Hypothesis Tests on Mixture Model Components with Applications in Ecology and Agriculture

Bayesian screening for feature selection

Biomedical applications such as genome-wide association studies screen large databases with high-dimensional features to identify rare, weakly expressed, and important continuous-valued features for subsequent detailed analysis. We describe an exact, rapid Bayesian screening approach with attractive diagnostic properties using a Gaussian random mixture model focusing on the missed discovery rate (the probability of failing to identify potentially informative features) rather than the false discovery rate ordinarily used with multiple hypothesis testing. The method provides the likelihood that a feature merits further investigation, as well as distributions of the effect magnitudes and the proportion of features with the same expected responses under alternative conditions. Important features include the dependence of the critical values on clinical and regulatory priorities and direct assessment of the diagnostic properties.

Shared kernel Bayesian screening

This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method using kernel mixtures, which improves performance by borrowing information across the different variables and groups through shared kernels and a common probability of group differences. The inclusion of shared kernels in a finite mixture, with Dirichlet priors on the weights, leads to a simple framework for testing that scales well for high-dimensional data. We provide closed asymptotic forms for the posterior probability of equivalence in two groups and prove consistency under model misspecification. The method is applied to DNA methylation array data from a breast cancer study, and compares favourably to competitors when Type I error is estimated via permutation.

A Bayesian normal mixture accelerated failure time spatial model and its application to prostate cancer

In the United States, prostate cancer is the third most common cause of death from cancer in males of all ages, and the most common cause of death from cancer in males over age 75. It has been recognized that the incidence of the prostate cancer is high in African Americans, and its occurrence and progression may be impacted by geographical factors. In order to investigate the spatial effects and racial disparities for prostate cancer in Louisiana, in this article we propose a normal mixture accelerated failure time spatial model, which does not require the proportional hazards assumption and allows the multi-model distribution to be modeled. The proposed model is estimated with a Bayesian approach and it can be easily implemented in WinBUGS. Extensive simulations show that the proposed model provides decent flexibility for a variety of parametric error distributions. The proposed method is applied to 2000–2007 Louisiana prostate cancer data set from the Surveillance, Epidemiology and End Results Program. The results reveal the possible spatial pattern and racial disparities for prostate cancer in Louisiana.