# Monica Musio: Proper Scoring Rules in Bayesian Model Selection

Monica Musio (University of Cagliari) will give a 30 min seminar in the lunch area, 8th floor N.H. Abel's House at 14:15 September 29th.

Title: The use of Proper Scoring Rules in Bayesian Model Selection

Abstract: A scoring rule S(x; q) provides a way of judging the quality of a quoted

probability density q for a random variable X in the light of its outcome

x. It is called proper if honesty is your best policy, i.e., when you believe

X has density p, your expected score is optimised by the choice q = p.

Every statistical decision problem induces a proper scoring rule, so there

is a very wide variety of these. Many of them have additional interesting

structure and properties. At a theoretical level, any proper scoring rule

can be used as a foundational basis for the theory of subjective probability.

At an applied level a proper scoring can be used to compare and improve

probability forecasts, and, in a parametric setting, as an alternative tool for

inference. We will discuss some characterisations and properties of proper

scoring rules, and we describe its use in the Bayesian model selection setting

in presence of improper priors.