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Recent Advances in Bayesian Inference for Complex Systems

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Women in Telecommunications

Part of the book series: Women in Engineering and Science ((WES))

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Abstract

In many real-world problems, the interest is in learning about unknowns from observed data. One widely adopted approach to learning is to employ Bayesian inference. Over the last half-century, Monte Carlo-based methods have kept the main stage of Bayesian reasoning, and they will not relinquish it any time soon. With these methods, Bayesianism has enjoyed tremendous success as they made possible the computation of posterior distributions of unknowns from very challenging models. In the new age of signal processing, the main problems of concern are those with large numbers of unknowns (complex systems) and/or large amounts of data (big data). This raises the concern that Bayesian inference may become computationally incapable of handling them because of the sheer size and complexity of the studied systems. This chapter discusses the main challenges related to the addressed problem and recent advances in the theory and practice of a class of Monte Carlo methods, adaptive importance sampling (AIS), for dealing exactly with the types of problems where the numbers of unknowns and/or data are large. The focus of the chapter will be on new schemes for adaptive importance sampling with emphasis on strategies for adaptive learning and for stable weight computation, model selection, and application of the theory to case-studies including reconstruction of gene regulatory (life science problem) and inference of demographic rates of penguin populations (ecological problem).

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Notes

  1. 1.

    Dynamic parameters are often referred to as state or hidden state and static parameters as model parameters (Adali and Haykin 2010; Liu and West 2001).

  2. 2.

    Asymptotic methods, multiple quadrature approaches, and subregion adaptive integration (Evans and Swartz 1995) are also used for approximation of integrals but cannot be applied in high-dimensional setups and only MC approaches become feasible in many practical applications.

  3. 3.

    Note that here we discuss initialization strategies for Bayesian models with only unknown static parameters for simplicity in the notation and presentation.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY, USA

    Mónica F. Bugallo

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  1. Mónica F. Bugallo
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Correspondence to Mónica F. Bugallo .

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Editors and Affiliations

  1. University of Pisa, Pisa, Pisa, Italy

    Maria Sabrina Greco

  2. University of L’Aquila, L’Aquila, Italy

    Dajana Cassioli

  3. University of Sannio, Benevento, Italy

    Silvia Liberata Ullo

  4. Freehold, NJ, USA

    Margaret J. Lyons

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Bugallo, M.F. (2023). Recent Advances in Bayesian Inference for Complex Systems. In: Greco, M.S., Cassioli, D., Ullo, S.L., Lyons, M.J. (eds) Women in Telecommunications. Women in Engineering and Science. Springer, Cham. https://doi.org/10.1007/978-3-031-21975-7_4

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