Monte Library

monte-library is a set of Monte Carlo methods in Python. The package is written to be flexible, clear to understand and encompass variety of Monte Carlo methods.

Installation

Preferred method to install monte-library is through Python’s package installer pip. To install monte-library, run this command in your terminal

pip install monte-library

Alternatively, you can install the package directly from GitHub:

git clone -b development https://github.com/draktr/monte-library.git
cd monte-library
python setup.py install

Features

Base module

  • saving samples and log probability values as .csv file

  • posterior mean, standard deviation and quantiles

  • diagnostic tools: effective sample size (ESS), autocorrelation plots, ergodic mean plots, acceptance rate

  • visualizations: histograms, kernel density estimation plots, traceplots

General Monte Carlo Methods

  • multidimensional Monte Carlo integration

  • multidimensional rejection sampling

  • multidimensional importance sampling

Markov Chain Monte Carlo Modelling Methods

  • symmetric proposal Metropolis algorithm

  • Metropolis-Hastings algorithm

  • Gibbs sampler

  • vanilla Hamiltonian Monte Carlo

Advantages

  • FLEXIBLE - the package allows users to use various existing Monte Carlo methods for their needs without needing to write the whole algorithm. At the same time, monte-library allows users to specify their own hyperparameters, posterior and proposal distributions as needed. Furthermore BaseSampler class can be used as parent class for any proprietary Monte Carlo algorithm thus utilizing its features for visualizations, posterior analysis and convergence checks.

  • SIMPLE AND CLEAR CODE BASE - code was intentionally kept simple to be understandable to those with limited exposure to Statistical Computing. monte-library is a great tool to supplement learning as it generally matches mathematical formulations of algorithms and simple syntax helps focus on the algorithm itself.

  • COMPREHENSIVE - includes Monte Calor methods for various applications. Bayesian modelling methods include both classical methods (Metropolis algorithm) as well as more advanced methods such as Hamiltonian Monte Carlo.

Usage

Package contains variety of Monte Carlo methods that can be applied to problems ranging from integration to modelling. Importantly, code is both simple and generalized as to match the respective mathematical formulations of algorithms. As such it can be a great supplement when learning these topics. Finally, the package is flexible and BaseSampler class can be used as a parent class to any user-defined sampler. Furthermore, it is easy to modify existing algorithms with proprietary improvements. Below is an example of Monte Carlo integration and more examples can be found by clicking on the Examples section of the documentation

Example 1: Monte Carlo Integration

The following example is a simple Monte Carlo implementation to solve the following integral:

\[\int_{-3}^{3} \int_{-3}^{3} x^2 + y^3 dxdy\]
from monte import integrator

def integrand(args):
        return args[0] ** 2 + args[1] ** 3

result = integrator(integrand, lower_bounds=[-3, -3], upper_bounds=[3, 3], n=10000000)
result

Contents:

Other

Alternatives and Complements

There are more sophisticated and computationally efficient implementations of Monte Carlo methods for off-the-shelf solutions

  • ArviZ - independent library for exploratory analysis of Bayesian models

  • vegas - uses improved version of the adaptive Monte Carlo vegas algorithm

  • OpenBUGS - open source implementation of BUGS language utilizing Gibbs sampler

  • JAGS - cross-platform and more extensible implementation of BUGS language

  • WinBUGS - software for Bayesian analysis utilizing Gibbs sampler (available, but discontinued in favour of OpenBUGS)

  • Stan - state-of-the-art probabilistic language implementing advanced version of No-U-Turn Sampler

  • PyMC - supports HMC and Metropolis-Hastings algorithms, as well as Sequential Monte Carlo methods

Project Principles

  • Easy to be understood and used by non-mathematicians

  • Potential to be used as pedagogical tool

  • Easy to modify algorithms with proprietary improvements

  • Flexibility and simplicity over computational efficiency

  • Tested

  • Dedicated documentation

  • Formatting deferred to Black

Indices and tables