## Bayesian goodness of fit

I was impressed by this paper introduced in lunch meeting.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1024691240

It is a difficult problem to assess the goodness of fit, especially for the model with large number of parameters. In contrast to the frequentist’s point of view, this problem is considered as an inference problem in this paper.

Anyway, the gist of this paper is,

1. Suppose that the posterior is REALLY the correct distribution generating data points by random sampling. This is a null hypothesis (H0).

2. Slightly perturb the posterior using a function. This is an alternative hypothesis (H1).

3. Then calculate Bayes factor, B10. If the null hypothesis is supported, the model is good. Otherwise, the model is bad. It’s simple !

Computation is done by post processing the posterior. All the gory details are matters of implementation which doesn’t look very straightforward to me though.