# MCMC convergence

(1.3 hours to learn)

## Summary

Markov chain Monte Carlo (MCMC) samplers eventually converge to their stationary distribution, but they may take a long time to do so. The "mixing time" of a chain refers to how long a chain must be run in order for one sample to be independent of another. Diagnosing mixing time is important for judging the reliability of estimates obtained from an MCMC algorithm.

## Context

This concept has the prerequisites:

- Markov chain Monte Carlo
- covariance (The accuracy of MCMC depends on the covariance of the function at different steps.)

## Core resources (read/watch one of the following)

## -Free-

→ Machine learning summer school: Markov chain Monte Carlo (2009)

→ Coursera: Probabilistic Graphical Models (2013)

An online course on probabilistic graphical models.

Location:
Lecture "Using a Markov chain"

Other notes:

- Click on "Preview" to see the videos.

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 24.4, pages 856-862

→ Probabilistic Graphical Models: Principles and Techniques

A very comprehensive textbook for a graduate-level course on probabilistic AI.

Location:
Section 12.3.5, pages 518-526

## See also

-No Additional Notes-