Non-deterministic inference using random set models: theory, approximation, and sampling method

• DOI: 10.48550/arxiv.1811.10446
• Publication Date: 2018-01-01
• Authors: Truong‐Vinh Hoang; Hermann G. Matthies
• Keywords: Statistical Inference

A random set is a generalisation of variable, i.e. set-valued variable. The theory allows unification other uncertainty descriptions such as interval mass belief function in Dempster-Shafer evidence, possibility theory, and probability distributions. aim this work to develop non-deterministic inference framework, including approximation sampling method, that deals with the inverse problems which represented using sets. proposed method yields posterior based on intersection prior measurement induced That an extension Dempster's rule combination, Bayesian well. direct evaluation might be impractical. We approximate by discrete whose domain samples generated distribution. use capacity transform density for This has special property: it yielded set. distribution can directly obtained methods developed framework. With becomes tractable.