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Abstract:
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When I started looking at hypothesis testing and model selection from a Bayesian perspective many years ago, I thought the following were true: (i) Use of p-values is better than fixed alpha-level testing, since p-values are conditional on the data. (ii) Frequentist and Bayesian testing are incompatible; for instance, Bayes tests do not depend on the stopping rule in sequential settings while frequentist tests do so depend, necessitating 'spending alpha' for looks at the data. (iii) The best single model is the highest posterior probability model. (iv) Finding the best (or a few of the best) models is sufficient. (v) Model selection priors cannot be derived from the data. I no longer think any of these are true and will review why. Included will be a discussion of large model spaces including methods for effective search in, and effective summarization of information from, such spaces.
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