25 research outputs found
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
Two-sample Bayesian nonparametric goodness-of-fit test
In recent years, Bayesian nonparametric statistics has gathered extraordinary
attention. Nonetheless, a relatively little amount of work has been expended on
Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian
nonparametric approach to the two-sample problem is established. Precisely,
given two samples
and , with and
being unknown continuous cumulative distribution functions, we wish to test the
null hypothesis . The method is based on the Kolmogorov
distance and approximate samples from the Dirichlet process centered at the
standard normal distribution and a concentration parameter 1. It is
demonstrated that the proposed test is robust with respect to any prior
specification of the Dirichlet process. A power comparison with several
well-known tests is incorporated. In particular, the proposed test dominates
the standard Kolmogorov-Smirnov test in all the cases examined in the paper.Comment: 25 pages, 8 figure