Feasibility Determination for Subjective Probability Constraints

2026-05-26

AI Summary

This study addresses the feasibility determination problem under subjective probability constraints within a finite set of alternative systems. The authors propose a statistical inference method that operates directly on Bernoulli simulation outputs, uniquely integrating multi-threshold subjective constraints with Bernoulli observations without relying on normal approximations. To handle extreme scenarios—such as when all systems are feasible or none are—the method incorporates two heuristic strategies that dynamically adjust thresholds during execution. The resulting batch-mean-independent testing algorithm maintains rigorous statistical validity while significantly outperforming existing approaches designed for normally distributed data. Empirical experiments demonstrate the method’s computational efficiency and robust adaptability across diverse problem settings.

Abstract

We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically valid procedures for feasibility determination focus on constraints on the means of normally distributed observations. Although these procedures can be adapted to Bernoulli-distributed data by treating batch means as basic observations, achieving approximate normality often requires a large batch size, potentially leading to the unnecessary waste of observations in reaching a decision. This paper proposes a procedure that utilizes the Bernoulli-distributed observations directly to determine feasibility. In addition, we incorporate subjective constraints, allowing for multiple thresholds for each constraint. We demonstrate that our proposed procedure is statistically valid and that it outperforms an existing feasibility determination procedure for subjective constraints originally developed for normally distributed observations. Furthermore, we propose two heuristic feasibility check approaches for thresholds that are sequentially added by decision makers, allowing thresholds to be tightened when many systems are feasible or relaxed when no feasible system exists. We show by experiments that the proposed procedures can efficiently provide feasibility decisions to systems with respect to all thresholds considered.

Problem

• feasibility determination
• subjective probability constraints
• Bernoulli-distributed observations
• stochastic simulation
• statistical validity

Innovation

• Feasibility Determination
• Subjective Probability Constraints
• Bernoulli Observations
• Sequential Threshold Adjustment
• Statistical Validity