Doubly intractable models are encountered in a number of fields, e.g. social networks, ecology and epidemiology. Inference for such models requires the evaluation of a likelihood function, whose normalising function depends on the model parameters and is typically computationally intractable. The normalising constant of the posterior distribution and the additional normalising function of the likelihood function result in a so-called doubly intractable posterior, for which it is difficult to directly apply Markov chain Monte Carlo (MCMC) methods. We propose a signed pseudo-marginal Metropolis-Hastings (PMMH) algorithm with an unbiased block-Poisson estimator to sample from the posterior distribution of doubly intractable models. As the estimator can be negative, the algorithm targets the absolute value of the estimated posterior and uses an importance sampling correction to ensure simulation consistent estimates of the posterior mean of any function. The advantages of our estimator over previous approaches are that its form is ideal for correlated pseudo-marginal methods which are well known to dramatically increase sampling efficiency. Moreover, we develop analytically derived heuristic guidelines for optimally tuning the hyperparameters of the estimator. We demonstrate the algorithm on the Ising model and a Kent distribution model for spherical data.

翻译：在许多领域,例如社交网络、生态学和流行病学领域,都遇到了难以解决的模式。这些模型的推论要求对概率函数进行评估,其正常化功能取决于模型参数,通常在计算上难以解决。后端分布的正常化常数和可能性函数的额外正常化功能导致所谓的加倍难处理的后端功能,因此很难直接应用Markov链 Monte Carlo(MCMC)方法。我们建议采用经签署的假边际大都会-哈斯廷(PMMH)算法,配有公正的块状波斯逊估测仪,用于从加倍棘手模型的后部分布中取样。此外,由于测算法可以是负的,因此算法针对估计后部分布的绝对值,并使用重要的取样校正,以确保对任何功能的后端平均值进行模拟一致的估计。我们的估测器比以往方法的优点是,其形式对于相关的伪边际测算法是理想的,人们熟知会大幅提高取样效率。此外,我们开发了高端模型的分析性测算模型和高空分配模型。我们为最佳地展示了高端数据模型。