2017/06/02 by Fabrizio Leisen, Leisen, Fabrizio, Cristiano Villa +3
Computer Science · Decision Sciences · Mathematics · #Applications (stat.AP) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Methodology (stat.ME) #Multi-Criteria Decision Making #Other Statistics (stat.OT) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1706.00599
openalex publication_date 2017/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off the chosen statistical model and in the majority of cases the resulting prior is improper, which can pose limitations to a practical implementation, even when the complexity of the model is moderate. In this paper we propose to take a novel look at the construction of objective prior distributions, where the connection with a chosen sampling distribution model is removed. We explore the notion of defining objective prior distributions which allow one to have some degree of flexibility, in particular in exhibiting some desirable features, such as being proper, or centered on specific values which would be of interest in nested model comparisons. The basic tool we use are proper scoring rules and the main result is a class of objective prior distributions that can be employed in scenarios where the usual model based priors fail, such as mixture models and model selection via Bayes factors. In addition, we show that the proposed class of priors is the result of minimising the information it contains, providing solid interpretation to the method.