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Evidence with uncertain likelihoods

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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  μ 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.

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Author information

Correspondence to Riccardo Pucella.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, pp. 243–250, 2005. Most of this work was done while the second author was at Cornell University.

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Halpern, J.Y., Pucella, R. Evidence with uncertain likelihoods. Synthese 171, 111–133 (2009). https://doi.org/10.1007/s11229-008-9381-z

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Keywords

  • Confirmation theory
  • Weight of evidence
  • Likelihood
  • Uncertainty