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https://github.com/zang-langyan/markov-chain-monte-carlo-mcmc
Markov Chain Monte Carlo MCMC methods are implemented in various languages (including R, Python, Julia, Matlab)
https://github.com/zang-langyan/markov-chain-monte-carlo-mcmc
julia markov-chain-monte-carlo matlab mcmc mcmc-methods mcmc-sampler python r
Last synced: 3 months ago
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Markov Chain Monte Carlo MCMC methods are implemented in various languages (including R, Python, Julia, Matlab)
- Host: GitHub
- URL: https://github.com/zang-langyan/markov-chain-monte-carlo-mcmc
- Owner: zang-langyan
- License: mit
- Created: 2022-04-03T23:07:19.000Z (almost 3 years ago)
- Default Branch: main
- Last Pushed: 2023-06-20T08:04:55.000Z (over 1 year ago)
- Last Synced: 2023-07-19T23:23:19.121Z (over 1 year ago)
- Topics: julia, markov-chain-monte-carlo, matlab, mcmc, mcmc-methods, mcmc-sampler, python, r
- Language: Python
- Homepage:
- Size: 27.3 KB
- Stars: 16
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
马尔可夫链蒙特卡洛方法 Markov Chain Monte Carlo（MCMC）
---
本程辑包仅为学习和练习之用
This repository is only for study and practice purposes
## 目录 Table of Contents
- [马尔可夫链蒙特卡洛方法 Markov Chain Monte Carlo（MCMC）](#马尔可夫链蒙特卡洛方法-markov-chain-monte-carlomcmc)
- [目录 Table of Contents](#目录-table-of-contents)
- [内容](#内容)
- [Overview](#overview)
- [Usage](#usage)
- [Metropolis](#metropolis)
- [Python](#python)
- [Julia](#julia)
- [Matlab](#matlab)
- [R](#r)
## 内容
- [x] [Metropolis Algorithm](#metropolis)
- [ ] Gibbs Sampling (待补充)
- [x] [Hamiltonian Monte Carlo (HMC) ](./Hamiltonian%20Monte%20Carlo/HMC.py) (目前只有python版本)
## Overview
- [x] Metropolis Algorithm
- [ ] Gibbs Sampling (to be added)
- [x] [Hamiltonian Monte Carlo (HMC)](./Hamiltonian%20Monte%20Carlo/HMC.py) (only python version)
## Usage
### Metropolis
#### Python
```python
>>> import metropolis
>>> from scipy.special import beta
>>> density = lambda x: x**14 * (1-x)**6 / beta(15,7) # Beta(15,7) distribution density function
>>> d = metropolis.MCMC(density, space = [0,1], burnin = 5, seed = 72)
>>> result = d.metropolis(chain = 50, theta_init = 0.1)
>>> result
[0.8176960093922774, 0.6965658096789994, 0.7918980615882665, 0.7742394795862185, 0.7742394795862185, 0.6215414421599866, 0.6215414421599866, 0.6468248283946754, 0.7523307146724492, 0.7523307146724492, 0.7680822171469903, 0.6717376155310788, 0.6717376155310788, 0.8189878864825765, 0.7533257832372013, 0.7648206889254298, 0.7648206889254298, 0.7648206889254298, 0.7648206889254298, 0.7648206889254298, 0.7967947965010628, 0.707139903476412, 0.707139903476412, 0.707139903476412, 0.707139903476412, 0.7949590848197712, 0.48018105229278457, 0.48018105229278457, 0.6163978253871556, 0.6163978253871556, 0.6163978253871556, 0.6241841537823003, 0.6241841537823003, 0.6241841537823003, 0.6241841537823003, 0.6922332333961135, 0.8204027203103916, 0.7521267229207833, 0.7521267229207833, 0.808566620237602, 0.808566620237602, 0.6460288022318678, 0.5452360032045938, 0.5452360032045938, 0.5934357613729606]
```
#### Julia
```julia
julia> p(θ) = Distributions.pdf(Beta(15,7),θ) # define a density function
julia> metropolis(p, 5000, 0.5; jump = Normal(0,0.2), space_min = 0, space_max = 1, burnin = 1000, rng = 42)
4000-element Vector{Float64}:
0.7254870615709366
0.5374079418869023
0.5374079418869023
0.5161750364065404
0.7377560837277216
0.7377560837277216
0.8127557482035582
⋮
0.7166820320569407
0.7166820320569407
0.7166820320569407
0.7166820320569407
0.7166820320569407
0.7586353644413187
julia> @time metropolis(θ -> Distributions.pdf(Beta(15,7),θ), 10000, 0.5; jump = Normal(0,0.5), space_min = 0, space_max = 1, burnin = 1000, rng = nothing)
0.061715 seconds (103.38 k allocations: 3.814 MiB, 88.90% compilation time)
9000-element Vector{Float64}:
0.6057362032299476
0.6057362032299476
0.6057362032299476
0.6057362032299476
0.6057362032299476
0.6057362032299476
0.6057362032299476
⋮
0.4516105573548591
0.4516105573548591
0.4516105573548591
0.5014099540247418
0.6720304713998495
0.6720304713998495
```
#### Matlab
```matlab
>> pd = makedist('Weibull','A',5,'B',2)
>> chain = metropolis(@(x) pdf(pd,x),5000,0.8,makedist('Normal','mu',0,'sigma',0.9),[0,Inf],1000,'shuffle');
```
#### R
```r
# Example
# posterior function
# prior Beta(a = 1, b = 1)
# likelihood Bernoulli: N = 20, z = 14
posterior <- function(theta, a, b, N, z) {
dbeta(theta, z + a, N - z + b)
}
a = 1
b = 1
N = 20
z = 14
posterior_func <- function(theta) posterior(theta, a, b, N, z)
dposterior1 <- metropolis(chain = 5000, theta_cur = 0.1, dfunc = posterior_func, space_min = 0, space_max = 1, burnin = 2500)
dposterior2 <- metropolis(chain = 5000, theta_cur = 0.9, dfunc = posterior_func, space_min = 0, space_max = 1, burnin = 2500)
dposterior3 <- metropolis(chain = 5000, theta_cur = 0.5, dfunc = posterior_func, space_min = 0, space_max = 1, burnin = 2500)
```