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

TL;DR

This paper introduces a high-performance, parallelized Bayesian inference framework for Hawkes processes, enabling analysis of large-scale spatiotemporal data such as over 85,000 gunshot events in Washington D.C., with an open-source R package for broad accessibility.

Contribution

It presents a scalable, GPU-accelerated Bayesian inference method for Hawkes processes and demonstrates its application to large gunfire datasets, significantly extending previous analyses.

Findings

Achieved over 100-fold speedup using parallel computing techniques.

Extended analysis from under 10,000 to over 85,000 observations.

Provided an open-source R package, hpHawkes, for scalable Bayesian inference.

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 wide-spread 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.