On Approximations of the Beta Process in Latent Feature Models

The beta process has recently been widely used as a nonparametric prior for different models in machine learning, including latent feature models. In this paper, we prove the asymptotic consistency of the finite dimensional approximation of the beta process due to Paisley \& Carin (2009). In addition, we derive an almost sure approximation of the beta process. This approximation provides a direct method to efficiently simulate the beta process. A simulated example, illustrating the work of the method and comparing its performance to several existing algorithms, is also included.Comment: 25 page

How to Measure Evidence: Bayes Factors or Relative Belief Ratios?

Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and so can be seen to be valid measures of statistical evidence. The question then is: which of these measures of evidence is more appropriate? Certainly Bayes factors are commonly used. It is argued here that there are questions concerning the validity of a current commonly used definition of the Bayes factor and, when all is considered, the relative belief ratio is a much more appropriate measure of evidence. Several general criticisms of these measures of evidence are also discussed and addressed

Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm