Posterior-based proposals for speeding up Markov chain Monte Carlo
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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.
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