Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the parameters that are highly correlated with the states \lq integrated out\rq{} in a pseudo marginal step; the rest of the parameters are generated conditional on the states. The novel contribution of our article is to make the pseudo-marginal step much more efficient by positively correlating the numerator and denominator in the Metropolis-Hastings acceptance probability. This is done in a novel way by expressing the target density of the PMCMC in terms of the basic uniform or normal random numbers used in the sequential Monte Carlo algorithm instead of the standard way in terms of state particles. We also show that the new sampler combines and generalizes two separate particle MCMC approaches: particle Gibbs and the correlated pseudo marginal Metropolis-Hastings. We investigate the performance of the hybrid sampler empirically by applying it to univariate and multivariate stochastic volatility models having both a large number of parameters and a large number of latent states and show that it is much more efficient than competing PMCMC methods.

翻译：粒子马尔可夫链蒙特卡洛（PMCMC）是一种用于一般状态空间模型贝叶斯推断的通用计算方法。本文通过以下方式在观测值和参数数量上扩展了PMCMC：在伪边缘步骤中生成与“积分消去”的状态高度相关的参数；其余参数则在状态条件下生成。本文的新贡献在于，通过使Metropolis-Hastings接受概率中的分子和分母正相关，大幅提升了伪边缘步骤的效率。这一创新实现方式是将PMCMC的目标密度表示为序贯蒙特卡洛算法中使用的均匀或正态随机数函数，而非传统的状态粒子表达形式。我们还展示了该新采样器能够结合并推广两种独立的粒子MCMC方法：粒子吉布斯和相关性伪边缘Metropolis-Hastings算法。通过将混合采样器应用于具有大量参数和潜在状态的单变量与多变量随机波动模型，我们实证研究了其性能，结果表明该采样器比现有竞争性PMCMC方法高效得多。