Testing Between Different Types of Poisson Mixtures with Applications to Neuroscience

We propose a hypothesis testing for different types of stochastic order of mixture distributions (PRML classifier) and a hypothesis testing for screening out data with mixture distributions (PRML filter), in a Bayesian framework using a recursive algorithm called predictive recursion marginal likelihood (PRML) algorithm. Of particular interest is the special case of testing between different types of Poisson mixtures and testing Poisson distribution versus Poisson mixtures. The first testing procedure applies Laplace approximation coupled with optimization algorithm. This testing helps neuroscientists to classify the activation patterns that a single neuron exhibits when preserving information from multiple stimuli. The second testing aims to screen out over-dispersed data to boost the scientific information. Simulation shows the new classifier and filter outperform the previous testing especially for over-dispersed data. We apply the PRML classifier on the analysis of inferior colliculus neurons filtered by PRML filter. We show the PRML classifier emphasizes second order stochasticity. We present empirical evidence that the PRML filter contributes to avoid mistaking trial-to-trial variation as second order stochasticity.