A Bayesian nonparametric testing procedure for paired samples

We propose a Bayesian hypothesis testing procedure for comparing the distributions of paired samples. The procedure is based on a flexible model for the joint distribution of both samples. The flexibility is given by a mixture of Dirichlet processes. Our proposal uses a spike-slab prior specification for the base measure of the Dirichlet process and a particular parametrization for the kernel of the mixture in order to facilitate comparisons and posterior inference. The joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. A Monte Carlo simulation study comparing the performance of this strategy to other traditional alternatives is provided. Finally, we apply the proposed approach to spirometry data collected in the United States to investigate changes in pulmonary function in children and adolescents in response to air polluting factors.

Bayesian Hidden Markov Models for Dependent Large-Scale Multiple Testing

An optimal and flexible multiple hypotheses testing procedure is constructed for dependent data based on Bayesian techniques, aiming at handling two challenges, namely dependence structure and non-null distribution specification. Ignoring dependence among hypotheses tests may lead to loss of efficiency and bias in decision. Misspecification in the non-null distribution, on the other hand, can result in both false positive and false negative errors. Hidden Markov models are used to accommodate the dependence structure among the tests. Dirichlet mixture process prior is applied on the non-null distribution to overcome the potential pitfalls in distribution misspecification. The testing algorithm based on Bayesian techniques optimizes the false negative rate (FNR) while controlling the false discovery rate (FDR). The procedure is applied to pointwise and clusterwise analysis. Its performance is compared with existing approaches using both simulated and real data examples.

Adjusting background noise in cluster analyses of longitudinal data

Background noise in cluster analyses can potentially mask the true underlying patterns. To tease out patterns uniquely to certain populations, a Bayesian semi-parametric clustering method is presented. It infers and adjusts background noise. The method is built upon a mixture of the Dirichlet process and a point mass function. Simulations demonstrate the effectiveness of the proposed method. The method is then applied to analyze a longitudinal data set on allergic sensitization and asthma status.

Perspective—Chance Explanations in the Management Sciences

We propose that random variation should be considered one of the most important explanatory mechanisms in the management sciences. There are good theoretical reasons to expect that chance events strongly impact organizational behavior and outcomes. We argue that models built on random variation can provide parsimonious explanations of several important empirical regularities in strategic management and organizational behavior. The reason is that random variation in a structured system can give rise to systematic patterns at the macro level. Here, we define the concept of a chance explanation; describe the theoretical mechanisms by which random variation generates patterns at the macro level; outline how key empirical regularities in management can be explained by chance models; and discuss the implications of chance models for theoretical integration, empirical testing, and management practice.