Numerical Generalized Randomized HMC processes for restricted domains

35 Pages Posted: 1 Dec 2023

See all articles by Tore Selland Kleppe

Tore Selland Kleppe

University of Stavanger

Roman Liesenfeld

University of Cologne, Department of Economics

Date Written: November 24, 2023

Abstract

We propose a generic approach for numerically efficient simulation from analytically intractable distributions with constrained support. Our approach relies upon Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes and combines these with a randomized transition kernel that appropriately adjusts the Hamiltonian flow at the boundary of the constrained domain, ensuring that it remains within the domain. The numerical implementation of this constrained GRHMC process exploits the sparsity of the randomized transition kernel and the specific structure of the constraints so that the proposed approach is numerically accurate, computationally fast and operational even in high-dimensional applications. We illustrate this approach with posterior distributions of several Bayesian models with challenging parameter domain constraints in applications to real-word data sets. Building on the capability of GRHMC processes to efficiently explore otherwise challenging and high-dimensional posteriors, the proposed method expands the set of Bayesian models that can be analyzed by using the standard Markov-Chain Monte-Carlo (MCMC) methodology. As such, it can advance the development and use of Bayesian models with useful constrained priors, which are difficult to handle with existing methods. The article is accompanied by an R-package (https://github.com/torekleppe/pdmphmc), which allows for automatically implementing GRHMC processes for arbitrary target distributions and domain constraints.

Suggested Citation

Kleppe, Tore Selland and Liesenfeld, Roman, Numerical Generalized Randomized HMC processes for restricted domains (November 24, 2023). Available at SSRN: https://ssrn.com/abstract=4643548 or http://dx.doi.org/10.2139/ssrn.4643548

Tore Selland Kleppe (Contact Author)

University of Stavanger ( email )

PB 8002
Stavanger, 4036
Norway

Roman Liesenfeld

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
D-50931 Köln
Germany

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