Author:
Gilchrist Alexei,J. Rogers Lachlan
Abstract
A wide range of systems exhibit stochastic transitions between different states that may be hidden from direct observation. Nevertheless, if the states are coupled to a signal, observation of the signal can provide necessary information to infer the state and switching characteristics. Here we explore a simple hidden Markov model with an observable Poissonian distributed count signal. Determining the parameters of this system from the signal can be difficult in the high-noise regime with non-Bayesian methods. However this system yields a simple Bayesian network description, and variable independencies allow the problem to be formulated in a way that allows tractable inference of the parameters just from the time series. This is an informative demonstration of Bayesian techniques, and in particular the interplay between modelling a system and the process of inference.