What is the difference?

This week we read some frequentist critiques of Bayesian methods (and statistical practice in general!):

Stark, P. B. (Submitted). Constraints versus Priors. SIAM/ASA Journal on Uncertainty Quantification.

Freedman, D. (1995). Some issues in the foundation of statistics. Foundations of Science, 1, 19–83.

And some supplemental reading:

Freedman, D. A., & Stark, P. B. (2003). What is the chance of an earthquake? In F. Mulargia & R. J. Geller (Eds.), Earthquake Science and Seismic Risk Reduction (Vol. 32, pp. 201–213). Dordrecht, The Netherlands: Kluwer.

Stark, P. B., & Tenorio, L. (2010). A primer of frequentist and Bayesian inference in inverse problems. In L. T. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, … K. Willcox (Eds.), Large Scale Inverse Problems and Quantification of Uncertainty. NY: John Wiley and Sons.

Ryan made a nice chart to capture some elements of the discussion. More generally, it seems that similar concerns arise again: how can we be thoughtful and conscientious about our science? Neither Bayes nor Fisher & Neyman provide an easy out.

Next week we’ll talk about arguments for Bayes.

Some issues that we’re thinking about down the road:

• “Theory” (as Ryan defines it)
• Non-parametric approaches
• Example of two bayesians choosing different priors yeilding different conclusions (follow Stark reference)
• Slomanoff induction
• Proper philosophy of science (e.g., Popper, Kuhn, etc.)