Posterior Manifolds over Prior Parameter Regions: Beyond Pointwise Sensitivity Assessments for Posterior Statistics from MCMC Inference

Jacobi Liana (), Kwok Chun Fung (), Ramírez-Hassan Andrés () and Nghiem Nhung ()
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Jacobi Liana: Department of Economics, The University of Melbourne, Melbourne, Australia
Kwok Chun Fung: Department of Economics, The University of Melbourne, Melbourne, Australia
Ramírez-Hassan Andrés: Universidad EAFIT, School of Finance, Economics and Government, Medellín, Colombia
Nghiem Nhung: Department of Public Health, University of Otago, Wellington, New Zealand
Authors registered in the RePEc Author Service: Andrés Ramírez Hassan ()

Studies in Nonlinear Dynamics & Econometrics, 2024, vol. 28, issue 2, 403-434

Abstract: Increases in the use of Bayesian inference in applied analysis, the complexity of estimated models, and the popularity of efficient Markov chain Monte Carlo (MCMC) inference under conjugate priors have led to more scrutiny regarding the specification of the parameters in prior distributions. Impact of prior parameter assumptions on posterior statistics is commonly investigated in terms of local or pointwise assessments, in the form of derivatives or more often multiple evaluations under a set of alternative prior parameter specifications. This paper expands upon these localized strategies and introduces a new approach based on the graph of posterior statistics over prior parameter regions (sensitivity manifolds) that offers additional measures and graphical assessments of prior parameter dependence. Estimation is based on multiple point evaluations with Gaussian processes, with efficient selection of evaluation points via active learning, and is further complemented with derivative information. The application introduces a strategy to assess prior parameter dependence in a multivariate demand model with a high dimensional prior parameter space, where complex prior-posterior dependence arises from model parameter constraints. The new measures uncover a considerable prior dependence beyond parameters suggested by theory, and reveal novel interactions between the prior parameters and the elasticities.

Keywords: Bayesian robustness; Gaussian process; prior elicitation; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C11 C31 C52 D12 I12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/snde-2022-0116

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