Friday, July 15, 2011

A Primer on Bayesian Philosophy: 5 - Other outstanding issues

From my small experience, the key to employing Bayesian methodology is always to have the `big tent' in mind and to stay aware of the variety of principled methods available. We want to avoid dogmatic Bayesianism, keeping in mind that the goal of these formal tools is to help us understand the world, not limit our understanding. To this end, I want to list some resources on other open topics in Bayesian philosophy. Here are some topics that come to mind:

  1. Vague probabilities.
  2. Collaboration.
  3. Rational choice theory.
  4. Dealing with uncertainty.
  5. Causal nets.
  6. Common fallacies.

I have mentioned some of these items in passing. I've talked about (4) and recommended Richard Jeffrey's Subjective Probability, available on his site. This text also discusses (2) and (3). Jeffrey, together with Carl Wagner, present the normal solution to the `old evidence problem', addressing how the success of a new theory in explaining old evidence should affect its probability. (See esp. Old Evidence and New Explanation (III).) Wagner's site contains many resources for (3) as well, as does Skyrms' listing at philpapers. For (5), Jon Williamson has some articles on Bayesian nets. (6) is admittedly a vague category, but one important example is in assuming that modus tollens probabilizes similarly to modus ponens. See Wagner's Modus Tollens Probabilized for an example how it can be probabilized, or Elliott Sober's Coincidences and How to Reason about Them for an example of the fallacy in action. Sober also has excellent articles on the application of parsimony in science and how it may be interpreted in probabilistic terms. Another common problem is the application of probabilistic independence, especially conditional independence, questions about which are discussed by Brandon Fitelson and Alan Hájek. Hájek's listing at philpapers contains excellent articles on virtually all of the above topics. Along with the interview of Wagner available on his page, Probability and Statistics: Five Questions, I would recommend Masses of Probability at Hájek's philpapers entry. Wagner and Hájek are more qualified to discuss the lay of the land than I am.

If you're interested in historical resources, some of the big names are Bayes, Laplace, Bruno de Finetti, Keynes, Hempel, and Carnap.

Those with access to databases should have no trouble finding what they need and knowing how to find it with such resources. I usually follow references on the relevant Stanford Encyclopedia articles and find the faculty pages of researchers to get resources, many of which do not require any subscription. With these resources and an introductory text such as Colin Howson and Peter Urbach's Scientific Reasoning, you will soon know more about this stuff than I do.

The point of all this is to do stuff, of course. So let's do stuff.

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