Some Issues in Bayesian Nonparametrics
The field of Bayesian nonparametrics encompasses ideas of both a foundational and technical nature. There are no unifying concepts, although the Dirichlet process and related ideas have become very popular. Here we illustrate some of the issues, and in some cases how computational ability has changed them.
The talk will address two questions. The first is: Why bother with Bayesian nonparametrics? We argue that it is a sensible intermediate between an analysis based on complete ignorance and one based on very specific knowledge. Problems where Bayesian nonparametric and computer-intensive techniques are applicable will be illustrated. Each has strengths for different types of problems.
The second question is: Why is the Dirichlet process so popular, and should it be? The Dirichlet process has many appealing features as a nonparametric prior, but it also has some shortcomings. Among undesirable features, we will discuss some aspects of the limited flexibility allowed to express prior opinion and a new inconsistency example which arises with bivariate censored data.
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