Posterior-based proposals for speeding up Markov chain Monte Carlo

03/25/2019
by   C. M. Pooley, et al.
0

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development of application specific implementations. This limits rigorous use of real-world data to inform development and testing of models in applications ranging from statistical genetics to finance. This paper introduces "posterior-based proposals" (PBPs), a new type of MCMC update applicable to a huge class of statistical models (whose conditional dependence structures are represented by directed acyclic graphs). PBPs generates large joint updates in parameter and latent variable space, whilst retaining good acceptance rates (typically 33 percent). Evaluation against standard approaches (Gibbs or Metropolis-Hastings updates) shows performance improvements by a factor of 2 to over 100 for widely varying model types: an individual-based model for disease diagnostic test data, a financial stochastic volatility model and mixed and generalised linear mixed models used in statistical genetics. PBPs are competitive with similarly targeted state-of-the-art approaches such as Hamiltonian MCMC and particle MCMC, and importantly work under scenarios where these approaches do not. PBPs therefore represent an additional general purpose technique that can be usefully applied in a wide variety of contexts.

READ FULL TEXT
research
03/22/2014

Firefly Monte Carlo: Exact MCMC with Subsets of Data

Markov chain Monte Carlo (MCMC) is a popular and successful general-purp...
research
03/24/2017

Rejection-free Ensemble MCMC with applications to Factorial Hidden Markov Models

Bayesian inference for complex models is challenging due to the need to ...
research
01/03/2018

A New Wald Test for Hypothesis Testing Based on MCMC outputs

In this paper, a new and convenient χ^2 wald test based on MCMC outputs ...
research
03/01/2023

Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systems

We introduce two new classes of exact Markov chain Monte Carlo (MCMC) sa...
research
06/18/2021

LNIRT: An R Package for Joint Modeling of Response Accuracy and Times

In computer-based testing it has become standard to collect response acc...
research
10/11/2018

The Statistical Physics of Real-World Networks

Statistical physics is the natural framework to model complex networks. ...
research
08/30/2018

An Introduction to Inductive Statistical Inference -- from Parameter Estimation to Decision-Making

These lecture notes aim at a post-Bachelor audience with a backgound at ...

Please sign up or login with your details

Forgot password? Click here to reset