by John Matese and Daniel Whitmire of the University of Lousiana-Lafayette, is not new: They have been making a case for Tyche since 1999, suggesting that the giant planet's presence in a far-flung region of the solar system called the Oort cloud would explain the unusual orbital paths of some comets that originate there.

of mass 1 − 4 M(Jupiter) orbiting in the
innermost region of the outer Oort cloud. Our most restrictive prediction is that the orientation
angles of the orbit normal in galactic coordinates are centered on
, the galactic longitude of
the ascending node = 319 and i, the galactic inclination = 103 (or the opposite direction)
with an uncertainty in the normal direction subtending 2% of the sky.

They posit that the elongated orbit of Sedna is a result of the presence of this planet.

So, the question, what reason is there to doubt the existence of Tyche?

Disproving the existence of or proving the non-existence of an object is practically impossible, so I'm going to rephrase the question a little bit. It might also get you better answers because they won't just be aimed at disproving Tyche but questioning the methods that suggest Tyche in the first place.
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called2voyage♦Oct 18 '13 at 14:41

As an example of the practical impossiblity I suggested, someone could say that Tyche existed at one point but got pulled out of orbit (in the case that Tyche were not where it should be observed).
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called2voyage♦Oct 18 '13 at 14:42

Now, to progress toward answering your question, the livescience article that you linked in the body of your question refers to several astronomers questioning the methods employed by Matese and Whitmire in the first place. It would be interesting to see someone actually debunk their statistics from their paper, if possible.
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called2voyage♦Oct 18 '13 at 14:53

@called2voyage yes, that is pretty much what I am after. Good edit by the way.
–
user8Oct 18 '13 at 19:59

1 Answer
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Generally it would be that peers of Matese and Whitmire looking at the statistics and viewing that the results are not conclusive enough to indicate the existence of Tyche. There can also be alternative reasons to explain the results mentioned in the paper other than a Jupiter sized planet in the Oort Cloud. As was mentioned in the comments, it is almost impossible to prove the non-existence of something.

At this time, the results from WISE are the best bet for locating Tyche if it exists. As it will not be visible in the visible light spectrum but more likely in the infrared and the WISE mission scanned the entire sky which means that it won't have been missed due to looking in the wrong place.

There isn't any hard science to show that Tyche doesn't exist. It is skepticism that this is the explanation for observations to date. These are the same reasons that Nemesis isn't thought to exist, the data isn't strong enough to support its existence.