Evidence with Uncertain Likelihoods

TL;DR

This paper extends the formal framework for evidence assessment in hypothesis testing to include uncertainty about the likelihood functions, allowing for more flexible modeling of evidence when likelihoods are not precisely known.

Contribution

It introduces a generalized approach to evidence that accounts for uncertainty in likelihood functions, expanding the traditional probabilistic framework.

Findings

Framework accommodates multiple likelihood functions per hypothesis.

Generalization of evidence as a function from priors to posteriors.

Enhances modeling of evidence with uncertain likelihoods.

Abstract

An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to formalize this intuition up to now have assumed that associated with each hypothesis h there is a likelihood function {\mu}h, which is a probability measure that intuitively describes how likely each observation is, conditional on h being the correct hypothesis. We consider an extension of this framework where there is uncertainty as to which of a number of likelihood functions is appropriate, and discuss how one formal approach to defining evidence, which views evidence as a function from priors to posteriors, can be generalized to accommodate this uncertainty.