Transient states: \exists k\in A(i),\ \ i\notin A(k) ,即存在可由状态 i 到达的状态 k,无法从该状态到达状态 i。 转移概率图 如果状态 i 是recurrent states,那么 A(i) 集合(recurrent class)里所有的状态是互相可达的。 马尔可夫链分解: 一条马尔可夫链可以分解成多个recurrent class,以及其他一...
So if the chain is reversible, we can have detailed balance. And there is also a good reference of distinguishing conditional probability and joint probability.[7] Theorem 4: Main Theorem A discrete dynamical system with a finite number of states can be guaranteed to converge to an equilibrium...
马尔可夫链(Markov Chain, MC)是概率论和数理统计中具有马尔科夫性质(Markov property)且存在于离散的指数集(index set)和状态空间(state space)内的随机过程(stochastic process)。适用于连续指数集的马尔可夫链被称为马尔科夫过程(Markov process),但有时也被视为马尔可夫链的子集,即连续时间马尔科夫链(Continuous...
Conservation of probability: Typically, When the system reaches its equilibrium, there is a particular distribution , fulfilling Ergodicity: after finite number of steps, the system from any state can evolve to any final state . In Markov chain, it’s also called irreducible. can be diagonal...
Liu, in Physica A: Statistical Mechanics and its Applications, 2018 3.2 Markov Chain Monte Carlo Markov Chain Monte Carlo (MCMC) algorithms are computational methods intended to recover the properties of an unknown probability distribution by constructing a Markov chain that has the desired ...
Hodge. Markov chain Monte Carlo linkage analysis: Effect of bin width on the probability of linkage. Genetic Epi- demiology, 21 Suppl 1:700-705, 2001.Slager SL, Juo SH, Durner M, Hodge SE. 2001. Markov chain Monte Carlo linkage analysis: effect of bin width on the probability of ...
马尔科夫链(markov chain) 技术标签:数学基础马尔科夫 A Markov chain is “a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.” 马尔科夫链虽然听上去很......
hp = hitprob(mc,target) returns the probability hp of hitting a specified subset of states target, beginning from each state in the Markov chain mc. If target forms a recurrent class, the elements of hp are absorption probabilities. example hp = hitprob(mc,target,'Graph',true) plots a ...
平稳马尔可夫链（stationary Markov chain）若一个马尔可夫链拥有唯一的平稳分布且极限分布收敛于平稳分布，则按定义等价于，该马尔可夫链是平稳马尔可夫链。平稳马尔可夫链是严格平稳随机过程，其演变与时间顺序无关：由极限定理可知，遍历链是平稳马尔可夫链。此外由上述定义，平稳马尔可夫链的转移矩阵是常数矩阵，...