Probabilistic Forecasting and Comparative Model Assessment Based on Markov Chain Monte Carlo Output
Probabilistic Forecasting and Comparative Model Assessment Based on Markov Chain Monte Carlo Output
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基于马尔可夫链蒙特卡罗输出的概率预测和比较模型评估
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
T. Gneiting
中科院分区：
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作者：
Fabian Kruger;Sebastian Lerch;T. Thorarinsdottir;T. Gneiting
在贝叶斯推断中，预测分布通常仅通过经由马尔可夫链蒙特卡罗（MCMC）或相关算法生成的样本可用。在本文中，我们进行了系统的分析，如何作出和评估概率预测，从这样的模拟输出。基于适当的评分规则，我们开发了一种一致性概念，可以评估估计模拟输出背后的平稳分布的方法的充分性。然后，我们回顾渐近的结果，占贝叶斯后验模拟器的显着特点，并推导出条件下，从文献中的选择满足我们的概念的一致性。重要的是，这些条件取决于所使用的评分规则，因此近似方法和评分规则的选择是交织在一起的。虽然对数规则需要相当严格的条件，连续排名的概率得分在最小的假设下产生一致的近似。这些结果在模拟研究和经济数据的例子中说明。总的来说，我们发现，混合参数近似，利用贝叶斯模型的参数结构表现得特别好。
In Bayesian inference, predictive distributions are typically available only through a sample generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate probabilistic forecasts from such simulation output. Based on proper scoring rules, we develop a notion of consistency that allows to assess the adequacy of methods for estimating the stationary distribution underlying the simulation output. We then review asymptotic results that account for the salient features of Bayesian posterior simulators, and derive conditions under which choices from the literature satisfy our notion of consistency. Importantly, these conditions depend on the scoring rule being used, such that the choices of approximation method and scoring rule are intertwined. While the logarithmic rule requires fairly stringent conditions, the continuous ranked probability score yields consistent approximations under minimal assumptions. These results are illustrated in a simulation study and an economic data example. Overall, we find that mixture-of-parameters approximations which exploit the parametric structure of Bayesian models perform particularly well.