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Statistical Modelling by Exponential Families

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  • Sundberg,Rolf

Abstract

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.

Suggested Citation

  • Sundberg,Rolf, 2019. "Statistical Modelling by Exponential Families," Cambridge Books, Cambridge University Press, number 9781108701112.
    • Handle: RePEc:cup:cbooks:9781108701112
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    Cited by:

    1. Frank Kwasniok, 2021. "Semiparametric maximum likelihood probability density estimation," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-33, November.
    2. Park, Jaewoo & Jin, Ick Hoon & Schweinberger, Michael, 2022. "Bayesian model selection for high-dimensional Ising models, with applications to educational data," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Michael Schweinberger, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 253-260, June.
    4. Aris Spanos, 2022. "Frequentist Model-based Statistical Induction and the Replication Crisis," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 133-159, September.
    5. Whiteley, Nick, 2021. "Dimension-free Wasserstein contraction of nonlinear filters," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 31-50.
    6. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.

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