Why I am not a non-Bayesian? [Medical diagnostics application]
Recently there has been much interest, and some hype, on the use of Bayesian methods in problems of machine learning and inference. While it is true that the Bayesian methodology offers a nice way of specifying uncertainties about a problem domain and carrying them through the modelling process to any inference one makes, there are very few convincing practical demonstrations of it. This is particularly the case when Bayesian techniques are coupled with powerful nonlinear function approximators such as neural networks. Since nonlinear models induce complicated probability densities, approximations become necessary. It is not clear how much of the elegance of the Bayesian framework is lost in the presence of these approximations. The alternative approach is to represent the probability densities in a nonparametric way, by resorting to Markov Chain Monte Carlo techniques. Here too, algorithmic as well as computational limitations exist. However, I have recently worked on some problems in which useful algorithmic advantages can be achieved using Bayesian techniques. This talk is a review of the above concepts with an emphasis on their application to two problems in medical diagnostics: (a) predicting adverse outcome in pregnancy, and (b) monitoring liver transplant patients for rejection of transplanted organ.