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Inference Given Summary Statistics

In: Handbook of Uncertainty Quantification

Author

Listed:
  • Habib N. Najm

    (Sandia National Laboratories, Combustion Research Facility, Reacting Flow Research)

  • Kenny Chowdhary

    (Sandia National Laboratories, Quantitative Modeling and Analysis)

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.

Suggested Citation

  • Habib N. Najm & Kenny Chowdhary, 2017. "Inference Given Summary Statistics," Springer Books, in: Roger Ghanem & David Higdon & Houman Owhadi (ed.), Handbook of Uncertainty Quantification, chapter 3, pages 33-67, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12385-1_68
    DOI: 10.1007/978-3-319-12385-1_68
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