Frederic Paik Schoenberg

Self-Exciting Point Process Modeling of Crime

Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime-specific patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, near the location of an initial event. Space–time clustering is modeled in seismology by self-exciting point processes and the focus of this article is to show that these methods are well suited for criminological applications. We first review self-exciting point processes in the context of seismology. Next, using residential burglary data provided by the Los Angeles Police Department, we illustrate the implementation of self-exciting point process models in the context of urban crime. For this purpose we use a fully nonparametric estimation methodology to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.

Accurate estimation of travel times from single-loop detectors

As advanced traveler information systems become increasingly prevalent the importance of accurately estimating link travel times grows. Unfortunately, the predominant source of highway traffic information comes from single-loop loop detectors which do not directly measure vehicle speed. The conventional method of estimating speed, and hence travel time, from the single-loop data is to make a common vehicle length assumption and to use a resulting identity relating density, flow, and speed. Hall and Persaud (Transportation Research Record 1232, 9-16, 1989) and Pushkar et al. (Transportation Research Record 1457, 149-157, 1994) show that these speed estimates are flawed. In this paper we present a methodology to estimate link travl times directly from the single-loop loop detector flow and occupancy data without heavy reliance on the flawed speed calculations. Our methods arise naturally from an intuitive stochastic model of traffic flow. We demonstrate by example on data collected on I-880 data (Skabardonis et al. Technical Report UCB-ITS-PRR-95-S, Institute of Transportation Studies, University of California, 1994) that when the loop detector data has a fine resolution (about one second), the single-loop based estimates of travel time can accurately track the true travel time through many degrees of congestion. Probe vehicle data and double-loop based travel time estimates corroborate the accuracy of our methods in our examples.

Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences

Residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space–time–magnitude distribution of earthquake occurrences, using, in particular, the multidimensional version of Ogatas epidemic-type aftershock sequence (ETAS) model and a 30-year catalog of 580 earthquakes occurring in Bear Valley, California. One method involves rescaled residuals, obtained by transforming points along one coordinate to form a homogeneous Poisson process inside a random, irregular boundary. Another method involves thinning the point process according to the conditional intensity to form a homogeneous Poisson process on the original, untransformed space. The thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate. Using rescaled residuals, it is shown that the temporal–magnitude distribution of aftershock activity is not separable, and that, in particular, in contrast to the ETAS model, the triggering density of earthquakes appears to depend on the magnitude of the secondary events in question. The residual analysis highlights that the fit of the space–time ETAS model may be improved by allowing the parameters governing the triggering density to vary for earthquakes of different magnitudes. Such modifications may be important because the ETAS model is widely used in seismology for hazard analysis.

Detection of non-linearities in the dependence of burn area on fuel age and climatic variables

Evidence from Los Angeles County in California, USA suggests that the relationships between wildfire burn area and fuel age, temperature, precipitation, and fuel moisture are not linear. Instead, the relationships appear to have thresholds.The data seem to support the notion that fire risk is nearly constant provided various conditions are met: that fuel age and temperature exceed a given threshold, and that fuel moisture and precipitation are sufficiently low. There appears to be little distinction in terms of wildfire risk between conditions that are sufficient for wildfires and those that are extreme.

A Space–Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index

Numerical indices are commonly used as tools to aid wildfire management and hazard assessment. Although the use of such indices is widespread, assessment of these indices in their respective regions of application is rare. We evaluate the effectiveness of the burning index (BI) for predicting wildfire occurrences in Los Angeles County, California using space–time point-process models. These models are based on an additive decomposition of the conditional intensity, with separate terms used to describe spatial and seasonal variability as well as contributions from the BI. We fit the models to wildfire and BI data from the years 1976–2000 using a combination of nonparametric kernel-smoothing methods and parametric maximum likelihood. In addition to using the Akaike information criterion (AIC) to compare competing models, we use new multidimensional residual methods based on approximate random thinning and rescaling to detect departures from the models and to ascertain the precise contribution of the BI to predicting wildfire occurrence. We find that although the BI appears to have a positive impact on wildfire prediction, the contribution is relatively small after taking into account natural seasonal and spatial variation. In particular, the BI does not appear to take into account increased activity during the years 1979–1981 and can overpredict during the early months of the year.

Linear and Nonlinear Relations between Relative Plate Velocity and Seismicity

Relationships between relative plate velocity and seismicity differ by plate-boundary class. We test the null hypothesis of linearity of earthquake rates with velocity in each of seven classes. A linear relationship is expected if earthquake rate is proportional toseismicmoment rate, whichis proportional torelative platevelocity. To reducebiasbyaftershocksandswarms,weestimateindependenceprobabilitiesofearth- quakes and use them as weights. We assign shallow earthquakes to boundary steps and classes,thensortboundarystepswithineachclassbyvelocityandplotcumulativeearth- quakesagainstcumulativemodelmomentrate.Weusetwomeasuresofnonlinearityand 10 4 stochastic simulations to assess significance. In subduction zones the relationship betweenseismicityandvelocityisnonlinearwith99.9%confidence.Slowersubduction at<66 mm=a(producing35%oftectonicmomentunderthenullhypothesis)produces only 20% of subduction earthquakes. Continental convergent boundaries display simi- larnonlinearity ( P< 0:001forthenullhypothesis). Oceanspreadingridgesshowseis- micity decreasing with velocity. Oceanic transform faults and oceanic convergent boundaries show marginal nonlinearity ( P< 0:01; P< 0:05). Continental rifts and continental transform faults follow the null hypothesis. Three effects may contribute to velocity dependence in subduction: (1) the brittle/ductile transition at a critical tem- peratureisadvecteddeeperbyfasterunderthrusting;(2)subductedsedimentisviscous, so lower stresses in slower boundaries discourage earthquakes; (3) pore pressures increase with velocity, encouraging frictional failure. Mechanism (1) has only minor effects on earthquake productivity, but mechanisms (2) and (3) could be important. Online Material: Earthquake subcatalogs and cumulative-distribution tables.

Standard Errors of Parameter Estimates in the ETAS Model

Abstract Point process models such as the epidemic-type aftershock sequence (ETAS) model have been widely used to analyze and describe seismic catalogs and to perform short-term forecasting. The standard errors of parameter estimates in the ETAS model are significant and cannot be ignored. This paper uses simulations to explore the accuracy of conventional standard error estimates based on the Hessian matrix of the log-likelihood function of the ETAS model. We show that such error estimates are not accurate when the observed space-time window is small. One must only cautiously trust the Hessian-based standard error estimates for this model when using local datasets with time windows of several years in length. The standard errors for all parameter estimates introduced by magnitude errors in typical earthquake catalogs are found to be smaller than those introduced by choosing a finite time window. However, neither effect is insignificant.

Transforming spatial point processes into Poisson processes

Transforming spatial point processes into Poisson processes Frederic Schoenberg*,^ Department of Statistics, University of California at Los Angeles, Los Angeles, CA 90095, USA Abstract In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualarts theorem applies only to a special class of point processes, since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator. The (F4) condition was removed in 1990 by Nair, but the convexity condition remained. Here both the (F4) condition and the convexity condition are removed by making use of predictable sets rather than stopping sets. As with Nairs theorem, the result extends to point processes in higher dimensions. Keywords: Compensator; intensity; point process; Poisson process; predictable set; random space change; spatial process; stopping time Introduction. Suppose A^ is a point process. Is it possible to rescale the domain in such a way that A is transformed into a Poisson process with rate 1? * Research supported by Michel and Line Loeve fellowship and by the University of California Campus- Laboratory Collaboration program Advanced Earthquake Hazard Research . tEmail: frederic@stat.ucla.edu

Prenatal exposure to hyperemesis gravidarum linked to increased risk of psychological and behavioral disorders in adulthood

Hyperemesis gravidarum (HG), severe nausea and vomiting of pregnancy, is characterized by long-term maternal stress, undernutrition and dehydration. While maternal stress and malnutrition of pregnancy are linked to poor neonatal outcome and associated with poor adult health, long-term outcome of fetal exposure to HG has never been explored. The purpose of this study is to determine whether long-term emotional and behavioral diagnoses may be associated with fetal exposure to HG. Emotional and behavioral diagnoses of adults born of a pregnancy complicated by HG were compared to diagnoses from non-exposed controls. Offspring exposed to HG in utero were significantly more likely to have a psychological and behavioral disorder (OR = 3.6, P < 0.0001) with diagnoses primarily of depression, bipolar disorder and anxiety. In utero exposure to HG may lead to increased risks of psychological and behavioral disorders in the offspring.

Risk factors, treatments, and outcomes associated with prolonged hyperemesis gravidarum

Objective: To identify factors associated with prolonged Hyperemesis Gravidarum (HG). Study Design: About 395 women completed a survey regarding pre-existing conditions, treatments and outcomes. Responses were compared using two-sided t-tests or the F-test. Results: Participants with prolonged HG are slightly younger and weigh more. Pre-existing factors associated with prolonged HG include allergies and a restrictive diet. Prolonged HG is associated with hematemesis, dizziness, fainting and antiemetic treatment. Following pregnancy, those with prolonged HG reported more posttraumatic stress, motion sickness, muscle weakness and infants with irritability, severe colic and growth restriction. Conclusion: Multiple pre-existing conditions and poor maternal and infant outcomes were associated with prolonged HG. The most significant condition prior to pregnancy was allergies suggesting a possible autoimmune component affecting duration of HG. In addition, the most significant lifestyle choice linked to prolonged HG was a restrictive diet. Future research is needed to determine whether a change in diet prior to pregnancy may lead to a shorter duration of HG and its associated outcomes.