The pie sharing problem: Unbiased sampling of N+1 summative weights. (February 2022)

• Record Type: Journal Article
• Authors: Mai, Juliane; Craig, James R.; Tolson, Bryan A.
• Is Part Of: Environmental modelling & software. Volume 148(2022)
• Publication Date: 2022-02
• Subjects: Weight sampling -- Identical distributions -- Random number generation -- Constrained random numbers; Environmental monitoring -- Computer programs -- Periodicals; Ecology -- Computer simulation -- Periodicals; Digital computer simulation -- Periodicals; Computer software -- Periodicals; Environmental Monitoring -- Periodicals; Computer Simulation -- Periodicals; Environnement -- Surveillance -- Logiciels -- Périodiques; Écologie -- Simulation, Méthodes de -- Périodiques; Simulation par ordinateur -- Périodiques; Logiciels -- Périodiques; Computer software; Digital computer simulation; Ecology -- Computer simulation; Environmental monitoring -- Computer programs; Periodicals; Electronic journals; 363.70015118
• DOI: 10.1016/j.envsoft.2021.105282
• Languages: English
• ISSNs: 1364-8152

Abstract

Abstract: A simple algorithm is provided for randomly sampling a set of N +1 weights such that their sum is constrained to be equal to one, analogous to randomly subdividing a pie into N +1 slices where the probability distribution of slice volumes are identically distributed. The cumulative density and probability density functions of the random weights are provided. The algorithmic implementation for the random number sampling are made available. This algorithm has potential applications in calibration, uncertainty analysis, and sensitivity analysis of environmental models. Three example applications are provided to demonstrate the efficiency and superiority of the proposed method compared to alternative sampling methods. Highlights: Present unbiased method to sample weights that sum up to 1. Examples demonstrating the benefit of unbiased sampling. Code made available in multiple languages.