报告题目：Bayesian approach to inverse problems
报告人：林逵，复旦大学数学科学学院
时间：2012年8月5日-8月6日，9：00am-11:00am
地点：广东省计算科学重点实验室（415栋旧生物楼421室）
报告概要：
In this talk, we will study the Bayesian statistics as applied to inverse problems. We begin with the basic idea of Bayesian solution, which is a posterior probability measure on the solution space. We will compare with the classical regularization methods and present some examples to show the similarities and differences between the statistical and the classical approaches. Then we introduce the common structure, which generalizes the Bayesian solution to the function space, i.e. the infinity dimensional setting, and the conditions that guarantee the existence and well-posedness of the Bayesian solutions to inverse problems. Finally, we concern on some algorithms, in particular the Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.
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