Currently, imprecise Bayesian methods lack rigorous accuracy-centered, philosophical justifications. Traditional Bayesian methods can be justified using what are variously known as epistemic scoring rules, epistemic utility functions or inaccuracy measures. Scoring rules measure the accuracy of the estimates that traditional methods produce, which is roughly a matter of how close those estimates are to the actual values of the quantities of interest. Drawing on the work of de Finetti (1974) and Savage (1971), contemporary Bayesians like Joyce (1998, 2009), Schervish et al. (2009) and Pettigrew (2016) use scoring rules, together with resources from decision theory, to show that traditional Bayesian methods provide decision-theoretically optimal strategies for securing accurate estimates. This approach has provided compelling justifications for a wide range of traditional Bayesian methods and principles: Probabilism, which specifies global coherence constraints on estimates (Joyce 1998, 2009; Predd et al. 2009; Pettigrew 2016); Conditionalization, which specifies how to update one’s estimates in light of new data (Greaves and Wallace 2006); the Principle of Indifference, which specifies appropriate estimates to employ when one lacks relevant information (Pettigrew 2014), and more.
Unfortunately, there has been very little work to date extending these justifications to the IP framework. The project team has now provided the first characterisation of reasonable IP scoring rules (and a method for constructing them). We have successfully achieved objective 1. This represents a hugely significant advance in the state of the art. With this milestone in hand, we are on track to reach our final 3 objectives:
- To use IP scoring rules to derive epistemic justifications for existing IP methods.
- To extend the range of IP tools available for individual inquirers by engineering new methods for selecting and updating IP distributions.
- To facilitate group inquiry by discovering new deference and aggregation principles for IP distributions.
Achieving these objectives will advance the field in two significant ways:
- It will provide the first sustained investigation into the epistemic foundations of imprecise probability theory. This will make IP a central focus in contemporary epistemology and shape ongoing philosophical debates about IP’s role in inference and decision-making.
- It will develop novel IP methods for both individual and group inquiry. This has the potential to influence how IP methods are used in a range of fields, for example, economics, climate science and bioinformatics.
