Dr. Michael Lavine (University of Massachusetts Amherst)

Title: Subjective Likelihood

Abstract: We describe a problem in physical oceanography in which we want to create a spatio-temporal model. However, there is no
plausible sampling density p(data|parameter).  We solved the problem by presenting simple data sets to the expert to learn how she changes her prior into her posterior.  From these simple data sets we infer the likelihood function.  (There is still no p(data|parameter).)  Then we apply that likelihood function to the large, spatio-temporal data set. Reference: "Subjective Likelihood for the Assessment of Trends in the Ocean's Mixed-Layer Depth, with Comments and Rejoinder", JASA (2007), 102, 771--787.

The interest lies in the foundations: how we handled the problem of no p(data|parameter).