Markov Chain Models
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.
Create Markov Chain
Determine Markov Chain Structure
Describe Markov Chain Evolution
- 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
dtmcclass 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
- 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.