Funny thing is that I would (contrary to other posters here) say that I intuitively find the Bayesian approach not that well founded philosophically (stemming from what little I know about epistemology). But I am not too sure about the Frequentist approach either. The Bayesian approach seems more intuitive practically, though.

]]>Likelihood inference is intuitively appealing and easy to understand. But here are a couple criticisms.

You could think of likelihood inference as Bayesian inference with uniform (improper) priors. A Bayesian might object that this puts too much prior weight on parameter values known to be unlikely or impossible. Another criticism would be that posterior mode (which is what maximum likelihood is, if you use a uniform prior) can be less robust than posterior mean.

]]>I recently heard someone describe himself as a ‘maximum likelihood guy’. He said that the bayesian-frequentest thing was a false choice and that maximum likelihood methods should be given their own category. Any thoughts? ]]>

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I’ve also seen pressure the other way, to use Bayesian methods just because they’re sexy. Some people go to tremendous effort — or ask other people to go to tremendous effort on their behalf– to tune a Bayesian method to behave like a comparable frequentist method. Why not just use the frequentist method they’re trying to ape? Because they get brownie points for using Bayesian methods.

]]>For more on Bayes see:

The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy – Sharon Bertsch McGrayne

An Introduction to Probability and Inductive Logic – Ian Hacking

]]>Happy New Year, GW

]]>There are many approaches to overcoming the objection to prior distributions. Here are a few off the top of my head.

- Do a sensitivity analysis and show that conclusions are not sensitive to priors (if that’s true).
- Special case of sensitivity analysis: show that skeptical and optimistic priors lead to the same conclusion.
- Use “objective” priors, i.e. priors chosen to satisfy some mathematical optimality condition rather than prior belief.
- Use empirical Bayes.
- Treat the Bayesian procedure as a black box and study its frequentist operating characteristics.