③燃烧期和混合时间:若一个Markov Chain经过t=1~m时间段的状态变换,在t=m+1时刻往后的随机变量就收敛到平稳分布,那么将t=[1,m]称为燃烧器,m称为mixing time。 MCMC方法相关概念简单小结: MH采样方法: 由于一个普通的Markov Chain每个时刻对应的随机变量Xt和每组相邻时刻间的{Pt,t+1}是不一样的,所以需要...
三、Markov Chain(马尔科夫链)(视频P2) 上一节讲了门特卡罗方法,这一节讲马尔科夫链。 Markov Chain:时间和状态都是离散的随机过程。 随机过程:研究对象是一个随机变量序列,而不是单个的随机变量。 这一章主要关注齐次(一阶)Markov Chain 满足马尔科夫性质:后一个状态只依赖于前一个状态,与更之前的无关。 P...
mixing timeWe address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. ...
Markovchain over CouplingConsider Markovchain Wewant mixingtime Markovchain stationarydistribution wewrite distributionassociated Markovchain wewant wherewe recall totalvariation distance Roughlyspeaking, ideabehind coupling runtwo copies Markovchain simultaneously eachcopy obeys originaltransition probabilities, two...
The Markov chain Monte Carlo paradigm has developed powerful and elegant techniques for estimating the time until a Markov chain approaches a stationary distribution. This time is known as mixing time. We introduce the reader into mixing time estimations via coupling arguments and use the mixing of...
markov英文版chainsexercisesnotesmixing MarkovChainsandMixingTimesDavidA.LevinYuvalPeresElizabethL.WilmerUniversityofOregonE-mailaddress:dlevin@uoregon.eduURL:http://.uoregon.edu/~dlevinMicrosoftResearch,UniversityofWashingtonandUCBerkeleyE-mailaddress:peres@microsoftURL:http://research.microsoft/~peres/Oberlin...
Since the publication of the first edition, the field of mixing times has continued to enjoy rapid expansion. In particular, many of the open problems posed in the first edition have been solved. The book has been used in courses at numerous universities, motivating us to update it. In the...
Here XX is the state space of the Markov chain, and ππ is its stationary distribution. Is there a stronger mixing condition than this, where we can say that the chain converges to its stationary distribution in finite time with probability 1? In other words, under what conditions can we...
Hidden Markov model Markov blanket Markov chain geostatistics Markov chain mixing time Markov chain Monte Carlo Markov decision process Markov information source Markov network Markov process Quantum Markov chain Semi-Markov process Telescoping Markov chain Variable-order Markov modelNotes...