jason palmer mrktgulrucsdedu im familiar frequentistbayesian debate view bayesian estimation useful regularization necessary small amount data parameter optimization underdetermined multimodal goal always estimate parameters distribution phenomenon interest make decision optimize function random quantities prior estimates relevant distributions understanding bayesians also believe fixed distributions given phenomena simply case true parameters unknown must estimated limited data case distribution nebulous state parameters assuming new values realization imprecise knowledge probabilities different imprecise probabilities whatever latter may defined main point wanted make got lost preliminary philosophical commentary doesnt make sense specify probability distribution individually probability discrete distribution want regularize estimate discrete distribution way put prior set discrete values eg requiring adjacent probabilities close value cant put priors individual probabilities without regard joint distribution since marginal distributions probablilities must consistent fact realization set must sum 1 jason original message arvey aaron mailtockhzyiaqme57claremontmckennaedu sent thursday november 17 2005 1012 jason palmer lotfi zadeh faqengrorstedu subject uai imprecise probabilitiesa simple yet computationallynontrivial problem see response original message nhipljlbixengrorstedu behalf jason palmer sent mon 11142005 342 lotfi zadeh faqengrorstedu subject uai imprecise probabilitiesa simple yet computationallynontrivial problem dear prof zadeh others view notion imprecise probabilities welldefined seems imagining something like experiment performed probability distribution drawn randomly set distributions experiment performed based distribution seems intermediary probabilities arent really probabilities model parameters still final distribution values outcome experiment model found marginalizing random probabilities essence probability event occurs according fixed distribution probability distribution cant apply one experiment whatever event observed either occur stationary distribution distribution impossible distinguish particular generating sequence random variables model yields final distribution marginalized possible might able talk distribution evolving time perhaps misunderstanding somewhat philosophical statistics frequentist statistician frequentist would likely agree say maximum likelihood point estimate used however bayesian statistician bayesian would likely state parameters model also modeled probabilistically unknown distant past mathematical bayesians mocked impreciseness however bayesian view largely accepted mathematical statistics community well computational community cursory google search comparison bayesian frequentist turned following link presentation statistician httpwwwpnlgovbayesianberryindexhtm hope shed light situation regards aaron original message nhipljlbixengrorstedu mailtonhipljlbixengrorsteduon behalf lotfi zadeh sent wednesday november 09 2005 515 pm faqengrorstedu cc gzrdaeecsberkeleyedu subject uai imprecise probabilitiesa simple yet computationally nontrivial problem realworld probabilities imprecise reason move age machine intelligence mechanized decisionmaking problem deal imprecise probabilities certain grow visibility importance major contribution theory imprecise probabilities peter walleys 1991 book statistical reasoning imprecise probabilities london chapman hall since considerable progress made yet obvious problem computation imprecise probabilities intrinsically complex far definitive solution case point posted uai list september 22 2005 seemingly simple problem simple solution following broadened version problem presented simplest version problem perception even simple problem computationally nontrivial simple solution solutions problems b c problem x random variables taking values set 1 2 n entries joint probability matrix p form approximately aij aij take values unit interval add unity marginal probability distribution x four special cases approximately aij interpreted interval centering aij b approximately aij interpreted triangular fuzzy number centering aij c approximately aij interpreted uniform probability distribution interval centering aij approximatelt aij interpreted triangular probability density function centering aij warm regards lotfi lotfi zadeh professor graduate school computer science division department electrical engineering computer sciences university california berkeley ca 94720 1776 director berkeley initiative soft computing bisc message scanned fsecure antivirus microsoft exchange information connect httpwwwfsecurecom wed 06 aug 2008 115819 0800 uai imprecise probabilitiesa simple yet computationallynontrivial problem