Parameter elimination in particle Gibbs sampling
Authors: Anna Wigren, Riccardo Sven Risuleo, Lawrence Murray, Fredrik Lindsten
Summary: Bayesian inference in state-space fashions is difficult because of high-dimensional state trajectories. A viable method is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to type “actual approximations” to in any other case intractable MCMC strategies. The efficiency of the approximation is restricted to that of the precise methodology. We concentrate on particle Gibbs and particle Gibbs with ancestor sampling, bettering their efficiency past that of the underlying Gibbs sampler (which they approximate) by marginalizing out a number of parameters. That is doable when the parameter prior is conjugate to the whole information chance. Marginalization yields a non-Markovian mannequin for inference, however we present that, in distinction to the overall case, this methodology nonetheless scales linearly in time. Whereas marginalization will be cumbersome to implement, current advances in probabilistic programming have enabled its automation. We display how the marginalized strategies are viable as environment friendly inference backends in probabilistic programming, and display with examples in ecology and epidemiology
