Interdisciplinary Bayesian Statistics - EBEB 2014
Interdisciplinary Bayesian Statistics - EBEB 2014
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跨学科贝叶斯统计 - EBEB 2014
DOI：
10.1007/978-3-319-12454-4_7
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Silva R
中科院分区：
文献类型：
--
作者：
Silva R
构造Copula函数的一种方法是乘法。考虑到累积分布函数（CDF）的乘积也是CDF，对这种乘法的调整将导致Copula模型，如Liebscher（J Mult Analysis，2008）所讨论的那样。通过CDF的产品参数化模型具有一些优势，无论是从Copula的角度来看（例如，它对任何维度都有明确的定义）还是从一般的多变量分析（例如，它提供了可以从参数中轻松读取小维度边缘分布的模型）。独立地，Huang和Frey（J Mach Learn Res，2011）展示了某些稀疏图形模型和CDF产品之间的联系，以及用于计算此类模型的似然函数的消息传递（动态编程）方案。这种方案允许用基于似然性的方法来估计模型。我们讨论和演示MCMC方法估计这样的模型在贝叶斯上下文中，其应用Copula建模，以及如何消息传递可以大大简化。重要的是，我们的消息传递的观点开辟了扩大这种方法的可能性，因为即使是动态编程也不是一个可扩展的解决方案，用于计算许多模型中的似然函数。
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some advantages, both from the copula perspective (e.g. it is well-defined for any dimensionality) and from general multivariate analysis (e.g. it provides models where small dimensional marginal distributions can be easily read-off from the parameters). Independently, Huang and Frey (J Mach Learn Res, 2011) showed the connection between certain sparse graphical models and products of CDFs, as well as message-passing (dynamic programming) schemes for computing the likelihood function of such models. Such schemes allow models to be estimated with likelihood-based methods. We discuss and demonstrate MCMC approaches for estimating such models in a Bayesian context, their application in copula modeling, and how message-passing can be strongly simplified. Importantly, our view of message-passing opens up possibilities to scaling up such methods, given that even dynamic programming is not a scalable solution for calculating likelihood functions in many models.