Bayes Estimates of Shifted Mixtures using Multimodal Discrete Data

Speaker: Dr Jamie Cross
Affiliation: University of Queensland (School of Economics)

Abstract

In several scientific fields important theoretical and practical issues exist involving multimodal discrete data distributions due to heterogeneity of the underlying population. For accurate approximation of such distributions, we propose a novel mixture of shifted Poisson distributions with a flexible number of mixture components, and estimate it with an efficient Sparse Finite Mixture Markov Chain Monte Carlo algorithm. In a simulation exercise, we find that the correct assessment of multimodality is obtained with substantial posterior probability, in contrast to frequentist tests that often fail to reject the null of unimodality. Using micro-datasets in genomics and finance, we show how the framework can deliver information about the quantification of number of modes, their location, and their uncertainty. The proposed methodology may therefore lead to improved prediction and policy analysis with multimodal discrete data.