The National Science Foundation (NSF), through its Division of Mathematical Sciences, awarded a $225,000 Project Grant to The Leland Stanford Junior University (Stanford University) to develop new algorithms for Bayesian computation. The grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), aims to address challenges in Bayesian inference for complex statistical models, such as hidden Markov models with continuous variables and models with intractable likelihood functions. The research will focus on creating efficient algorithms to sample from the posterior distribution in these scenarios, enabling wider application of Bayesian methods in various scientific and engineering fields. The project will also contribute to the training of graduate students through their involvement in the research.