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Multiple testing on dependent count data faces two basic modelling elements: the choice of distributions under the null and the non-null states and the modelling of the dependence structure across obser- vations. A Bayesian hidden Markov model is constructed for Pois- son count data to handle these two issues. The proposed Bayesian method is based on the posterior probability of the null state and exhibits the property of an optimal test procedure, which has the lowest false-negative rate with the false discovery rate under con- trol. Furthermore, the model has either single or mixture of Poisson distributions used under the non-null state. Model selection meth- ods are employed here to decide the number of components in the mixture. Different approaches of calculating marginal likelihood are discussed. Extensive simulation studies and a case study are employed to examine and compare a collection of commonly used testing procedures and model selection criteria.
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.
A history of eating highly palatable foods reduces physiological and emotional responses to stress. For instance, we have previously shown that limited sucrose intake (4 ml of 30 % sucrose twice daily for 14 days) reduces hypothalamic-pituitary-adrenocortical (HPA) axis responses to stress. However, the neural mechanisms underlying stress relief by such 'comfort' foods are unclear, and could reveal an endogenous brain pathway for stress mitigation. As such, the present work assessed the expression of several proteins related to neuronal activation and/or plasticity in multiple stress- and reward-regulatory brain regions of rats after limited sucrose (vs. water control) intake. These data were then subjected to a series of statistical analyses, including Bayesian modeling, to identify the most likely neurocircuit mediating stress relief by sucrose. The analyses suggest that sucrose reduces HPA activation by dampening an excitatory basolateral amygdala-medial amygdala circuit, while also potentiating an inhibitory bed nucleus of the stria terminalis principle subdivision-mediated circuit, resulting in reduced HPA activation after stress. Collectively, the results support the hypothesis that sucrose limits stress responses via plastic changes to the structure and function of stress-regulatory neural circuits. The work also illustrates that advanced statistical methods are useful approaches to identify potentially novel and important underlying relationships in biological datasets.