Evidence with Uncertain Likelihoods
This work addresses a foundational issue in decision theory and statistics for agents making choices under uncertainty, but it appears incremental as it builds on existing formalizations without introducing a new paradigm.
The paper tackles the problem of formalizing evidence when there is uncertainty about which likelihood function applies to hypotheses, extending existing frameworks that assume fixed likelihoods. It generalizes a formal approach to define evidence as a function from priors to posteriors to accommodate this uncertainty.
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 μh, 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.