Bayesian Inference for Discrete Markov Chains: Their Relevance to Infectious Diseases
Lyle David Broemeling · 2021
This chapter begins with the formal approach to using Bayesian methods of making inferences for infectious diseases, modeled as time series in particular those processes with a countable number of states and an index over discrete time units. It shows that Bayesian inferences will be provided for each case of a Markov chain. In order to fully understand the long-term behavior of a chain, one must know how often the states of a chain are visited, and this in turn relates to the idea of a communicating class, the ideas of recurrent and transient states, and finally the idea of an irreducible chain. The chapter explores how to compute the n-step transition probabilities of a Markov process, the joint distribution of such a process at arbitrary time points, and the marginal distribution of the process at a given time point. It provides Bayesian inferences for the stationary distribution of a stochastic process.