Forschungsseminar am Institut für Angewandte Statistik
23. Juni, 14:00 - Liana Jacobi: “Posterior Manifolds over Hyperparameter Regions (and Joint Prior Parameter Dependence): Moving Beyond Localized Assessments of Prior Parameter Specifications in MCMC Inference”, joint with Andres Ramirez-Hassan, Jackson Kwok and Nhung Nghiem
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meeting ID: 937 6054 7545
Prior parameter sensitivity has moved into the focus of prior robustness analysis in response to the increased use of Bayesian inference in applied work, in particular with the popularity of Markov chain Monte Carlo (MCMC) inference under conjugate priors. It is commonly investigated in terms of local or pointwise assessments, in the form of derivatives or multiple evaluations. As such it provides limited localized information about the impact of prior parameter specifications, with the scope further restricted due to analytical and computational complexities in most MCMC applications.
This paper introduces an approach based on the geometry of posterior statistics over hyperparameter regions (posterior manifolds) that encompasses and expands upon two common localized strategies to obtain more information about prior parameter dependence. The proposed estimation strategy is based on multiple point evaluations with Gaussian processes with efficient selection of evaluation points achieved via Active Learning, that is further complemented with derivative information via a recent Automatic Differentiation approach for MCMC output. The approach gives rise to formal measures that can quantify additional aspects of prior parameter dependence and uncover more complex dependencies across prior parameters that are particularly relevant in practical applications which often involve the setting of many location and precision parameters. The real data example investigates the impact of joint changes in prior demand parameter specifications on elasticity inference under a common multivariate demand framework for 5 main good groups using data from a recent virtual supermarket experiment. We identify and estimate sensitivity manifolds for the three-most sensitive (cross-)price and expenditure elasticities and show how conclusions regarding substitutionary versus complementary relationships as well as price sensitivity characteristics (normal versus inferior goods, elastic vs inelastic) can change across the prior parameter space.
14:00 - 15:15 Uhr
S2 Z74, Science Park 2