UCSC-SOE-18-07: A Bayesian model for estimation and order selection in high order Markov chains

Matthew Heiner, Athanasios Kottas, and Stephan Munch
04/03/2018 09:29 AM
Applied Mathematics & Statistics
We develop a model for Bayesian selection in high order Markov chains through an extension of the mixture transition distribution of Raftery (1985). We demonstrate two uses for the model: parsimonious approximation of high order dynamics by mixing lower order transition models, and model selection through over-specification and shrinkage via priors for sparse probability vectors. We discuss properties of the model and demonstrate its utility with simulation studies. We further apply the model to a data analysis from the high-order Markov chain literature and a novel application to pink salmon abundance time series.