Exact Markov Chain Monte Carlo for a Class of Diffusions

This dissertation focuses on the simulation efficiency of the Markov process for two scenarios: Stochastic differential equations(SDEs) and simulated weather data. 

For SDEs, we propose a novel Gibbs sampling algorithm that allows sampling from a particular class of SDEs without any discretization error and shows the proposed algorithm improves the sampling efficiency by orders of magnitude against the existing popular algorithms.  

In the weather data simulation study, we investigate how representative the simulated data are for three popular stochastic weather generators. Our results suggest the need for more than a single realization when generating weather data to obtain suitable representations of climate.