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Scalable Bayesian inference for self-excitatory stochastic processes applied to big American gunfire data

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Abstract

The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these stochastic process models within a host of economic sectors and scientific disciplines is undercut by the processes’ computational burden: complexity of likelihood evaluations grows quadratically in the number of observations for both the temporal and spatiotemporal Hawkes processes. We show that, with care, one may parallelize these calculations using both central and graphics processing unit implementations to achieve over 100-fold speedups over single-core processing. Using a simple adaptive Metropolis–Hastings scheme, we apply our high-performance computing framework to a Bayesian analysis of big gunshot data generated in Washington D.C. between the years of 2006 and 2019, thereby extending a past analysis of the same data from under 10,000 to over 85,000 observations. To encourage widespread use, we provide hpHawkes, an open-source R package, and discuss high-level implementation and program design for leveraging aspects of computational hardware that become necessary in a big data setting.

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Acknowledgements

The research leading to these results has received funding through National Institutes of Health Grant U19 AI135995 and National Science Foundation Grant DMS1264153. AJH is supported by NIH Grant K25AI153816. We gratefully acknowledge support from Nvidia Corporation with the donation of parallel computing resources used for this research.

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Authors and Affiliations

  1. Department of Biostatistics, University of California, Los Angeles, Los Angeles, USA

    Andrew J. Holbrook & Marc A. Suchard

  2. Department of Criminology, University of Pennsylvania, Philadelphia, USA

    Charles E. Loeffler

  3. Department of Mathematics, Imperial College London, London, UK

    Seth R. Flaxman

  4. Department of Biomathematics, University of California, Los Angeles, Los Angeles, USA

    Marc A. Suchard

  5. Department of Human Genetics, University of California, Los Angeles, Los Angeles, USA

    Marc A. Suchard

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  1. Andrew J. Holbrook
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  2. Charles E. Loeffler
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  4. Marc A. Suchard
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Correspondence to Andrew J. Holbrook.

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Holbrook, A.J., Loeffler, C.E., Flaxman, S.R. et al. Scalable Bayesian inference for self-excitatory stochastic processes applied to big American gunfire data. Stat Comput 31, 4 (2021). https://doi.org/10.1007/s11222-020-09980-4

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