https://github.com/ethanuppal/metropolis

An implementation of the Metropolis algorithm.
https://github.com/ethanuppal/metropolis

bayesian monte-carlo statistics

Last synced: 11 months ago
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An implementation of the Metropolis algorithm.

• Host: GitHub
• URL: https://github.com/ethanuppal/metropolis
• Owner: ethanuppal
• Created: 2023-04-21T02:36:22.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2023-04-21T02:36:24.000Z (about 3 years ago)
• Last Synced: 2024-01-29T23:11:26.337Z (over 2 years ago)
• Topics: bayesian, monte-carlo, statistics
• Language: Swift
• Homepage:
• Size: 200 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# metropolis

This repository contains my implementation of the [Metropolis algorithm](src/MCMC/Metropolis.swift), which is used for Bayesian statistical analysis, as well as a [custom graph renderer](src/Graphics/Graph.swift). Here is example output from a run of the program.

![A histogram showing an example run of the Metropolis algorithm.](assets/ex_run.png)

```

Bayesian Analysis

using Markov chain Monte Carlo

==============================

Observations

------------

  - 2 coin flips

  - 1 head(s)

Prior

-----

  We use an uninformed prior: beta(a=1, b=1)

Likelihood

----------

  P(data|θ) = bernoulli(N=2, z=1)

Metropolis

----------

  We perform the metropolis algorithm to estimate the central tendency of the posterior distribution.

  Random seed: 0.834189865344514

  Steps: 10000

  Burn-in Period: 3000

  Est. Mean: 0.4934783753798731

  Est. StdDev: 0.22304677011859197

Actual

------

  P(θ|data) = beta(a=2, b=2)

  Act. Mean: 0.5 (-1.0% error)

  Act. StdDev: 0.22360679774997896 (-0.0% error)

```