Classifying Markov Chains Up to now, we have not put the Markov Chains into different categories yet. We will do that in this section. A Markov Chain is ergodic if it corresponds with a connected graph. We are only concerned about these Markov Chains here. A Markov Chain is regular if ...
Behrends, E.: Introduction to Markov Chains. Advanced Lectures in Mathematics Vieweg (1999)E. Behrends. Introduction to Markov chains. With special emphasis on rapid mixing. Advanced Lectures in Mathematics. Vieweg, Braunschweig, 1999.E. Behrends. Introduction to Markov Chains, with special ...
我们接下来看一个有限维空间马尔可夫链的简单例子: Example: Predicting the weather with a finite state-space Markov chain 假如加州大学伯克利分校的天气有三种: 晴天,雾天和雨天(这用来模拟状态空间的三个离散的值)。这里的天气状态十分稳定,所以伯克利的天气预报员可以轻松地根据当前的天气来预测下周的天气,按照...
Markov chains are a type of mathematical system that undergoes transitions from one state to another according to certain probabilistic rules. They were first introduced by Andrey Markov in 1906 as a way to model the behavior of random processes, and have since been applied to a wide range of ...
Markov chains are useful in that if they are constructed properly, and allowed to run for a long time, the states that a chain will take also sample from a target probability distribution. Therefore we can construct Markov chains to sample from the distribution whose integral we would like to...
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, howev...
An Introduction to Stochastic Modeling (Revised Edition)Taylor HM, Karlin S (1998) Markov chains: introduction. In: An introduction to stochastic modelling. Academic Press, San Diego, pp 95–198Taylor, H.M., and Karlin, S. 1998. Markov chains: introduction, 95-198. In: An Introduction to...
Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and gra...
Chapter 1. Elements of Combinatorial Analysis and Simple Random Walks Chapter 2. The Modern Probability Language Part II. Conditional Expectations, Martingales and Markov Chains Introduction Chapter 3. Conditional Expectations Chapter...
We also comment on how the convergence of a Markov chain to equilibrium can be assessed in practice and provide an illustrating example. Finally, we review some of the freely available, existing software for implementing MCMC methods. Keywords: Monte Carlo simulation; Markov chains; Bayesian ...