还有一篇Andrieu和Jordan的大作也不错：
C. Andrieu, N.D. Freitas, A. Doucet, and M.I. Jordan, "An Introduction to MCMC for Machine Learning", Machine Learning, 2003, pp.5-43.

引用

Stochastic Sampling
The basic goal of stochastic sampling is to draw random samples from a given distribution p(x). Sometimes, p(x) is not exactly known, for example, knowing only f(x)=p(x)/K.

Given the ability of stochastic sampling, we may do the following things: (i) approximate p(x), (ii) integrate p(x), and (iii) optimize p(x).

A difficulty for stochastic sampling is that the form of p(x) or f(x) is usually complex, however, we can only sample directly from some easy-formed distributions, like discrete distribution, uniform distribution or unit Gaussian. So, usually we sample from an easy-to-sample distribution q(x) instead of from p(x) or f(x), then we either assign each sample point a "weight", or an "acceptance probability" which decides whether we accept this point as a sample from p(x) or f(x).

Some basic sampling methods include:

• Monte Carlo: Sample from q(x). No weight or acceptance probability is calculated. Just pretends that samples from q(x) is from p(x), and use the samples to compute the integration of p(x).
• Weighted Sampling: Sample from q(x). Assign each sample x a weight w=p(x)/q(x). Use the weighted samples to compute the integration of p(x).
• Rejection Sampling: Sample from q(x), where q(x) > p(x) in the whole domain of p(x). Accept each sample x by an acceptance probability a=p(x)/q(x).

In above methods, we have to choose q(x) which is easy-to-sample and approximate p(x). These two requirements are often contradictory. In order not to be bothered by choosing q(x), we may resort to Markov Chain Monte Carlo methods, which constructively approach p(x) without q(x) along a Markov chain.

• Metropolis Sampling: Sample xt from a transition proposal q(xt|xt-1). Accept the sample by the probability
  
  The intuition is to accept xt with high probability if f(xt) > f(xt-1). This requires that q(a|b)=q(b|a).
• Metropolis-Hasting Sampling: Change the acceptance probability to
  
  This trick removes the requirement of q(a|b)=q(b|a).
• Gibbs Sampling: In case that f(x) is very high-dimensional, it is expansive to compute f(x). So we avoid computing acceptance probability by assuming a=1, which means always accept the sample.
• Simulated Annealing: Change the acceptance probability to
  
  where T(t) decreases from a large value to 1. The intuition is that initially, a large T increases the probability to accept an xt which does not increase the value of f(xt).

Few more words for simulated annealing: to take it as a sampling method, we decrease T down to 1; to make it an optimization method, we decrease T down to 0.

References:

1. B. Walsh. Markov Chain Monte Carlo and Gibbs Sampling. Lecture notes. 2004.
2. David J.C. MacKay. Information Theory, Inference, and Learning Algorithms. Chapter 29 and Chapter 30.

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    根据2009年国家留学基资助出国留学选拔简章及《2009年国家公派研究生项目实施方案》，经组织专家对各校推荐的候选人进行评审并经教育部批准，国家留学基金管理委员会确定了2009年国家公派专项研究生奖学金项目及国家建设高水平大学公派研究生项目第一批录取人员名单，现予公布，详见附件。
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    英国剑桥大学博士生项目、英国牛津大学博士生项目、英国爱丁堡大学博士生项目、日本政府（文部科学省）博士生奖学金项目、中英优秀青年学者奖学金项目、中德DAAD博士生奖学金项目等因尚需与外方确定或进行联合面试，录取结果将另行通知。”

国家留学基金管理委员会
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2009年5月12日