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Bayesian model comparison with un-normalised likelihoods

机译：具有未归一化可能性的贝叶斯模型比较

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摘要

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes' factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.
机译：只能对直到参数相关的未知归一化常数最多可以评估似然函数的模型（例如Markov随机场模型）广泛用于计算机科学，统计物理学，空间统计和网络分析中。但是，由于其似然函数的难处理性，因此无法使用标准蒙特卡洛方法对这些模型进行贝叶斯分析。最近已经开发了几种允许从后验分布进行精确或接近精确模拟的方法。但是，总体上估计这些模型的证据和贝叶斯因素仍然具有挑战性。本文介绍了新的随机权重重要性采样和顺序蒙特卡洛方法来估计高炉，这些方法使用模拟来规避难处理可能性的评估，并将它们与现有方法进行比较。在某些情况下，我们发现使用有偏权重估计值有优势。提出了对此类方法的理论和经验性质的初步研究。提出了一些使用偏差估计的支持，但是我们提倡使用此类估计时要谨慎。

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