Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher dimensional state vectors than previous approaches. The improvement is achieved by the following innovations. First, the trimmed mean of the unbiased likelihood estimates of the multiple particle filters is used. Second, a novel block version of PMMH that works with multiple particle filters is proposed. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap disturbance filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, a novel sorting algorithm, which is as effective as previous approaches but significantly faster than them, is developed to preserve the correlation between the logs of the likelihood estimates at the current and proposed parameter values. The performance of the sampler is investigated empirically by applying it to non-linear Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities and to multivariate stochastic volatility in the mean models. Although our focus is on applying the method to state space models, the approach will be useful in a wide range of applications such as large panel data models and stochastic differential equation models with mixed effects.

翻译：粒子边际Metropolis-Hastings（PMMH）是一种在似然函数难以求解但仍可无偏估计时进行贝叶斯推断的通用方法。本文开发了一种高效的PMMH方法，相较于现有方法，该方法能更好地扩展到更高维的状态向量。这一改进通过以下创新实现：首先，采用多个粒子滤波器无偏似然估计的截尾均值；其次，提出了一种与多个粒子滤波器协同工作的新型块版本PMMH；第三，本文开发了一种高效辅助扰动粒子滤波器，该滤波器在自举扰动滤波器效率低下且状态转移密度无法以封闭形式表达时尤为必要；第四，提出了一种新型排序算法，该算法在保持当前参数值与提议参数值下似然估计对数之间相关性的同时，其效率与现有方法相当但速度显著更快。通过将采样器应用于状态维度较高且状态转移密度难以处理的非线性动态随机一般均衡模型，以及均值多元随机波动模型，本文实证研究了其性能。尽管本文聚焦于将该方法应用于状态空间模型，但该方法在大型面板数据模型和含混合效应的随机微分方程模型等广泛领域中亦具有实用价值。