Concise and well-stated. If the prior proability of the hypothesis is indeed low then we shouldn't blindly believe it.
However, I don't know the prior probability of him cheating in a major OTB tournament. Having previously cheated online, his motivation to do well and the importance of this tournament, the stakes involved, the danger of getting caught and the fact that he is confident (arrogant?) about his own chess abilities, I'd have said maybe in the range 1% to 10%. Are you willing to put forward an estimate?
Good luck with those priors! What's your prior, for example, of Carlsen walking out of a tournament for no good reason? I haven't checked this carefully, but I would bet my bottom dollar that the result of conditioning on the totality of evidence in this case is going to be acutely sensitive to the ratio of one very small number to another, the estimation of which is going to be more or less completely arbitrary.
Concise and well-stated. If the prior proability of the hypothesis is indeed low then we shouldn't blindly believe it.
However, I don't know the prior probability of him cheating in a major OTB tournament. Having previously cheated online, his motivation to do well and the importance of this tournament, the stakes involved, the danger of getting caught and the fact that he is confident (arrogant?) about his own chess abilities, I'd have said maybe in the range 1% to 10%. Are you willing to put forward an estimate?
Good luck with those priors! What's your prior, for example, of Carlsen walking out of a tournament for no good reason? I haven't checked this carefully, but I would bet my bottom dollar that the result of conditioning on the totality of evidence in this case is going to be acutely sensitive to the ratio of one very small number to another, the estimation of which is going to be more or less completely arbitrary.