Generalized Bayesian Inference for Discrete Intractable Likelihood
针对离散状态空间中似然函数难以计算的问题，提出用离散Fisher散度替代似然来更新参数信念，得到可用标准MCMC采样的广义后验，并分析了其统计性质，适用于格点模型和计数数据模型。
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalization constants requires summation over large or possibly infinite sets, which can be impractical. This article addresses this computational challenge through the development of a novel generalized Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalized posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalizing constant. The statistical properties of the generalized posterior are analyzed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalized posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalized Bayesian inference at low computational cost. Supplementary materials for this article are available online.