Generalized Fiducial Inference on Differentiable Manifolds

author: Alexander Murph

For questions, issues or clarifications please reach out to Murph: acmurph@unc.edu.

Overview

Code implementations of the models discussed in Generalized Fiducial Inference on Differentiable Manifolds by A. C. Murph, J. Hannig, and J. Williams. Manuscript on arXiv.

This repository is organized according to the three different experiments that use three different MCMC algorithms. The first algorithm considered (HMC) is Brubaker et al's Constrained Hamiltonian Monte Carlo method and the second algorithm considered (MH) is Zappa et al's Constrained Metropolis-Hastings algorithm. The three problems considered are: inference for data from a multivariate normal density with the mean parameters on a sphere, a linear logspline density estimation problem, and a reimagined approach to the AR(1) mode

Reference

[1] Murph, A. C., Hannig, J., Williams, J. P. Generalized Fiducial Inference on Differentiable Manifolds

Citations

[2] Brubaker, M. A., Salzmann, M. and Urtasun, R. (2012) A Family of MCMC Methods on Implicitly Defined Manifolds. In Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, vol. 22, 161–172.
[3] Zappa, E., Holmes-Cerfon, M. and Goodman, J. (2018) Monte Carlo on Manifolds: Sampling Densities and Integrating Functions. Communications on Pure and Applied Mathematics, 71, 2609–2647.

R Packages Required

ggplot2, reshape