Markov Chain Models

Discrete state-space processes characterized by transition matrices

A discrete state-space Markov process, or Markov chain, is represented by a directed graph and described by a right-stochastic transition matrix P. The distribution of states at time t + 1 is the distribution of states at time t multiplied by P. The structure of P determines the evolutionary trajectory of the chain, including asymptotics.

For an overview of the Markov chain analysis tools, see Markov 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`	Determine Markov chain asymptotics
`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`	Plot Markov chain redistributions
`eigplot`	Plot Markov chain eigenvalues
`graphplot`	Plot Markov chain directed graph
`simplot`	Plot Markov 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
The dtmc class 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 using dtmc plotting 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) model characterizing state transitions.
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
Generate and visualize random walks through a Markov chain.
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.