Sensitivity Properties of Markovian Models

Markovian models specify a considerable number of parameter probabilities. Whether estimated from data or assessed by experts, these parameters tend to be inaccurate to at least some degree. Sensitivity analysis provides for studying the effects of these inaccuracies on the model’s output probabilities. In this paper, we extend previous work on sensitivity analysis of Bayesian networks, to Markovian models. More specifically, we study the sensitivity properties of the transition behaviour of hidden Markov models. We show that the output probability can be expressed as a quotient of two functions that are polynomial in a transition or an observation parameter. We present a scheme for computing the constants in these functions. In addition, we present a method for approximating the quotient for further use.