A copula-based rank histogram ensemble filter

TL;DR

This paper introduces the copula rank histogram filter (CoRHF), a novel serial ensemble filter that captures conditional dependencies between variables using empirical copulas, improving high-dimensional Bayesian inference.

Contribution

The paper proposes a new serial ensemble filter, CoRHF, that effectively captures conditional dependencies via empirical copulas, enhancing multidimensional posterior sampling.

Findings

Successfully applied to Lorenz '63 and Lorenz '96 models.

Demonstrates improved dependency modeling over traditional methods.

Localization extends applicability to high-dimensional problems.

Abstract

Serial ensemble filters implement triangular probability transport maps to reduce high-dimensional inference problems to sequences of state-by-state univariate inference problems. The univariate inference problems are solved by sampling posterior probability densities obtained by combining constructed prior densities with observational likelihoods according to Bayes' rule. Many serial filters in the literature focus on representing the marginal posterior densities of each state. However, rigorously capturing the conditional dependencies between the different univariate inferences is crucial to correctly sampling multidimensional posteriors. This work proposes a new serial ensemble filter, called the copula rank histogram filter (CoRHF), that seeks to capture the conditional dependency structure between variables via empirical copula estimates; these estimates are used to rigorously implement the triangular (state-by-state univariate) Bayesian inference. The success of the CoRHF is demonstrated on two-dimensional examples and the Lorenz '63 problem. A practical extension to the high-dimensional setting is developed by localizing the empirical copula estimation, and is demonstrated on the Lorenz '96 problem.