Estimation of CAR processes observed in noise using Bayesian inference

We consider the problem of estimating continuous-time autoregressive (CAR) processes from discrete-time noisy observations. This can be done within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Existing methods include the standard random walk Metropolis algorithm. On the other hand, least-squares (LS) algorithms exist where derivatives are approximated by differences and parameter estimation is done in a least-squares manner. In this paper, we incorporate the LS estimation into the MCMC framework to develop a new MCMC algorithm. This new algorithm is combined with the standard Metropolis algorithm and is found to improve performance compared to the standard MCMC algorithm. Simulation results are presented to support our findings