Richard Price, Bayes’ theorem, and God

The God delusion Richard

The God Delusion Richard Dawkins Bantam Press, 2006

The temptation with a rallying cry such as Dawkins’s latest effort is to join the chorus of praise or boos, or note dismissively that it is a popular book not really worthy of academic attention. While we might imagine a theological journal taking a passing interest (along with passing pot-shots), surely a social scientific journal need not pay attention to The God Delusion. But Dawkins quite s...

William Karush and the KKT Theorem Richard

This chapter is mainly about William Karush and his role in the Karush-KuhnTucker theorem of nonlinear programming. It tells the story of fundamental optimization results that he obtained in his master’s thesis: results that he neither published nor advertised and that were later independently rediscovered and published by Harold W. Kuhn and Albert W. Tucker. The principal result – which concer...

Bayes Theorem for Improper Priors

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. A consequence is the occurrence of seemingly paradoxical results. The most famous example is perhaps given by the marginalization paradoxes presented by Stone and Dawid (1972). It is demonstrated here that the seemingly paradoxical results are removed by a more careful formulation of the ...

Bayesian Posteriors Without Bayes' Theorem

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. The...