Estimating the Probability that a Function Observed with Noise Is Convex

Nanjing Jian () and Shane G. Henderson ()
Additional contact information
Nanjing Jian: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14850
Shane G. Henderson: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14850

INFORMS Journal on Computing, 2020, vol. 32, issue 2, 376-389

Abstract: Consider a real-valued function that can be only observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function values at the design points. We develop an asymptotically consistent Bayesian sequential sampling procedure that estimates the posterior probability of this being true. In each iteration, the posterior probability is estimated using Monte Carlo simulation. We offer three variance reduction methods: change of measure, acceptance-rejection, and conditional Monte Carlo. Numerical experiments suggest that the conditional Monte Carlo method is preferred.

Keywords: convexity detection; Bayesian sequential models; variance reduction; likelihood ratio o conditional Monte Carlo (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1287/ijoc.2018.0847 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:32:y:2020:i:2:p:376-389

Access Statistics for this article

More articles in INFORMS Journal on Computing from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().