Exact Bayesian estimation in constrained Triplet Markov Chains

The Jump Markov state-space system (JMSS) is a well known model for representing dynamical models with jumps. However inference in a JMSS model is NP-hard, even in the conditionally linear and Gaussian case. Suboptimal solutions include Sequential Monte Carlo (SMC) and Interacting Multiple Models (IMM) methods. In this paper, we build a constrained Triplet Markov Chain (TMC) model which is close to the given JMSS model, and in which moments of interest can be computed exactly (without resorting to numerical nor Monte Carlo approximations) and at a computational cost which is linear in the number of observations. Additionally, a side advantage of our technique is that it can be used easily in a partially known model context.