Path analysis of continuous-time stochastic systems
Theodore Perkins , Ottawa Hospital Research Institute

Abstract:

In analyzing a stochastic dynamical system, one of the most natural questions we may ask is: What is the most probable path the system takes between a point A and a point B? This basic question is at the core of many applied computing problems, including speech recognition, motion tracking, error correction, etc. When time is discrete, the Viterbi algorithm provides an efficient and optimal solution. When time is continuous, however, the problem has not been adequately addressed. I will present several new results and ongoing work in the area of path inference for continuous-time Markov chains -- a class of continuous-time discrete-state stochastic systems. A key observation is that the right solution to path inference in these systems is not simply to discretize time and apply the Viterbi algorithm. Rather, one must reformulate the problem appropriately for the continuous-time case, and develop new solutions to that problem. I will describe these solutions and demonstrate them on applications in fault diagnosis, HIV virus evolution, and the dynamics of neural ion channels.