Sampling from Conditional Distributions of Simplified Vines

TL;DR

This paper introduces a Hamiltonian Monte Carlo method for sampling from conditional distributions of simplified vine copulas, enabling better modeling of high-dimensional dependence structures in statistical data.

Contribution

It presents a novel MCMC approach using Hamiltonian Monte Carlo to efficiently sample from complex conditional distributions of simplified vine copulas.

Findings

Accurate sampling demonstrated through simulation studies.

Applied to maize trait data for prediction and dependence estimation.

Method improves understanding of high-dimensional dependence structures.

Abstract

Simplified vine copulas are flexible tools over standard multivariate distributions for modeling and understanding different dependence properties in high-dimensional data. Their conditional distributions are of utmost importance, from statistical learning to graphical models. However, the conditional densities of vine copulas and, thus, vine distributions cannot be obtained in closed form without integration for all possible sets of conditioning variables. We propose a Markov Chain Monte Carlo based approach of using Hamiltonian Monte Carlo to sample from any conditional distribution of arbitrarily specified simplified vine copulas and thus vine distributions. We show its accuracy through simulation studies and analyze data of multiple maize traits such as flowering times, plant height, and vigor. Use cases from predicting traits to estimating conditional Kendall's tau are presented.