9805598 Stramer Many physical systems are described by continuous-time models (diffusions) which incorporate the variability and randomness that occurs in the real world. The PI will carry out research on two different aspects of such systems: the first enables the use of diffusions to give more efficient computing methods in simulation, and the second leads to better inference of the properties of systems. Part I: Development of new Markov Chain Monte Carlo (MCMC) algorithms for efficient computation of a given high-dimensional density pi which is known up to a factor of proportionality. These new algorithms will be based on multi-dimensional diffusion approximations. The basic idea is to find, for a given probability density pi, a class of diffusion processes (continuous-time, continuous sample-path Markov chains) which have pi as an equilibrium distribution. It is expected that the proposed new MCMC algorithms will speed up simulations of a broad class of distributions pi. Part II: Contribution to statistical inference in non-linear continuous time modeling. It is often appropriate to model the time evolution of dynamic systems by using continuous time stochastic processes whose dynamics are characterized by stochastic differential equations. It is proposed to employ a Bayesian approach for model estimation based on MCMC methods. New simulation techniques for estimating the posterior distribution for a broad class of non-linear Continuous time models will be studied. The existing estimation methods in the literature depend on the length of the interval between two observations and hence Metropolis sub-algorithms for augmenting the data set will be studied. This research is expected to provide a new approach for inference in a broad class of continuous time models. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
