Reconciling Curvature and Importance Sampling Based Procedures for Summarizing Case Influence in Bayesian Models
Autor: | Steven N. MacEachern, Mario Peruggia, Zachary M Thomas |
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Rok vydání: | 2018 |
Předmět: |
Statistics and Probability
Kullback–Leibler divergence Covariance matrix 05 social sciences Bayesian probability Curvature 01 natural sciences Measure (mathematics) Statistics::Computation 010104 statistics & probability 0502 economics and business Principal component analysis Statistics Statistics::Methodology Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Divergence (statistics) Importance sampling 050205 econometrics Mathematics |
Zdroj: | Journal of the American Statistical Association. 113:1669-1683 |
ISSN: | 1537-274X 0162-1459 |
DOI: | 10.1080/01621459.2017.1360777 |
Popis: | Methods for summarizing case influence in Bayesian models take essentially two forms: (1) use common divergence measures for calculating distances between the full-data posterior and the case-deleted posterior, and (2) measure the impact of infinitesimal perturbations to the likelihood to study local case influence. Methods based on approach (1) lead naturally to considering the behavior of case-deletion importance sampling weights (the weights used to approximate samples from the case-deleted posterior using samples from the full posterior). Methods based on approach (2) lead naturally to considering the local curvature of the Kullback–Leibler divergence of the full posterior from a geometrically perturbed quasi-posterior. By examining the connections between the two approaches, we establish a rationale for employing low-dimensional summaries of case influence obtained entirely via the variance–covariance matrix of the log importance sampling weights. We illustrate the use of the proposed diagnos... |
Databáze: | OpenAIRE |
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