Grapham: Graphical Models with Adaptive Random Walk Metropolis Algorithms

TL;DR

Grapham is an open-source software package implementing adaptive MCMC algorithms tailored for graphical models, enabling flexible and efficient Bayesian inference with features like adaptive covariance, scale adjustment, and Metropolis-within-Gibbs updates.

Contribution

It introduces a comprehensive, flexible implementation of adaptive MCMC algorithms specifically designed for graphical models, with customizable variants and an easy-to-use configuration system.

Findings

Efficient sampling in complex Bayesian models.

Flexible adaptation of proposal distributions.

Open source with user-friendly configuration.

Abstract

Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance according to the history of the chain and a Metropolis algorithm adjusting the proposal scale based on the observed acceptance probability. Different variants of the algorithms allow one, for example, to use these two algorithms together, employ delayed rejection and adjust several parameters of the algorithms. The implemented Metropolis-within-Gibbs update allows arbitrary sampling blocks. The software is written in C and uses a simple extension language Lua in configuration.