  Models of updating a set of priors either do not allow a decision maker to
make inference about her priors (full bayesian updating or FB) or require an
extreme degree of selection (maximum likelihood updating or ML). Therefore I
characterize a general method for updating a set of priors, partial bayesian
updating (PB), in which the decision maker (i) utilizes a threshold to
determine whether a prior is likely enough, conditional on observed
information, and then (ii) applies Bayes' rule to the sufficiently likely
priors. I show that PB nests FB and ML and explore its behavioral properties.
