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Inference Given Summary Statistics

  • Habib N. NajmEmail author
  • Kenny Chowdhary
Reference work entry

Abstract

In many practical situations, where one is interested in employing Bayesian inference methods to infer parameters of interest, a significant challenge is that actual data is not available. Rather, what is most commonly available in the literature are summary statistics on the data, on parameters of interest, or on functions thereof. In this chapter, we present a general framework relying on the maximum entropy principle, and employing approximate Bayesian computation methods, to infer a joint posterior density on parameters of interest given summary statistics, as well as other known details about the experiment or observational system behind the published statistics. By essentially redoing the experimental fitting using proposed data sets, the method ensures that the inferred joint posterior density on model parameters is consistent with the given statistics and with the model.

Keywords

Approximate bayesian computation Bayesian inference Maximum entropy Missing data Sufficient statistic 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Combustion Research Facility, Reacting Flow ResearchSandia National LaboratoriesLivermoreUSA
  2. 2.Quantitative Modeling and AnalysisSandia National LaboratoriesLivermoreUSA

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