arXiv subjects

David Sher

Publications and source records attributed to David Sher.

22 records · Page 2Linked to original sources

arXiv2017

Analytic torsion and R-torsion of Witt representations on manifolds with cusps

We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact hyperbolic spaces of finite volume, but we do not assume that the metric has constant curvature nor that the link of the cusp is a torus. We use renormalized traces in the sense of Melrose to define the analytic torsion and we relate it to the intersection R-torsion of Dar of the natural compactification to a stratified space. Our proof relies on our recent work on the behavior of the Hodge Laplacian spectrum on a closed manifold undergoing degeneration to a manifold with fibered cusps.

math.DG↗

arXiv2013

Towards a Normative Theory of Scientific Evidence

A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a system that derives probability intervals from objective evidence in those forms. Our reasoning system can manage uncertainty about data and rules in a rule based expert system. We expect that our system will be particularly applicable to diagnosis and analysis in domains with a wealth of experimental evidence such as medicine. We discuss limitations of this solution and propose future directions for this research. This work can be considered a generalization of Nilsson's "probabilistic logic" [Nil86] to intervals and experimental observations.

cs.AI↗

arXiv2013

Appropriate and Inappropriate Estimation Techniques

Mode {also called MAP} estimation, mean estimation and median estimation are examined here to determine when they can be safely used to derive {posterior) cost minimizing estimates. (These are all Bayes procedures, using the mode. mean. or median of the posterior distribution). It is found that modal estimation only returns cost minimizing estimates when the cost function is 0-t. If the cost function is a function of distance then mean estimation only returns cost minimizing estimates when the cost function is squared distance from the true value and median estimation only returns cost minimizing estimates when the cost function ts the distance from the true value. Results are presented on the goodness or modal estimation with non 0-t cost functions

cs.AI↗

arXiv2013

Developing and Analyzing Boundary Detection Operators Using Probabilistic Models

Most feature detectors such as edge detectors or circle finders are statistical, in the sense that they decide at each point in an image about the presence of a feature, this paper describes the use of Bayesian feature detectors.

cs.CV↗