Reference Bayesian inference in nonregular models

Exact reference prior and posterior are obtained and their properties examined for two nonregular models: a structural low-price, sealed-bid auction model and a job-search model. A model is nonregular if the support of the data depends on the parameters. Reference priors, by definition, take this “nonregularity” of the data into account. Linkages with classical inference emerge as a result. On the basis of these linkages and the properties of the reference prior and posterior in the two nonregular models, this paper suggests that reference priors could be an alternative in nonregular models when subjective prior elicitation is difficult.