Testing Poisson versus Poisson Mixtures with Application to Neuronscience.

Abstract

A second order stochasticity may manifest in a single neuron’s activation patterns when preserving information from multiple stimuli (Caruso et al, 2018; Glynn et al., 2019). Considering two simultaneously presented stimuli for simplicity, we develop a hypothesis testing to test between distinct competing modes of second order stochastic variations, which corresponds to a testing of different types of Poisson mixtures with unknown mixing distributions. Under a Bayesian paradigm, the testing requires an integration of an infinite-dimensional nonparametric mixing distribution for the marginal likelihood estimation, bringing a practicability challenge. We circumvent this computing problem by adopting a pseudo-Bayesian framework of Predictive Recursion Marginal Likelihood (PRML) proposed by Martin and Tokdar (2011) and design a PRML-based test. We further introduce a modified test based on a clearer separation of model space induced by a truncation hyperparameter. Simulation results show our PRML-based test can characterize overdispersed distribution of spike counts under dual-stimuli, which is common in practice, and improve the confidence of classification greatly. We analyze spike trains of a single neuron in the inferior colliculus region, suggesting a single neuron in dual-stimuli trials does exhibit a second order stochasticity by randomly interweaving between constituent signals.