https://github.com/timudk/introduction_to_mcmc

A brief introduction to Markov chain Monte Carlo methods
https://github.com/timudk/introduction_to_mcmc

markov-chain markov-chain-monte-carlo matlplotlib numpy python stochastic

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A brief introduction to Markov chain Monte Carlo methods

• Host: GitHub
• URL: https://github.com/timudk/introduction_to_mcmc
• Owner: timudk
• License: mit
• Created: 2018-07-01T19:13:20.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2018-07-28T21:09:11.000Z (over 6 years ago)
• Last Synced: 2024-11-05T11:09:12.668Z (3 months ago)
• Topics: markov-chain, markov-chain-monte-carlo, matlplotlib, numpy, python, stochastic
• Language: Python
• Homepage:
• Size: 1.5 MB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Introduction to Markov chain Monte Carlo methods

This project has been developed as part of the class AMATH777 - Stochastic Processes in the Physical Sciences at the University of Waterloo. The code is entirely written in Python. A documentation in form of a report as well as a presentation can be found [here](https://github.com/timudk/introduction_to_mcmc/tree/master/documentation).

# Code description

The code is based on the following packages:

* NumPy

* matplotlib

Check (and potentially download the two packages) using pip:

```console

foo@bar:~$ pip install numpy matplotlib

```

## uniform_samples_using_linear_congruential_generator.py

This example produces a sequence of samples for the uniform distribution U([0,1]) using a linear congruential generator (LCG). A description of the method can be found at https://en.wikipedia.org/wiki/Linear_congruential_generator.



  

## pi_monte_carlo.py

This example approximates pi numerically using a Monte Carlo estimator I = (4/N) SUM_{i=1}^{N} h(x^(i), y^(i)) where h() is the indicator function h(x,y) = {1 if x^2+y^2 <= 1 and 0 otherwise} and the tupels (x^(i), y^(i)) are drawn from the uniform distribution U([0,1]x[0,1]).



  

  

## metropols.py

This examples produces a sequence of samples drawn from the non-normalized distribution f(x) = 0.3exp(-0.2x^2) + 0.7exp(-0.2(x-10)^2) using the Metropolis algorithm with a normal proposal distribution (see [Andrieu et al.](http://www.cs.ubc.ca/~arnaud/andrieu_defreitas_doucet_jordan_intromontecarlomachinelearning.pdf) for further details).