Quasi-Monte Carlo methods for Choquet integrals
arXiv:1411.07732 citationsh-index: 8
Originality Incremental advance
AI Analysis
Provides a novel numerical integration method for Choquet integrals, relevant to decision theory and risk analysis.
Proposed quasi-Monte Carlo methods for Choquet integrals with capacities defined by distortion functions, providing error bounds based on the modulus of continuity and star discrepancy.
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can be seen as quasi-Monte Carlo methods in this framework. We give bounds on the approximation errors in terms of the modulus of continuity of the integrand and the star discrepancy.