Jesper Martinsson: A conclusion based on prejudices is optimal on average -- a medley of applied Bayesian solutions to challenging problems

Abstract

This seminar explores the practical benefits of using informative prior distributions in statistical analyses, particularly in challenging scenarios like industrial applications with sparse and outlier-contaminated data. The choice of the prior model also presents an interesting human perspective with options to choose more inclusive parameterizations, allowing parameters at the likelihood level (e.g. individual level) to be outliers/extreme values, or priors (such as the normal distribution) that aim for stricter grouping. The properties of these priors raises questions about when to choose which approach and the advantages and disadvantages of these models.While there is a strong emphasis in academia to advocate for non-informative and sometimes parameterization invariant priors in pursuit of objectivity, we'll question the status quo. Is there value in embracing the influence of priors and making deliberate choices in parameterization? The examples presented in this seminar explore the strengths in pursuing the opposite direction. This direction is deemed more powerful and exciting but perhaps also riskier, as it involves truly embracing the influence of priors.