Bayesian Model Comparison with the Hyvarinen Score: Computation and Consistency
Bayesian Model Comparison with the Hyvarinen Score: Computation and Consistency
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DOI：
10.1080/01621459.2018.1518237
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发表时间：
2019-03-21
影响因子：
3.7
通讯作者：
Tarokh, Vahid
中科院分区：
文献类型：
--
作者：
Shao, Stephane;Jacob, Pierre E.;Tarokh, Vahid
贝叶斯因子是模型比较中广泛使用的标准，其对数是对数评分规则下样本外预测分数的差异。然而，当某些候选模型的参数涉及模糊先验时，对数贝叶斯因子会具有任意加性常数，从而阻碍其解释。作为替代方案，我们考虑使用 Hyvarinen 评分进行模型比较。我们提出了一种使用顺序蒙特卡罗方法来一致估计参数模型分数的方法。我们表明，对于具有易处理似然性的模型以及具有难处理似然性的非线性非高斯状态空间模型，可以估计该分数。我们在非嵌套模型的情况下证明了这种新模型选择标准在强规律性假设下的渐近一致性，并为嵌套情况提供了定性见解。我们还使用离散空间上适当评分规则的现有特征，将 Hyvarinen 评分扩展到离散观测。我们的数值说明包括利维驱动的随机波动模型和人口动态的扩散模型。本文可在线获取。
The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on their parameters, the log-Bayes factor features an arbitrary additive constant that hinders its interpretation. As an alternative, we consider model comparison using the Hyvarinen score. We propose a method to consistently estimate this score for parametric models, using sequential Monte Carlo methods. We show that this score can be estimated for models with tractable likelihoods as well as nonlinear non-Gaussian state-space models with intractable likelihoods. We prove the asymptotic consistency of this new model selection criterion under strong regularity assumptions in the case of nonnested models, and we provide qualitative insights for the nested case. We also use existing characterizations of proper scoring rules on discrete spaces to extend the Hyvarinen score to discrete observations. Our numerical illustrations include Levy-driven stochastic volatility models and diffusion models for population dynamics. for this article are available online.