paper.md

In andyyao95/walkr: Random Walks in the Intersection of Hyperplanes and the N-Simplex

title: 'walkr: MCMC Sampling from Non-Negative Convex Polytopes' tags: - Monte Carlo Markov Chain - sampling - random walks - convex polytope authors: - name: Andy Yu Zhu Yao orcid: 0000-0003-3898-8782 affiliation: 1 - name: David Kane affiliation: 2 affiliations: - name: Williams College index: 1 - name: IQSS, Harvard University index: 2 date: 10 September 2016 bibliography: paper.bib

Summary

Consider the intersection of two spaces: the complete solution space to Ax = b and the N-simplex. The intersection of these two spaces is a non-negative convex polytope. The R package walkr samples from this intersection using two Monte-Carlo Markov Chain (MCMC) methods: hit-and-run [@kannan] and Dikin walk [@vempala]. Walkr also provide tools to examine sample quality [@shinystan].

MCMC sampling is of great interest in applied statistics, as it is a common approach to sample data drawn from a theoretical distribution [@gelman]. In application, walkr will be a powerful tool for estimating expectations for Bayesian statistics. The walkr package will also be found useful by users who are interested in generating random weight vectors in high dimensions given specific constraints.

The real world application to MCMC sampling is vast. In the context of finance, we've had users use walkr to generate random portfolios satisfying specific constraints. We've also had users use walkr to sample from solution spaces obtained empirically from mass spectrometry analysis of proteins, which can provide insight into the biological systems of interest. Finally, walkr is one of the first open-sourced softwares to implement the Dikin walk.

References

andyyao95/walkr documentation built on June 4, 2019, 7:18 a.m.