). We also show corollaries addressing situations of interest that result from that theorem. In Section 3 we introduce the notion of infinite exchangeability, which allows us to identify the quantity Θ, guarantying conditional independence. We then show a result offering a representation of the dependence (copula density function), given the property of infinite exchangeability. The final considerations are given in Section 4.
We begin this section by introducing the notion of conditional independence and then exemplifying it. We introduce in the sequence the notion of copula function. From these notions follows our main result, Theorem 2.1 which shows the impact of conditional independence on the dependence, that is, in this case, on the copula structure. We emphasize the consequences that result from Theorem 2.1 in two corollaries and we show also some examples.
Given two continuous random variables X and Y, X and Y are conditionally independent given Θ, where Θ is a random variable, if
with and denoting the conditional density functions, given θ, of (X,Y), X and Y respectively.
The next example shows a case of conditional independence given Θ.
Set the joint density function of X, Y, Θ, as
where IA (x) = 1, if x ∈ A, and IA (x) = 0, if x ∉ A. The marginal distributions fX,Y, fX, fY and fΘ are respectively, , and Moreover, then X and Y are conditionally independent given Θ = θ, with different conditional distributions, being identically distributed given θ, when k = 1.
From the previous example we see that conditional independence does not impose the same conditional distribution. Note that Definition 2.1 allows θ to be considered as a constant value, and in such case θ is a parameter.
The result that we show in Theorem 2.1 seeks to understand the meaning that Θ plays in the construction of the dependence between X and Y (not conditioned to Θ = θ). For dependence between X and Y we understand the copula between them. In rough terms, the copula is a function that, combined with the marginal cumulative distributions, returns the joint cumulative distribution.
Next we formally introduce the notion of copula explaining how this notion serves to represent the dependence between X and Y.
A copula (in dimension 2) is a function C: [0, 1]2 → [0, 1] with the following properties,
∀u,v ∈ [0, 1], C(u,0) = C(0,v) = 0, and C(u,1) = u,C(1,v) = v;
for every ui, vi ∈ [0, 1], i = 1, 2, such that and
It is possible to show that every copula given by Definition 2.2 is a cumulative distribution function on [0, 1]2, in the strict sense of the term. We now show how Definition 2.2 is formally related to the dependence between the variables of a random vector.
According to Sklar's theorem [6], if HX,Y is the joint distribution function of (X, Y) with margins FX and FY, there exists a copula CX,Y (called 2-copula of (X, Y)) such that
If FX and FY are continuous, then CX,Y is unique. Conversely, if C is a copula (following Definition 2.2), F and G are distribution functions, then the function H(x,y) = C(F(x),G(y)) is a joint distribution function with margins F and G.
From what is given in Sklar's theorem, the dependence between X and Y is represented by the 2-copula of (X,Y), CX,Y, since the margins FX and FY depend on X and Y, respectively. Then, our purpose is to see the effect of Definition 2.1 in CX,Y.
The next theorem provides an analytical representation of the copula, knowing that the variables are conditionally independent given the entity Θ.
Given X and Y under the assumptions of Definition 2.1, if CX,Y is the 2-copula of (X,Y), Θ the random variable of Definition 2.1 with density function πΘ,
with CX,Θ and CY,Θ denoting the 2-copulas of (X,Θ) and (Y,Θ) respectively, and FΘ denoting the cumulative distribution of Θ.
Proof. Since X, Y are continuous random variables we can write the cumulative distribution HX,Y between X and Y as follows, applying Definition 2.1,
Considering the cumulative distribution between X and Θ, by Sklar's theorem, HX,Θ(s,θ) = CX,Θ (FX(s), FΘ(θ)) then, the joint density function between X and Θ is given by (3)
with cX,Θ denoting the density function related to the copula CX,Θ. Then, from equation (3), we obtain,
□We proceed to integrate the equation (4). Define u = FX(s), then, du = fX (s)ds and
We have similar expressions for fY,Θ(t,θ) and fY|θ(t). Then, applying equation (5) in equation (2), we obtain
Consider u and v in [0, 1], there exist values x and y, such that u = FX(x) and v = FY(y), then, by Sklar's theorem and equation (6),
We use in the following example a family of copulas that corresponds to weak dependence. It is the Farlie–Gumbel–Morgenstern family, and it encompasses the case of independence. See Nelsen [6].
Consider (X,Y) with a 2-copula
with parameters α ∈ [−1, 1] and β ∈ [−1, 1]. Then, (X,Y) has a Farlie–Gumbel–Morgenstern 2-copula with parameter Consider Θ as a continuous random variable, with Uniform distribution in (0,1).
If we set the 2-copulas of (X, Θ) and (Y, Θ) as being Farlie–Gumbel–Morgenstern 2-copulas with parameters α ∈ [ 1, 1] and β ∈ [−1, 1], respectively. Since θ ~ U(0,1), we have
And, we obtain,
As a consequence,
One question that arises is whether every expression given by the right side of equation (1) is a copula, where CX,Θ and CY,Θ are copulas. The Theorem 1, in González-López and Litvinoff Justus [10], states that the expression is always a copula. That is, postulating two copulas of (X, Θ) and (Y, Θ), we get a copula that could be used to deal with the dependence between X and Y. An example of what is stated in this paragraph appears in the previous example, since taking (X, Θ) and (Y, Θ) with Farlie–Gumbel–Morgenstern copulas, with parameters α and β, respectively, the resulting copula between X and Y (using the right side of equation (1)) is a Farlie–Gumbel–Morgenstern copula, with parameter
The following corollary shows the version of Theorem 2.1 in terms of density functions of copulas.
Under the assumptions of Theorem 2.1, if cX,Y, cX,Θ and cY,Θ are the density functions related to the 2-copulas CX,Y, CX,Θ and CY,Θ, respectively,
Proof: Consider that and The results follow differentiating both sides of equation (1) and permuting the integral with □
Considering the Example 2.2. Since Then,
and, according to the equation (7), it is the copula density function of a FGM copula with parameter
The following corollary shows the version of Theorem 2.1 under the assumptions of identical conditional margins. The impact of the assumption appears in the integrating term of equation (1). This assumption about margins will become relevant later, in this paper.
Under the assumptions of Theorem 2.1, if the variables X and Y are conditionally (to Θ) independent and identically distributed,
Considering the Example 2.2, if α = β, the copula of (X,Y) is a Farlie–Gumbel–Morgenstern copula with Then, the restriction (on the margins) imposes on the relationship between X and Y a positive Kendall's τ coefficient .
Theorem 2.1 shows that the conditional independence of X and Y given Θ defines the structure of the copula between X and Y. See equation (1) for the form of the copula and see Corollary 2.1 for the form of the density function of copula between X and Y. We exemplify both results in Examples 2.2 and 2.3, respectively. Corollary 2.2 shows the case covered by Corollary 2.1, under the assumption of identical margins. The latter is exemplified in Example 2.4. The Corollary 2.2 is especially interesting for the situation that we will address in the next section.The results of this section describe the analytical form of the copula between X and Y, no longer depending on Θ. This means we have offered a representation for the predictive copula between X and Y.
The key to determining conditional independence between X and Y is to know that there exists a variable Θ establishing this independence. This leads us to the following reflections, showing a context where such an entity can be identified. That is the goal of de Finetti's theorems of representation.
We start the section with the definition of infinite exchangeability. This notion is weaker than independence and makes it possible to identify Θ. Then, we exemplify certain characteristics that result from this imposition. And, we present in Corollary 3.1, the impact of this notion on the dependence structure, that is, on the copula function.
A sequence X1,X2,X3,... of random variables is infinitely exchangeable, if for each collection of n variables the joint distribution is identical for all the permuted set of variables with σ: {1, 2,…,n} → {1, 2,…,n} any permutation function.
The success in identifying the Θ entity stems from de Finetti's representation theorem, see de Finetti [8]. de Finetti [8] proves that, a binary sequence X1, X2,... follows Definition 3.1, if and only if, there exists a distribution function FΘ on [0, 1] such that for all n the joint probability mass function where FΘ is the cumulative distribution function of the entity and xi ∈ {0, 1}. As a consequence, the conditional mass probability is decomposed in a product of Bernoulli's
with being θ a value of the variable Θ. Such a result is extended for all types of random variables in Hewitt and Savage [9]. For a sequence X1,X2,... of continuous random variables following Definition 3.1, there exists a variable Θ, such that the conditional density function can be decomposed as The previous relation happens for each value θ of the variable Θ, then, the structure imposed by Definition 3.1 in the sequence X1,X2,⋯ guarantee the existence of the entity Θ.
We see in the remark to follow (Remark 3.1) that this notion leads us to conditional independence, and implies identical margins. But as we show in Example 3.1, exchangeability coexists with dependence.
Infinitely exchangeable variables (following Definition 3.1) are identically distributed conditionally to θ (value of the variable Θ identified by de Finetti's theorem). If the infinitely exchangeable sequence is composed by absolutely continuous random variables and Θ has a density function πΘ (·), for each as a consequence, since,
The concept of infinite exchangeability could be considered unrealistic, but it can be seen applied in usual inferential strategies. If a sample is available, say X1,…,Xn, when constructing the likelihood function its elements are considered independent given a certain parameter. And how does this assumption is related to Definition 3.1? If the distribution of X1,…,Xn is invariant under permutations of the elements of X1,…,Xn, then we say that X1…,Xn is exchangeable. If X1,…,Xn is exchangeable , then, we say that X1, X2,… is infinitely exchangeable. If X1,…,Xn can be embedded in an infinitely exchangeable sequence X1, X2,…, then we say that X1,…,Xn is infinitely exchangeably extendable. Bayesian and frequentist approaches, in general, treat observable values as infinitely exchangeably extendable and, as a consequence of de Finetti's representations, independent and identically distributed conditional on some unknown entity Θ.
Although identically distributed independent random variables must be exchangeable, identically distributed exchangeable random variables need not be independent. Consider for instance the bivariate case of Gumbel distribution as shown by the next example.
Let (X,Y) be a random vector, H its joint distribution function, given by and H(x,y) = 0, otherwise, with α a parameter in [0, 1]. We see that X and Y are exchangeable. Note also that X and Y have identical marginal distribution (exponential distribution). But, since the 2-copula of (X,Y) is X and Y are not independent.
The previous example shows us a case where exchangeability occurs, the variables share the same marginal distribution, but X and Y are not independent. Thus we see that exchangeability is a distinctly different notion from the notion of independence. It also follows from Example 3.1 that identically distributed variables can be dependent since every copula is a joint distribution with uniform marginal distributions, in particular, the copula of Example 3.1.
The next example shows a case of dependent variables, with identical marginal distributions but not exchangeable.
Let (X,Y) be a random vector, H its joint distribution function, given by H(x,y) = xy − x3y(1 − x)(1 − y), x,y ∈ [0, 1]. Then, H is a copula, since fits the conditions of Definition 2.2. X and Y are identically distributed but, not exchangeable since H is not symmetrical.
Bearing in mind the previous example, it is now necessary to mention Theorem 2.7.4 [6] which shows how the margins should be and also the copula to guarantee the exchangeability between a pair of variables. Let X and Y be continuous random variables with joint distribution function H, margins FX and FY, respectively, and copula C. Then X and Y are exchangeable if and only if FX = FY and C is symmetric (C(u,v) = C(v,u), ∀(u,v) ∈ [0, 1]2).
In the treatment and modeling via copulas, it is very common to operate with the original variables transformed by their margins, so below we summarize the impact of Definition 3.1 on such variables.
A property that is straight from Definition 3.1, is the preservation of the infinite exchangeability from the original sequence to the standardized ones. Namely, if the sequence X1, X2, X3,… of random variables is absolutely continuous, the sequence U1, U2, U3,… is also infinitely exchangeable, where Since, for any collection i1,…in, with arbitrary n, for any permutation σ and arbitrary values u1,…,un ∈ [0, 1].
where equation (10) results from Definition 3.1 and equation (11) follows from Remark 3.1 ( ).
We note that if the variables U1, U2, U3,… of Remark 3.2 are infinitely exchangeable, this does not imply that the variables X1, X2, X3,… are infinitely exchangeable. It is enough that one of the marginal distributions is different from the rest which would violate Remark 3.1.
Under the framework of Definition 3.1 and assuming the continuity of the variable identified by the de Finetti representation, say Θ, we will have the copula between pairs of variables of the infinitely exchangeable sequence given by the copula between a member of the sequence (the first one is enough) and the variable Θ, let's see.
Let X1, X2,… be a sequence of continuous random variables following Definition 3.1. If Θ is the variable identified in the de Finetti representation, producing the conditional independence, and Θ has density function πΘ(·), then, for each pair of variables Xi and Xj, i ≠ j,
where and are the density functions related to the 2-copulas and respectively.
Proof. Since infinitely exchangeable variables are conditionally independent (to the random variable of de Finetti's theorem) for each pair Xi and Xj (from Corollary 2.1).
Infinitely exchangeable sequences of absolutely continuous random variables share their unconditional marginal distributions from Remark 3.1. Also, for each θ value of Θ, since,
where equation (13) follows from Sklar's theorem. And, using that we can see that □
However, a question that arises is whether there is any restriction on the type of copula that could result from Corollary 3.1, a hint is given in O' Neill [11], formulated in the next remark.
Let X1,X2,… be a sequence of continuous random variables following Definition 3.1. Then, from Theorem 2 of O' Neill [11], for each pair of variables Xi and Xj, i ≠ j, i, j ≥ 1, with denoting the Pearson's rho correlation coefficient. Then, from Remark 3.2, since the variables U1,U2,… follow Definition 3.1, for each pair of variables Xi and Xj, i ≠ j, i, j ≥ 1, with denoting the Spearman's rho correlation coefficient.
The above remark indicates that the possible copulas identified in Corollary 3.1 cannot correspond to negative correlations, under Definition 3.1.
The following example shows a case under Definition 3.1, and the resulting predictive copula.
Let X1, X2,… be an infinite sequence, under Definition 3.1, of exponential random variables with parameter θ, conditionally independent, given θ, a value of the continuous random variable Θ with exponential distribution and hyperparameter λ. Then, each conditional density function is and the prior density function of Θ is is proportional to for Since, for and Using the previous proportionality we obtain On the other hand, for then, the right side of equation (12) is proportional to Verifying the Corollary 3.1.
Then, since we have the copula density function and the predictive 2-copula is
We start the section with some notes and examples so that Corollary 3.1 is a natural consequence of the impact of conditional independence in the framework of infinite exchangeability. Remark 3.1 shows that infinite exchangeability implies conditionally independence and identical margins. While independence implies permutability, the opposite is not valid, see Example 3.1. Also, if the margins are all equal this does not imply permutability, see Example 3.2. Under Definition 3.1, we show in Corollary 3.1 that infinite exchangeability allows to obtain a representation of the copula between pair of elements of the infinite sequence in terms of the copula between each element of the infinite sequence and the entity Θ, quantity identified by de Finetti's theorem. Also, note that the right side of equation (12) reflects that is only necessary to know the copula between one element of the infinite sequence and Θ to obtain the predictive copula between pairs of elements of the infinite sequence. Example 3.3 exposes how works in practice the corollary.
In the framework of absolutely continuous random variables X and Y, we use the notion of conditional independence between X and Y (conditional on Θ), to obtain a representation of the predictive 2-copula between X and Y (Theorem 2.1, see also Corollary 2.1). Such a result tells us that the representation involves the 2-copula between X and Θ, the 2-copula between Y and Θ, and the distribution of Θ. Being the property of identically distributed useful for inferential procedures, in Corollary 2.2 we reveal the impact of such an assumption on the representation of the predictive 2-copula between X and Y. There are indications (see Example 2.4) that the restriction imposed by the condition of identical margins could lead to restrictions on the values of coefficients of dependence, such as Kendall's τ coefficient, Spearman's ρ coefficient.
Since the notion of conditional independence requires the identification of the entity Θ making X and Y conditionally independent given Θ, we introduce the concept of infinite and exchangeable sequences, X1, X2, X3.... This condition appears as one of the inferential strategies applicable in the process of manipulating finite samples. It is reasonable to suppose that a finite sequence is part of an infinite sequence. Under Definition 3.1, by representation theorems [8, 9] we can guarantee that Θ exists and that it is a random variable. To give the reader a more precise notion of the meaning of infinite exchangeability, we show that it imposes the same margins on X and Y (conditional or not, see Remark 3.1), but that it does not impose unconditional independence (see Example 3.1) and it does impose conditional independence on Θ. Then, under infinite exchangeability, we revisit the copula density function structure and prove Corollary 3.1, which shows the structure of the predictive 2-copula density function between Xi and Xj, i ≠ j elements of the infinite sequence. We complete our findings with examples and notes for the reader. Corollaries 2.2 and 3.1, although they start from different assumptions, show that the predictive density function of the 2-copula between pairs of variables X and Y can be analytically expressed as a function of the density functions of the copula between only one variable (say X) and Θ. That is to say that the dependence, represented by the predictive 2-copula between X and Y, is only a consequence of the dependence between X and Θ. This fact shows the relevance of the identification of Θ, for the description of the predictive 2-copula.
Vinícius Litvinoff Justus gratefully acknowledges the support provided by CNPq with a fellowship of scientific initiation from University of Campinas. The authors wish to thank the referees and editors for their many helpful comments and suggestions on an earlier draft of this paper.
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Global Marijuana March calls for pot possession pardons, level playing field for entrepreneurs
With pot on the verge of being legalized, dozens of marijuana entrepreneurs gathered in Queen's Park on Saturday to demand a level playing field for all in the industry.
New government model doesn't give market what it wants, activist says at Queen's Park
CBC News · Posted: May 05, 2018 6:41 PM ET | Last Updated: May 5, 2018
Activists at Saturday's Global Marijuana March called on government to pass an amnesty bill that would provide for pardons for all individuals who have criminal records relating to pot possession. (Sean Kilpatrick/Canadian Press)
Saturday's Global Marijuana March was also aimed at persuading the government to pass an amnesty bill that would provide for pardons for those with criminal records related to pot possession offences.
New campaign calls for marijuana possession convictions to go up in smoke
No plan for pot-conviction amnesty amid legalization move, Liberals say
Pot possession suspects face uncertain future
"With just the government stores operating, they are trying to shut down dispensaries. The new government model does not exactly give the market what it wants," marijuana activist Erin Goodwin told CBC Toronto.
"There's edibles and concentrates and all kinds of other products involved in cannabis dispensing that the government's a bit slow on, so the black market that we've set up here is for filling those needs."
Goodwin, who runs vapour lounges and dispensaries, said she's been arrested four times since legalization plans were announced.
Pot activist Erin Goodwin says the new government model does not exactly give the market what it wants. (Garry Asselstine/CBC)
She said rallies like the one held Saturday serve as a confidence booster for some entrepreneurs.
"There are a lot of young entrepreneurs who want to be involved in the industry," Goodwin said. "These new Ontario laws are going to have a bit of a monopoly that not everyone's happy with.
"It's clear that this many people getting together publicly and making our voices heard has won our favour that the laws are changing because we demanded it. It's nice to see that more and more people can come out and be public, that we don't have to hide."
Petition launched for pot possession amnesty
On Friday, a group of Toronto lawyers, activists and entrepreneurs launched a petition calling on the federal government to grant amnesty to people convicted of simple cannabis possession charges.
The petition urges parliament to pass legislation granting full pardons for people convicted of possessing 30 grams of marijuana or less. Right now, the bill legalizing marijuana does nothing address those with criminal records for pot-related offences.
"We know that there are hundreds and thousands of Canadians today that have that on their record and those offences prevent them from having access to housing, from having access to credit, from crossing the border, from getting jobs, from getting volunteer opportunities," Annamaria Enenajor told CBC Toronto.
"With the legalization of cannabis just around the corner, we want to make sure that those people are included in that calculus as well."
Lawyer Annamaria Enenajor is among a group which on Friday launched a petition calling on the federal government to grant amnesty to people convicted of simple cannabis possession charges. (Garry Asselstine/CBC)
Enenajor, a defence lawyer and director of a campaign for cannabis amnesty, said the government's response thus far has been less than acceptable.
"They are focused on passing the current legislation which is a very narrow legalization of marijuana, and implementation of a broad regulation scheme around marijuana sale and distribution consumption," she explained.
"To them, the impact that these kinds of offenses have on people is really an afterthought. So they said, 'Let's just park it for now, and we'll deal with it later.' We're saying no, this needs to be part of the conversation now because it's affecting people's lives now."
The Global Marijuana March, an annual event, drew hundreds of cannabis users and others from the cannabis industry.
Enenajor said the aim is to collect 5,000 signatures by the end of May, and she thinks they have the potential to get over a million.