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

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.Comment: Submitted to Statistics and Computin

Fully Bayesian tests of neutrality using genealogical summary statistics

<p>Abstract</p> <p>Background</p> <p>Many data summary statistics have been developed to detect departures from neutral expectations of evolutionary models. However questions about the neutrality of the evolution of genetic loci within natural populations remain difficult to assess. One critical cause of this difficulty is that most methods for testing neutrality make simplifying assumptions simultaneously about the mutational model and the population size model. Consequentially, rejecting the null hypothesis of neutrality under these methods could result from violations of either or both assumptions, making interpretation troublesome.</p> <p>Results</p> <p>Here we harness posterior predictive simulation to exploit summary statistics of both the data and model parameters to test the goodness-of-fit of standard models of evolution. We apply the method to test the selective neutrality of molecular evolution in non-recombining gene genealogies and we demonstrate the utility of our method on four real data sets, identifying significant departures of neutrality in human influenza A virus, even after controlling for variation in population size.</p> <p>Conclusion</p> <p>Importantly, by employing a full model-based Bayesian analysis, our method separates the effects of demography from the effects of selection. The method also allows multiple summary statistics to be used in concert, thus potentially increasing sensitivity. Furthermore, our method remains useful in situations where analytical expectations and variances of summary statistics are not available. This aspect has great potential for the analysis of temporally spaced data, an expanding area previously ignored for limited availability of theory and methods.</p

An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as appendices

Unifying the spatial epidemiology and molecular evolution of emerging epidemics

We introduce a conceptual bridge between the previously unlinked fields of phylogenetics and mathematical spatial ecology, which enables the spatial parameters of an emerging epidemic to be directly estimated from sampled pathogen genome sequences. By using phylogenetic history to correct for spatial autocorrelation, we illustrate how a fundamental spatial variable, the diffusion coefficient, can be estimated using robust nonparametric statistics, and how heterogeneity in dispersal can be readily quantified. We apply this framework to the spread of the West Nile virus across North America, an important recent instance of spatial invasion by an emerging infectious disease. We demonstrate that the dispersal of West Nile virus is greater and far more variable than previously measured, such that its dissemination was critically determined by rare, long-range movements that are unlikely to be discerned during field observations. Our results indicate that, by ignoring this heterogeneity, previous models of the epidemic have substantially overestimated its basic reproductive number. More generally, our approach demonstrates that easily obtainable genetic data can be used to measure the spatial dynamics of natural populations that are otherwise difficult or costly to quantify

Bayesian modeling of recombination events in bacterial populations

Background: We consider the discovery of recombinant segments jointly with their origins within multilocus DNA sequences from bacteria representing heterogeneous populations of fairly closely related species. The currently available methods for recombination detection capable of probabilistic characterization of uncertainty have a limited applicability in practice as the number of strains in a data set increases. Results: We introduce a Bayesian spatial structural model representing the continuum of origins over sites within the observed sequences, including a probabilistic characterization of uncertainty related to the origin of any particular site. To enable a statistically accurate and practically feasible approach to the analysis of large-scale data sets representing a single genus, we have developed a novel software tool (BRAT, Bayesian Recombination Tracker) implementing the model and the corresponding learning algorithm, which is capable of identifying the posterior optimal structure and to estimate the marginal posterior probabilities of putative origins over the sites. Conclusion: A multitude of challenging simulation scenarios and an analysis of real data from seven housekeeping genes of 120 strains of genus Burkholderia are used to illustrate the possibilities offered by our approach. The software is freely available for download at URL http://web.abo.fi/fak/ mnf//mate/jc/software/brat.html