Abstract: Some scientists prefer to exercise substantial judgment in formulating a likelihood function for their data. Others prefer to try to get the data to tell them which likelihood is most appropriate. We suggest here that one way to reduce the judgment component of the likelihood function is to adopt a mixture of potential likelihoods and let the data determine the weights on each likelihood. We distinguish several different types of subjectivity in the likelihood function and show with examples how these subjective elements may be given more equitable treatment.