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The self-exciting Hawkes point process model (Hawkes, 1971) has been used to describe and forecast communicable diseases. A variant of the Hawkes model, called the recursive model, was proposed by Schoenberg et al. (2019) and has been shown to fit well to various epidemic disease datasets. Unlike the Hawkes model, the recursive model allows the productivity to vary as the overall rate of incidence of the disease varies. Here, we extend the data-driven nonparametric expectation-maximization method of Marsan and Lengliné (2008) in order to fit the recursive model without assuming a particular functional form for the productivity. The nonparametric recursive model is trained to fit to weekly reported cases of mumps in Pennsylvania during the January 1970-September 1990 time frame and then assessed using one week forecasts for the October 1990-December 2001 time period. Both its training and predictive ability are evaluated compared to that of other candidate models, such as Hawkes and SVEILR (susceptible, vaccinated, exposed, infected, lightly infected, recovered) compartmental models.

We present a fast, accurate estimation method for multivariate Hawkes self-exciting point processes widely used in seismology, criminology, finance and other areas. There are two major ingredients. The first is an analytic derivation of exact maximum likelihood estimates of the nonparametric triggering density. We develop this for the multivariate case and add regularization to improve stability and robustness. The second is a moment-based method for the background rate and triggering matrix estimation, which is extended here for the spatiotemporal case. Our method combines them together in an efficient way, and we prove the consistency of this new approach. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media.

To investigate the perential question of how to measure luck versus skill, we perform a detailed simulation study of Texas Hold’em poker hands. We define luck and skill as the player equity changes...

A variety of nonparametric models have been proposed for estimating earthquake triggering. We investigate the ability of the model-independent stochastic declustering method developed by Marsan and Lengliné (2008) to estimate variable spatial triggering that can vary with direction, magnitude, and region. We develop an approach for local fault estimation and demonstrate forecasting methods that use the nonparametric estimates. Simulation studies are conducted to verify the effectiveness of the method, and the nonparametric estimates are applied to a California earthquake catalog. Model forecast performance is evaluated retrospectively by comparing our models with the long-term forecast of Helmstetter et al. (2007), using both deviance and Voronoi residuals. We show improved performance compared with Helmstetter et al. (2007) in various regions while using a full nonparametric estimation and forecasting approach.

Coccidioidomycosis is an infectious disease of humans and other mammals that has seen a recent increase in occurrence in the southwestern United States, particularly in California. A rise in cases and risk to public health can serve as the impetus to apply newly developed methods that can quickly and accurately predict future caseloads. The recursive and Hawkes point process models with various triggering functions were fit to the data and their goodness of fit evaluated and compared. Although the point process models were largely similar in their fit to the data, the recursive point process model offered a slightly superior fit. We explored forecasting the spread of coccidioidomycosis in California from December 2002 to December 2017 using this recursive model, and we separated the training and testing portions of the data and achieved a root mean squared error of just 3.62 cases/week.

Dynamic estimation of the reproduction number of COVID-19 is important for assessing the impact of public health measures on virus transmission. State and local decisions about whether to relax or strengthen mitigation measures are being made in part based on whether the reproduction number, Rt, falls below the self-sustaining value of 1. Employing branching point process models and COVID-19 data from Indiana as a case study, we show that estimates of the current value of Rt, and whether it is above or below 1, depend critically on choices about data selection and model specification and estimation. In particular, we find a range of Rt values from 0.47 to 1.20 as we vary the type of estimator and input dataset. We present methods for model comparison and evaluation and then discuss the policy implications of our findings.

Recently developed methods for the non-parametric estimation of Hawkes point process models facilitate their application for describing and forecasting the spread of epidemic diseases. We use data from the 2014 Ebola outbreak in West Africa to evaluate how well a simple Hawkes point process model can forecast the spread of Ebola virus in Guinea, Sierra Leone, and Liberia. For comparison, SEIR models that fit previously to the same data are evaluated using identical metrics. To test the predictive power of each of the models, we simulate the ability to make near real-time predictions during an actual outbreak by using the first 75% of the data for estimation and the subsequent 25% of the data for evaluation. Forecasts generated from Hawkes models more accurately describe the spread of Ebola in each of the three countries investigated and result in a 38% reduction in RMSE for weekly case estimation across all countries when compared to SEIR models (total RMSE of 59.8 cases/week using SEIR compared to 37.1 for Hawkes). We demonstrate that the improved fit from Hawkes modeling cannot be attributed to overfitting and evaluate the advantages and disadvantages of Hawkes models in general for forecasting the spread of epidemic diseases.

An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood estimators of these productivities. This estimator is compared with an empirical estimator and ways are explored of stabilizing both estimators by lower truncating, smoothing, and rescaling the estimates. Properties of the estimators are explored in simulations, and the methods are applied to seismological and epidemic datasets to show and quantify substantial variation in productivity.

Winning a hand in poker takes luck and skill – but which contributes most to victory? Frederic Paik Schoenberg sets out to quantify these two elements of the game using real-life examples

Hyperemesis gravidarum (HG), severe nausea and vomiting of pregnancy, occurs in 0.3–2% of pregnancies and is associated with maternal and fetal morbidity. The cause of HG remains unknown, but familial aggregation and results of twin studies suggest that understanding the genetic contribution is essential for comprehending the disease etiology. Here, we conduct a genome-wide association study (GWAS) for binary (HG) and ordinal (severity of nausea and vomiting) phenotypes of pregnancy complications. Two loci, chr19p13.11 and chr4q12, are genome-wide significant (p, Hyperemesis gravidarum (HG) is a severe form of nausea and vomiting associated with unfavourable outcomes during pregnancy. Here, Fejzo et al. perform genome-wide scans for HG and pregnancy nausea and vomiting and identify genetic associations at two loci implicating the genes GDF15 and IGFBP7.

Increasingly, government policies directed towards limiting pharmaceutical prices have emphasized value-based criteria. This regulatory approach is most clearly formalized in the United Kingdom where the National Institute for Health and Clinical Excellence (NICE) was created within the British National Health Service (NHS), whose function is to apply cost-effectiveness analysis to new drugs. In contrast to Britain, there is no formal regulatory mechanism assuring cost-effectiveness in the United States. Instead, questions of cost effectiveness are left to market processes. In this paper, we examine the pricing implications of these alternate regimes. From our empirical analysis, we conclude that value-based pricing is enforced by both regulatory and market processes, and with similar outcomes.

This book surveys the main topics in spatial statistics, including modeling random fields, variogram estimation, hierarchical models, and spatial point processes. The book is meant for graduate stu...

As of June 16, 2019, an Ebola virus disease (EVD) outbreak has led to 2136 reported cases in the northeastern region of the Democratic Republic of the Congo (DRC). As this outbreak continues to threaten the lives and livelihoods of people already suffering from civil strife and armed conflict, relatively simple mathematical models and their short-term predictions have the potential to inform Ebola response efforts in real time. We applied recently developed non-parametrically estimated Hawkes point processes to model the expected cumulative case count using daily case counts from May 3, 2018, to June 16, 2019, initially reported by the Ministry of Health of DRC and later confirmed in World Health Organization situation reports. We generated probabilistic estimates of the ongoing EVD outbreak in DRC extending both before and after June 16, 2019, and evaluated their accuracy by comparing forecasted vs. actual outbreak sizes, out-of-sample log-likelihood scores and the error per day in the median forecast. The median estimated outbreak sizes for the prospective thee-, six-, and nine-week projections made using data up to June 16, 2019, were, respectively, 2317 (95% PI: 2222, 2464); 2440 (95% PI: 2250, 2790); and 2544 (95% PI: 2273, 3205). The nine-week projection experienced some degradation with a daily error in the median forecast of 6.73 cases, while the six- and three-week projections were more reliable, with corresponding errors of 4.96 and 4.85 cases per day, respectively. Our findings suggest the Hawkes point process may serve as an easily-applied statistical model to predict EVD outbreak trajectories in near real-time to better inform decision-making and resource allocation during Ebola response efforts. Keywords: Ebola virus disease, Hawkes point process, Mathematical modeling, Democratic Republic of Congo, Compartmental models

Earthquake focal mechanism estimates have been posited to have predictive value for forecasting future seismicity. In particular, for strike‐slip earthquakes, aftershocks should occur roughly along the estimated mainshock strike. However, the errors in such estimated strike angles are considerable. We compare the degree to which estimated strike angles forecast the direction of future seismicity around a given earthquake with that of uniformly distributed angles and with strike angles estimated based on previous seismicity. The fit of nonparametrically estimated Hawkes models using the estimated strike angle that best fits the post‐mainshock set of events for each mainshock is compared with that of corresponding models that exclude these estimates. Strike angle estimates are shown to have marginal predictive value for forecasting the direction of future seismicity but no more than the better fitting of a uniformly distributed angle and its complement.

Voronoi residuals, deviances, super-thinning, and some other residual analysis methods are applied to a selection of earthquake forecast models in the Collaboratory for the Study of Earthquake Predictability (CSEP). Unlike simple numerical summaries such as the N-test, L-test, or R-test, graphical residual methods are proposed which can be useful for comparing multiple models and for highlighting when and where a given model does not agree closely with the observed seismicity. For gridded forecasts, deviances seem ideally suited for model comparison, and Voronoi residuals seem preferable to simple grid-based residuals for assessing one model individually. For models outputting an estimated conditional rate at any particular space–time location, Voronoi residuals and super-thinning can be especially useful at identifying departures from the data.

This paper presents a collection of dissimilarity measures to describe and then classify spatial point patterns when multiple replicates of different types are available for analysis. In particular, we consider a range of distances including the spike-time distance and its variants, as well as cluster-based distances and dissimilarity measures based on classical statistical summaries of point patterns. We review and explore, in the form of a tutorial, their uses, and their pros and cons. These distances are then used to summarize and describe collections of repeated realizations of point patterns via prototypes and multidimensional scaling. We also show a simulation study to evaluate the performance of multidimensional scaling with two types of selected distances. Finally, a multivariate spatial point pattern of a natural plant community is analyzed through various of these measures of dissimilarity.

Aim: The aim of this study is to determine whether psychiatric symptoms affect recurrence risk of hyperemesis gravidarum (HG). Methods: The study sample included 108 women with HG treated with i.v. fluids in their first pregnancy. Women were divided into two groups based on recurrence of HG in their second pregnancy. Participants submitted medical records and completed a survey regarding pregnancy characteristics and psychiatric symptoms. The χ 2 -test and Student’s t-test were performed to compare the two groups. Results: Eighty-four women (71%) had a recurrence of HG requiring i.v. fluid for dehydration, and were compared with 34 women (29%) who did not have a recurrence. There were no significant differences in obstetric history, although there was a trend toward greater time between first and second pregnancy in the recurrence group (P = 0.08). There were no differences in pre-existing psychiatric diagnoses including anxiety, depression, bipolar disorder, panic or eating disorders. Following the first HG pregnancy, participants in both groups were well matched for all post-traumatic stress symptoms. Conclusion: This study is the first to analyze the relationship of psychiatric factors to risk of recurrence of HG. No factors were identified that increase the risk of recurrence including stress symptoms following a HG pregnancy. Psychological sequelae associated with HG are probably a result of the physical symptoms of prolonged severe nausea and vomiting, medication and/or hospitalization, and likely play no role in disease

Current assumptions on the level of inter-dependency between the magnitudes of earthquakes and the magnitudes of their aftershocks vary significantly, ranging from assumed independence for models like epidemic type aftershock-sequence (ETAS) to assumed positive correlation, at least for the events leading up to the largest earthquakes, for models like accelerated moment release. Recently, a method was developed by Marsan and Lengline for model independent stochastic de-clustering (MISD) of a multidimensional Hawkes self-exciting process, or as is the case here, earthquake activity. After expanding the algorithm to allow for a spatially dependent background rate (henceforth SDMISD), repeated application of SDMISD to a global earthquake catalog allows for estimates with confidence bounds for the average magnitude of an aftershock conditioned upon the magnitude(s) of the earthquake(s) that caused the aftershock. 15 years of data on M 5.3 earthquakes from the global Centroid Moment Tensor earthquake catalog indicate that the magnitudes of aftershocks are dependent on the magnitudes of the earthquakes that cause them, and indeed, larger than average earthquakes are more likely to trigger larger than average aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.

The extent to which the apparent increase in wildre incidence and burn area inCalifornia from 1990 to 2006 is aected by population and temperature increasesis examined. Using generalized linear models with random eects, we focus onthe estimated impacts of increases in mean daily temperatures and populationsin dierent counties on wildre in those counties, after essentially controlling forthe overall dierences between counties in their overall mean temperatures andpopulations. We nd that temperature increase appears to have a signicant posi-tive impact on both total burn area and number of observed wildres. Populationgrowth appears to have a much less pronounced impact on total burn area thando annual temperature increases, and population growth appears to be negativelycorrelated with the total number of observed wildres. These eects are especiallypronounced in the winter season and in Southern California counties.

A B S T R A C T Objective: The purpose of this study is to determine the frequency of adverse perinatal outcome in women with hyperemesis gravidarum and identify prognostic factors. Study design: This is a case–control study in which outcomes of first pregnancies were compared between 254 women with hyperemesis gravidarum treated with intravenous fluids and 308 controls. Prognostic factors were identified by comparing the clinical profile of patients with hyperemesis gravidarum with a normal and an adverse pregnancy outcome. Binary responses were analyzed using either a Chi-square or Fisher exact test and continuous responses were analyzed using a t-test. Results: Women with hyperemesis gravidarum have over a 4-fold increased risk of poor outcome including preterm birth and lower birth weight (p < 0.0001). Among maternal characteristics, only gestational hypertension had an influence on outcome (p < 0.0001). Treatment as an outpatient and/or by alternative medicine (acupuncture/acupressure/Bowen massage) was associated with a positive outcome (p < 0.0089). Poor outcomes were associated with early start of symptoms (p < 0.019), and treatment with methylprednisolone (p < 0.0217), promethazine (p < 0.0386), and other antihistamines [diphenhydramine (Benadryl), dimenhydrinate (Gravol), doxylamine (Unisom), hydroxyzine (Vistaril/Atarax), doxylamine and pyridoxine (Diclectin/Bendectin)] (p < 0.0151) independent of effectiveness. Among these medications, only the other antihistamines were prescribed independent of severity: they were effective in less than 20% of cases and were taken by almost 50% of patients with an adverse outcome. Conclusion: Poor outcomes are significantly greater in women with HG and are associated with gestational hypertension, early symptoms, and antihistamine use. Given these results, there is an urgent need to address the safety and effectiveness of medications containing antihistamines in women with severe nausea of pregnancy.

An approximation technique is introduced that greatly facilitates the estimation of the epidemic‐type aftershock sequence (ETAS) model introduced by Ogata (1988), which is widely used to describe earthquake catalogs. The proposed approximation greatly simplifies the integral term in the log‐likelihood, the computation of which is by far the greatest hurdle in maximum likelihood estimation. The approximation is close, provided the observed region contains most of the aftershock activity caused by earthquakes within the observation region. Through simulations and an example involving earthquakes in Hector Mine, California, the proposed method is shown to produce stable and accurate results, with rapid convergence.

Space–time Hawkes point process models for the conditional rate of earthquake occurrences traditionally make many parametric assumptions about the form of the triggering function for the rate of aftershocks following an earthquake. As an alternative, Marsan and Lengliné [Science 319 (2008) 1076–1079] developed a completely nonparametric method that provides an estimate of a homogeneous background rate for mainshocks, and a histogram estimate of the triggering function. At each step of the procedure the model estimates rely on computing the probability each earthquake is a mainshock or aftershock of a previous event. The focus of this paper is the improvement and assessment of Marsan and Lengliné’s method in the following ways: (a) the proposal of novel ways to incorporate a spatially inhomogeneous background rate; (b) adding error bars to the histogram estimates which quantify the sampling variability in the estimation of the underlying seismic process. A simulation study is designed to evaluate and validate the ability of our methods to recover the triggering function and spatially varying background rate. An application to earthquake data from the Tohoku District in Japan is discussed at the end, and the results are compared to a well-established parametric model of seismicity for this region.

© Cambridge University Press 2015. Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time. We adopt a self-exciting Hawkes process model for this behaviour. First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made. Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks. Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a non-vanishing derivative. Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy. The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed. The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy.

Rescaling, thinning, and superposition are useful methods for the residual analysis of spatial-temporal point processes. These techniques involve transforming the original point process into a new process that is a homogeneous Poisson process if and only if the fitted model is correct, so that one may inspect the residual process using standard tests for homogeneity as a means of assessing the goodness-of-fit of the model. Unfortunately, when the modeled conditional intensity of the original process is volatile, tests of homogeneity performed on residuals on the basis of these three residual methods tend to have low power. For such circumstances, we propose the method of super-thinning, which combines thinned residuals and superposition. This technique involves the use of a tuning parameter, k, which controls how much thinning and superposition are performed to homogenize the process. The method is applied to the assessment of a parametric space–time point process model for the origin times and epicentral locations of recent major California earthquakes. Copyright © 2012 John Wiley & Sons, Ltd.

Earthquake occurrences are often described using a class of branching models called epidemic-type aftershock sequence (ETAS) models. The name derives from the fact that the model allows earthquakes to cause aftershocks, and then those aftershocks may induce subsequent aftershocks, and so on. Despite their value in seismology, such models have not previously been used in studying the incidence of invasive plant and animal species. Here, we apply ETAS models to study the spread of an invasive species in Costa Rica (Musa velutina, or red banana). One challenge in this ecological application is that fitting the model requires the originations of the plants, which are not observed but may be estimated using filed data on the heights of the plants on a given date and their empirical growth rates. We then characterize the estimated spatial-temporal rate of spread of red banana plants using a space-time ETAS model.

The Pareto distribution is often used to describe environmental phenomena such as the sizes of earthquakes or wildfires, or the interevent times or distances between such environmental disturbances. Because it is heavy-tailed, the Pareto distribution, or power-law distribution as it is occasionally called, suggests that a higher frequency of extremely large values occur compared to other, more familiar distributions such as the normal, exponential, or uniform. However, an alternative distribution called the tapered Pareto has been shown in some cases to fit as well or better to data than the Pareto distribution, and the tapered Pareto distribution is not heavy-tailed, suggesting a far lower frequency of extreme events. Even with rather large datasets, it is often quite difficult to distinguish which of these distributions is preferable, as they only differ markedly in the extreme upper tail where few, if any, observations are recorded. This article reviews the evidence and arguments related to these two competing distributions, especially in the context of earthquakes and wildfires.