arXiv subjects

Gauri S. Datta

Publications and source records attributed to Gauri S. Datta.

4 recordsLinked to original sources

arXiv2017

A Bayesian Generalized CAR Model for Correlated Signal Detection

Over the last decade, large-scale multiple testing has found itself at the forefront of modern data analysis. In many applications data are correlated, so that the observed test statistic used for detecting a non-null case, or signal, at each location in a dataset carries some information about the chances of a true signal at other locations. Brown, Lazar, Datta, Jang, and McDowell (2014) proposed in the neuroimaging context a Bayesian multiple testing model that accounts for the dependence of each volume element on the behavior of its neighbors through a conditional autoregressive (CAR) model. Here, we propose a generalized CAR model that allows for inclusion of points with no neighbors at all, something that is not possible under conventional CAR models. We consider also neighborhoods based on criteria other than physical location, such as genetic pathways in microarray determined from existing biological knowledge. This generalization provides a unified framework for the simultaneous modeling of dependent and independent cases, resulting in stronger Bayesian learning in the posterior and increased precision in the estimates of interesting signals. We justify the selected prior distribution and prove that the resulting posterior distribution is proper. We illustrate the effectiveness and applicability of our proposed model by using it to analyze both simulated and real microarray data in which the genes exhibit dependence that is determined by physical adjacency on a chromosome or predefined gene pathways.

stat.ME↗

arXiv2008

Objective Bayes testing of Poisson versus inflated Poisson models

The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a zero-inflated Poisson (ZIP) distribution is often proposed. This article addresses testing a Poisson versus a ZIP model, using Bayesian methodology based on suitable objective priors. Specific choices of objective priors are justified and their properties investigated. The methodology is extended to include covariates in regression models. Several applications are given.

math.ST↗

arXiv2008

A Bayesian test for excess zeros in a zero-inflated power series distribution

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate distribution at zero, with a mixing probability $p$ for the degenerate distribution. This distribution is useful for modeling count data that may have extra zeros. One question is whether the mixture model can be reduced to the power series portion, corresponding to $p=0$, or whether there are so many zeros in the data that zero inflation relative to the pure power series distribution must be included in the model i.e., $p\geq0$. The problem is difficult partially because $p=0$ is a boundary point. Here, we present a Bayesian test for this problem based on recognizing that the parameter space can be expanded to allow $p$ to be negative. Negative values of $p$ are inconsistent with the interpretation of $p$ as a mixing probability, however, they index distributions that are physically and probabilistically meaningful. We compare our Bayesian solution to two standard frequentist testing procedures and find that using a posterior probability as a test statistic has slightly higher power on the most important ranges of the sample size $n$ and parameter values than the score test and likelihood ratio test in simulations. Our method also performs well on three real data sets.

math.ST↗

arXiv2006

Nonsubjective priors via predictive relative entropy regret

We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and show that this approach to prior construction has a number of attractive features. The approach here differs from previous work that uses either prior or posterior relative entropy regret in that we consider predictive performance in relation to alternative nondegenerate prior distributions. The theory is illustrated with an analysis of some specific examples.

math.ST↗