Quasi-random numbers for copula models

Parametric dependence between random vectors via copula-based divergence measures

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific …

CopulaDTA: An R Package for Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework

The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression and the bivariate random-effects meta-analysis model (BRMA). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large. This tutorial on advanced statistical methods for meta-analys…

Copulas.jl：一个完全兼容 Distributions.jl 的 copula 包

Copulas.jl: A fully Distributions.jl-compliant copula package

Julia 包 Copulas.jl 实现了随机数生成、分布评估等功能，完全兼容 Distributions.jl API，支持与 Turing.jl 等包互操作。

Tail approximations for sums of dependent regularly varying random variables under Archimedean copula models

In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables exceeds a high threshold under Archimedean copula models. The first method is based on conditional Monte Carlo. We present four estimators and show that most of them have bounded relative errors. The second method is based on analytical expressions of the multivariate survival or cumulative distribution functions of the regularly varying random variables and provides sharp and deterministic bounds of the probability of exceedance. We discuss implementat…

On the distribution of the sum of dependent standard normally distributed random variables using copulas

The distribution function of the sum $Z$ of two standard normally distributed random variables $X$ and $Y$ is computed with the concept of copulas to model the dependency between $X$ and $Y$. By using implicit copulas such as the Gauss- or t-copula as well as Archimedean Copulas such as the Clayton-, Gumbel- or Frank-copula, a wide variety of different dependencies can be covered. For each of these copulas an analytical closed form expression for the corresponding joint probability density function $f_{X,Y}$ is derived. We apply a numerical approximation algorithm in Matlab to evaluate the res…

基于贝叶斯 Copula 的空间随机效应模型，用于复杂空间数据的推断

Bayesian copula-based spatial random effects models for inference with complex spatial data

本文提出了一种完全贝叶斯、基于 copula 的空间随机效应模型，通过低秩表示实现计算高效的推断，在参数估计和空间过程预测上优于 FRK 等基准方法，并成功应用于卫星大气甲烷分布制图。