Exploring Uncertainty, Sensitivity and Robust Solutions in Mathematical Programming Through Bayesian Analysis

Mike G. Tsionas (), Dionisis Philippas and Constantin Zopounidis ()
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Mike G. Tsionas: Lancaster University Management School
Constantin Zopounidis: Technical University of Crete

Computational Economics, 2023, vol. 62, issue 1, No 9, 205-227

Abstract: Abstract The paper examines the effect of uncertainty on the solution of mathematical programming problems, using Bayesian techniques. We show that the statistical inference of the unknown parameter lies in the solution vector itself. Uncertainty in the data is modeled using sampling models induced by constraints. In this context, the objective is used as prior, and the posterior is efficiently applied via Monte Carlo methods. The proposed techniques provide a new benchmark for robust solutions that are designed without solving mathematical programming problems. We illustrate the benefits of a problem with known solutions and their properties, while discussing the empirical aspects in a real-world portfolio selection problem.

Keywords: Mathematical programming; Robustness analysis; Bayesian analysis; Monte Carlo; C11; C61; G11 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10614-022-10277-z

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