arXiv subjects

Arthur P. Dempster

Publications and source records attributed to Arthur P. Dempster.

3 recordsLinked to original sources

arXiv2021

A Gibbs sampler for a class of random convex polytopes

We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities "for", "against", and "don't know" about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate the DS inference. The sampler relies on an equivalence between the iterative constraints of the vertex configuration and the non-negativity of cycles in a fully connected directed graph. Illustrations include the testing of independence in 2x2 contingency tables and parameter estimation of the linkage model.

stat.CO↗

arXiv2012

Nonparametric survival analysis and vaccine efficacy using Dempster-Shafer analysis

We introduce an extension of nonparametric DS inference for arbitrary univariate CDFs to the case in which some failure times are (right)-censored, and then apply this to the problem of assessing evidence regarding assertions about relative risks across two populations. The approach enables exploration of the sensitivity of survival analyses to assumed independence of the missing data process and the failure proces. We present an application to the partially efficacious RV144 (HIV-1) vaccine trial, and show that the strength of conclusions of vaccine efficacy depend on assumptions about the maximum failure rates of the subjects lost-to-followup.

stat.ME↗

arXiv2009

Estimating limits from Poisson counting data using Dempster--Shafer analysis

We present a Dempster--Shafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. Dempster--Shafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the event space. This eliminates the Bayesian dependence on prior distributions while allowing the incorporation of prior information when it is available. We use the Poisson Dempster--Shafer model (DSM) to derive a posterior DSM for the ``Banff upper limits challenge'' three-Poisson model. The results compare favorably with other approaches, demonstrating the utility of the approach. We argue that the reduced dependence on priors afforded by the Dempster--Shafer framework is both practically and theoretically desirable.

stat.AP↗