Markov Chain Models

以过渡矩阵为特征的离散状态空间过程

A discrete state-space Markov process, orMarkov chain，由有向图表示，并由右式过渡矩阵描述P. The distribution of states at timet+ 1 is the distribution of states at timetmultiplied byP. The structure ofPdetermines the evolutionary trajectory of the chain, including asymptotics.

For an overview of the Markov chain analysis tools, seeMarkov Chain Modeling.

Functions

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Create Markov Chain

`dtmc`	Create discrete-time Markov chain
`mcmix`	Create random Markov chain with specified mixing structure

Determine Markov Chain Structure

`asymptotics`	确定马尔可夫链渐近学
`isergodic`	Check Markov chain for ergodicity
`isreducible`	Check Markov chain for reducibility
`classify`	Classify Markov chain states
`lazy`	Adjust Markov chain state inertia
`subchain`	Extract Markov subchain

Describe Markov Chain Evolution

`hitprob`	Compute Markov chain hitting probabilities
`hittime`	Compute Markov chain hitting times
`redistribute`	Compute Markov chain redistributions
`simulate`	Simulate Markov chain state walks

Visualize Markov Chain

`distplot`	情节马尔可夫chain redistributions
`eigplot`	情节马尔可夫chain eigenvalues
`graphplot`	情节马尔可夫链的定向图
`simplot`	情节马尔可夫chain simulations

Topics

Discrete-Time Markov Chains
Markov chains are discrete-state Markov processes described by a right-stochastic transition matrix and represented by a directed graph.
Markov Chain Modeling
Thedtmcclass provides basic tools for modeling and analysis of discrete-time Markov chains. The class supports chains with a finite number of states that evolve in discrete time with a time-homogeneous transition structure.
Create and Modify Markov Chain Model Objects
Create a Markov chain model object from a state transition matrix of probabilities or observed counts, and create a random Markov chain with a specified structure.
Visualize Markov Chain Structure and Evolution
Visualize the structure and evolution of a Markov chain model by usingdtmcplotting functions.
Work with State Transitions
This example shows how to work with transition data from an empirical array of state counts, and create a discrete-time Markov chain (dtmc）表征状态转换的模型。
Determine Asymptotic Behavior of Markov Chain
Compute the stationary distribution of a Markov chain, estimate its mixing time, and determine whether the chain is ergodic and reducible.
Compare Markov Chain Mixing Times
Compare the estimated mixing times of several Markov chains with different structures.
Identify Classes in Markov Chain
Programmatically and visually identify classes in a Markov chain.
Simulate Random Walks Through Markov Chain
生成和可视化随机行走穿过马尔可夫链。
Compute State Distribution of Markov Chain at Each Time Step
Compute and visualize state redistributions, which show the evolution of the deterministic state distributions over time from an initial distribution.