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Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins

机译：具有离散和混合边缘的高维Archimedean Copulas的计算上高效贝叶斯估计

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Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating terms, with J the number of discrete variables. Our article focuses on the estimation of Archimedean copulas, for example, Clayton and Gumbel copulas. Currently, data augmentation methods are used to carry out inference for discrete copulas and, in practice, the computation becomes infeasible when J is large. Our article proposes two new fast Bayesian approaches for estimating high-dimensional Archimedean copulas with discrete margins, or a combination of discrete and continuous margins. Both methods are based on recent advances in Bayesian methodology that work with an unbiased estimate of the likelihood rather than the likelihood itself, and our key observation is that we can estimate the likelihood of a discrete Archimedean copula unbiasedly with much less computation than evaluating the likelihood exactly or with current simulation methods that are based on augmenting the model with latent variables. The first approach builds on the pseudo-marginal method that allows Markov chain Monte Carlo simulation from the posterior distribution using only an unbiased estimate of the likelihood. The second approach is based on a variational Bayes approximation to the posterior and also uses an unbiased estimate of the likelihood. We show that the two new approaches enable us to carry out Bayesian inference for high values of J for the Archimedean copulas where the computation was previously too expensive. The methodology is illustrated through several real and simulated data examples.
机译：使用离散边际分布的估计金属屑是具有挑战性的，特别是在高维度下，因为计算每个观察的似然贡献需要评估术语，并使用J的离散变量的数量。我们的文章侧重于Achimedean Copulas的估计，例如Clayton和Gumbel Copulas。目前，数据增强方法用于对离散的Copulas进行推断，并且在实践中，当J很大时，计算变得不可行。我们的文章提出了两种新的快速贝叶斯术方法，用于使用离散边缘或离散和连续边缘的组合来估算高维阿基甸共用。这两种方法都是基于贝叶斯方法的最新进展，其与似乎不偏不倚的估计而不是可能本身的估计，我们的主要观察是我们可以估计离散的Archimedean Copula的可能性，而不是评估可能性的计算完全或具有基于使用潜在变量的模型来增强模型的电流模拟方法。第一种方法在伪边缘方法上建立了允许Markov链蒙特卡罗从后部分布模拟，仅使用不偏不倚的估计的可能性。第二种方法基于对后后的变形贝叶斯近似，并且还使用对似然的无偏见的估计。我们展示这两种新方法使我们能够对Achimedean Copulas进行贝叶斯推断，为Achimedean Copulas进行了计算，其中计算预先昂贵。通过几个实际和模拟数据示例说明了方法。

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