About Markov Chain Monte Carlo Method (MCMC Method) ・ What is the MCMC method? -MCMC method types and Python modules I tried to summarize.

0. What is the Markov chain Monte Carlo method (MCMC method)?

By using Markov chains, the Monte Carlo method is strengthened.

I will write in detail later, The Monte Carlo method is for sampling truly randomly. ・ Calculation cost is high ・ Accuracy does not improve There is a problem. So the Markov chain Monte Carlo method This problem was improved by using Markov chains.

1. 1. What is the Monte Carlo method?

"Introduction to Monte Carlo Method with Python" http://aidiary.hatenablog.com/entry/20140620/1403272044 The Monte Carlo method is carefully explained from the beginning, Moreover, it comes with a Python implementation.

You can learn the theory with very detailed explanations while trying this amount. I have the original book, but it's better to read this page I think it should be much less laborious and easy to understand.

There are quite a few types of Monte Carlo methods. ・ Inverse conversion method ・ Box-Muller method ・ Acceptance rejection law ・ Priority sampling

In the original, after this, the Markov chain Monte Carlo method (and the Metropolis method) There is an explanation of, but there is no description there on this site.

2. What is a Markov chain?

Roughly, to make a stochastic transition in time series It performs matrix operations. (Not accurate ...) You can also think of it as an automaton that makes a stochastic transition.

"Introduction to Markov chain : simplified!" http://www.analyticsvidhya.com/…/07/markov-chain-simplified/ English, but good article.

3. 3. Markov chain Monte Carlo method (MCMC method)

1) What is the MCMC method?

The Monte Carlo method is for sampling truly randomly. ・ Calculation cost is high ・ Accuracy does not improve There is a problem.

Markov chain Monte Carlo method By sampling with a Markov chain as a steady distribution, This is a method that improves the above problems.

2) MCMC algorithm

step1. Determine the initial point step2. Determine the distribution for the next sampling by Markov chain

There seems to be an object near the initial point (sampling so far) step3. Repeat step2 until the distribution converges

4. Practice with Python

1) First MCMC (Metropolis-Hastings method)

https://tatsyblog.wordpress.com/

From the side of reading the source code I feel like MCMC can understand.

The Metropolis-Hastings method is based on the most natural idea It is an orthodox method designed. In a certain probability when going to the lower probability It is a stopper to prevent the steady distribution from transitioning.

If you do not make a transition, you will easily fall into a local solution.
In the above algorithm, the transition is always made primitively.

2) Types of MCMC method

Other, ・ Gibbs sampling method ・ Hybrid Monte Carlo method ・ Slice sampling method Is introduced, but see ↑ article.

3) Python module

↑ The link uses the mcmc module, Besides that, it seems that the pymc3 module is also often used. http://qiita.com/kenmatsu4/items/a0c703762a2429e21793

5. To learn the theoretical system

The Institute of Statistical Mathematics by Professor Yukito Iba MCMC Lecture (https://www.youtube.com/watch?v=-H28H1unn0M)

From the stationary distribution to the nature of Markov chains and the physical aspects The explanation is simple and easy to understand. If you look at this, you can easily understand the foundation of MCMC.

6. Finally

MCMC method is a wonderful commentary on a recently talked-about book [Special feature] Bayesian inference and MCMC free software support page https://sites.google.com/site/iwanamidatascience/vol1/support_tokushu It may be enough to see.

But here,

The entrance to what the Markov chain Monte Carlo method is
How to use the Python module I wrote the basics of, and I wondered if I could differentiate ...

[PYTHON] I tried to organize about MCMC.