Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation of the posterior through specialised and typically expensive MCMC methods. In this paper, we provide a computationally efficient alternative in the form of a novel generalised Bayesian posterior that allows for conjugate inference within the class of exponential family models for discrete data. We derive theoretical guarantees to characterise the asymptotic behaviour of the generalised posterior, supporting its use for inference. The method is evaluated on a range of challenging intractable exponential family models, including the Conway-Maxwell-Poisson graphical model of multivariate count data, autoregressive discrete time series models, and Markov random fields such as the Ising and Potts models. The computational gains are significant; in our experiments, the method is between 10 and 6000 times faster than state-of-the-art Bayesian computational methods.

翻译：双重难解问题出现在似然函数和后验分布均仅以未归一化形式存在且归一化常数计算上难以处理的情况中。此时贝叶斯推断通常需要通过专门且计算代价高昂的MCMC方法直接近似后验分布。本文提出一种计算高效的替代方案——针对离散数据指数族模型的新型广义贝叶斯后验分布，支持在该模型类内进行共轭推断。我们推导了理论保证以刻画广义后验的渐近行为，为其推断应用提供支撑。该方法在多个具有挑战性的难解指数族模型上得到验证，包括多元计数数据的Conway-Maxwell-Poisson图模型、自回归离散时间序列模型，以及Ising模型与Potts模型等马尔可夫随机场。计算效率提升显著：实验表明，该方法比当前最先进的贝叶斯计算方法快10至6000倍。