ACCP 37thAnnual Meeting, Philadelphia, PA[1] Approaches to Statistics ◮ Frequentists: From Neymann/Pearson/Waldsetup. An orthodox view that sampling is infinite and decision rules can be sharp. ◮ Bayesians: From Bayes/Laplace/de Finettitradition.

International Society for Bayesian Analysis, 9 th World Meeting, Hamilton Island, Australia, 2008. A Theory of (Un)congeniality (between **Bayesiansand** Frequentists?)

•Thereisavery lively debate currently raging on in the philosophy of statistical inference (and in philosophy of science generally) between (subjective) **Bayesiansand** (objective or frequentist) non-Bayesianswhoboth share predictive/verisimilitudinous leanings in this sense[ 13 ], [ 1 ].

It is argued also that proponents of alternative conceptions of probability, such asfrequentists, **Bayesiansand** Popperians, are unable to avoid committing themselves to the basic principles of logical probability.

Issues in the Foundations of Statistics: Probability and Statistical Models 3 **Bayesiansand** frequent is tsdisagreeont heme an ingofprobability and otherfoundational issues, but both schools facet he problem of model validation.

The differences between contemporary default **Bayesiansand** subjective Bayesians, many think, are even more dramatic than the differences between Fisherianand Neyman-Pearsonianfrequentists (see Stephen Senn'scontribution).

This difierencein approach to probabilityafiects the way **Bayesiansand** frequentistsdeal with statistical procedures. We illustrate this below by considering parameter determination. 1.3.2 Bayesian approach The Bayesianapproach makes use of Bayes'Theorem: p ( AjB ) = p ( Bj A ) £p ( A ) =p ( B ) ; ...

4 Bayesian Model Averaging *Researcher often has many possible models and the common strategy (for virtually all non-**Bayesiansand** manyBayesians) is to select one model.

**Bayesiansand** confirmation theorists have argued that simpler theories merit stronger belief in light of simple data than do complex theories. Such arguments, however, assume either explicitly or implicitly that simpler possibilities are more probable a prior i. 5 That argument is circular ...