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Inference Given Summary Statistics

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Handbook of Uncertainty Quantification

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.

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Notes

  1. 1.

    It is worth noting that, presuming reported error bars in lnk(T) over a sufficient number of temperature points and considering a Gaussian parameter PDF, the joint correlation structure of p(A, n, E) has been inferred through other means [23]. However, neither of these assumptions is required in the present approach.

  2. 2.

    We will assume that the author had an assumption of normality, hence their interpretation as 95 % quantiles.

  3. 3.

    Again, we do this to reduce the computational cost of generating data sets over multiple dimensions. Although we do not marginalize over the dimensionality, we show that for a reasonable choice of the dimension parameter N = 5, we can still recover consistent data sets.

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Author information

Authors and Affiliations

  1. Combustion Research Facility, Reacting Flow Research, Sandia National Laboratories, P.O.Box 969, MS 9051, 94551, Livermore, CA, USA

    Habib N. Najm

  2. Quantitative Modeling and Analysis, Sandia National Laboratories, P.O.Box 969, MS 9159, 94551, Livermore, CA, USA

    Kenny Chowdhary

Authors
  1. Habib N. Najm
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  2. Kenny Chowdhary
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Correspondence to Habib N. Najm .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, Virginia, USA

    David Higdon

  3. Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, USA

    Houman Owhadi

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Najm, H.N., Chowdhary, K. (2017). Inference Given Summary Statistics. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-12385-1_68

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