Epistemic Utility for Imprecise Probability

Scientific inference is principally a matter of using observable data to estimate the parameters of models of interest, e.g., models of the climate system. In traditional Bayesian statistics, uncertainty about model parameters is quantified using a single, precise probability distribution. This approach has proved extremely successful in applications where data is plentiful and model parameters are few. But many models are high dimensional (thousands of parameters), and relevant data is comparatively sparse. In such contexts, imprecise probabilities are required to adequately capture uncertainty. The mathematical foundations of imprecise probability theory (IP) have been in place for 25 years, and IP has proved successful in practice. But IP methods lack rigorous accuracy-centered, philosophical justifications. Traditional Bayesian methods can be justified using epistemic scoring rules, which measure the accuracy of the estimates that they produce. But there has been little work extending these justifications to the IP framework. Thus, the key aim of the proposed research is to develop scoring rules for IP distributions (IP scoring rules), and use them to justify and extend IP methods. There are four main objectives: (1) characterise reasonable IP scoring rules; (2) derive scoring-rule based justifications for existing IP methods; (3) use IP scoring rules to discover novel methods for selecting and updating IP distributions; (4) use IP scoring rules to engineer new deference and aggregation principles for IP distributions. Objectives 1 and 2 will deliver firm foundations for existing IP methods. Objectives 3 and 4 will extend the range of IP methods available for both individual and group inquiry. The results of this project will not only make IP a central focus in contemporary epistemology, and shape ongoing philosophical debates about IP’s role in inference and decision-making, but also furnish new tools aimed at influencing how IP methods are used in practice.