Improving the efficiency of Markov chain Monte Carlo

马尔可夫链蒙特卡罗(MCMC)算法在科学界得到了广泛的应用。它们被用来从统计和应用概率模型产生的复杂目标分布中产生近似样本。特别是，Metropolis和Langevin算法等通用算法由于易于实现而非常流行。然而，众所周知，选择最好的提案分布并不是一件容易的事情。如果做不到这一点，可能会导致算法效率低下并产生误导性结果。我的研究项目将专注于MCMC算法的理论和实现，通常是在无界欧几里德状态空间上，受分布的激励，例如在贝叶斯推理中遇到的那些分布。我提议的研究计划的三个主要目标是：

Markov chain Monte Carlo (MCMC) algorithms are widely used in the scientific community. They are used to generate approximate samples from complicated target distributions resulting from statistical and applied probability models. In particular, generic algorithms such as Metropolis and Langevin algorithms are very popular because of the ease of implementations. However, it is well known that choosing the best proposal distribution is not an easy task. Failing to do that can result in an inefficient algorithm and misleading results. My research program will focus on the theory and implementation of MCMC algorithms, typically on unbounded Euclidean state spaces, motivated by distributions such as those encountered in Bayesian inference. The three main objectives of my proposed research program are: