Robust generalised Bayesian inference for intractable likelihoods
Robust generalised Bayesian inference for intractable likelihoods
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DOI：
10.1111/rssb.12500
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发表时间：
2021-04
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影响因子：
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通讯作者：
Takuo Matsubara;Jeremias Knoblauch;François‐Xavier Briol;C. Oates
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文献类型：
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作者：
Takuo Matsubara;Jeremias Knoblauch;François‐Xavier Briol;C. Oates
广义贝叶斯推理使用损失函数而不是似然来更新先验信念，因此可以用于赋予可能的似然错误指定的鲁棒性。在这里，我们认为广义贝叶斯推断与斯坦差异作为一个损失函数，在其中的可能性包含一个棘手的归一化常数的应用程序的动机。在这种情况下，斯坦差异规避评价的归一化常数，并产生广义后验，要么是封闭的形式或使用标准的马尔可夫链蒙特卡洛访问。在理论层面上，我们展示了广义后验的一致性、渐近正态性和偏倚稳健性，突出了这些属性如何受到Stein差异选择的影响。然后，我们提供了一系列难以处理的分布的数值实验，包括基于核的指数族模型和非高斯图形模型的应用。
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis‐specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using the standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias‐robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel‐based exponential family models and non‐Gaussian graphical models.