Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to carry out Bayesian inference when the likelihood is intractable but can be estimated unbiasedly. Our article develops an efficient PMMH method for estimating the parameters of complex and high-dimensional state-space models and has the following features. First, it runs multiple particle filters in parallel and uses their averaged unbiased likelihood estimate. Second, it combines block and correlated PMMH sampling. The first two features enable our sampler to scale up better to longer time series and higher dimensional state vectors than previous approaches. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, it uses delayed acceptance to make the make the sampler more efficient. The performance of the sampler is investigated empirically by applying it to Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities. 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:PMMH是一种在可能性难以克服但可以无偏见地估计的情况下进行巴伊西亚矢量推断的一般方法。 我们的文章开发了一种高效的PMMH方法来估计复杂和高维状态- 空间模型的参数, 具有以下特点。 首先, 它平行运行多个粒子过滤器, 并使用其平均的不偏袒可能性估计值。 其次, 它结合了块状和相关的 PMMH 取样。 前两个特征使我们的取样员能够比以前的方法更好地扩大到更长的时间序列和更高的维度矢量。 第三, 文章开发了一个高效的辅助扰动粒子过滤器, 当靴套过滤器效率低时这是必要的, 但状态转换密度不能以封闭的形式表示。 第四, 它使用延迟的接受度来提高取样器的效率。 通过将取样员的性能应用具有相对高的状态和坚固性状态过渡密度的动态调控一般调理器模型, 对取样员的性能进行了实验性研究。 尽管我们的重点是对州空间模型应用该方法, 但该方法对于数据模型和大方程式应用的混合变式模型是有用的。