Similarity measures of conditional intensity functions to test separability in multidimensional point processes

Separability in the context of multidimensional point processes assumes a multiplicative form for the conditional intensity function. This hypothesis is especially convenient since each component of a separable process may be modeled and estimated individually, and this greatly facilitates model building, fitting, and assessment. This is also related to the problem of reduction in the number of dimensions. Following previous approximations to this problem, we focus on the conditional intensity function, by considering nonparametric kernel-based estimators. Our approach calculates thinning probabilities under the conditions of separability and nonseparability and compares them through divergence measures. Based on Monte Carlo experiments, we approximate the statistical properties of our tests under a variety of practical scenarios. An application on modeling the spatio-temporal first-order intensity of forest fires is also developed.     

Multiscale structure of UXO site characterization: spatial estimation and uncertainty quantification

Unexploded ordnance (UXO) site characterization must consider both how the contamination is generated and how we observe that contamination. Within the generation and observation processes, dependence structures can be exploited at multiple scales. We describe a conceptual site characterization process, the dependence structures available at several scales, and consider their statistical estimation aspects. It is evident that most of the statistical methods that are needed to address the estimation problems are known but their application-specific implementation may not be available. We demonstrate estimation at one scale and propose a representation for site contamination intensity that takes full account of uncertainty, is flexible enough to answer regulatory requirements, and is a practical tool for managing detailed spatial site characterization and remediation. The representation is based on point process spatial estimation methods that require modern computational resources for practical application. These methods have provisions for including prior and covariate information.     

Point process-based modeling of multiple debris flow landslides using INLA: an application to the 2009 Messina disaster

We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a hierarchical Bayesian estimation framework, we can use the integrated nested Laplace approximation methodology to make inference and obtain the posterior estimates of spatially distributed covariate and random effects. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the stronger morphodynamic-oriented slope units. Here we integrate both mapping units into a single hierarchical model, by treating the landslide triggering locations as a random point pattern. This approach diverges fundamentally from the unanimously used presence–absence structure for areal units since we focus on modeling the expected landslide count jointly within the two mapping units. Predicting this landslide intensity provides more detailed and complete information as compared to the classically used susceptibility mapping approach based on relative probabilities. To illustrate the model’s versatility, we compute absolute probability maps of landslide occurrences and check their predictive power over space. While the landslide community typically produces spatial predictive models for landslides only in the sense that covariates are spatially distributed, no actual spatial dependence has been explicitly integrated so far. Our novel approach features a spatial latent effect defined at the slope unit level, allowing us to assess the spatial influence that remains unexplained by the covariates in the model. For rainfall-induced landslides in regions where the raingauge network is not sufficient to capture the spatial distribution of the triggering precipitation event, this latent effect provides valuable imaging support on the unobserved rainfall pattern.     

Spatio-temporal epidemic type aftershock sequence model for Tangshan aftershock sequence

Shallow earthquakes usually show obvious spatio-temporal clustering patterns. In this study, several spatio-temporal point process models are applied to investigate the clustering characteristics of the well-known Tangshan sequence based on classical empirical laws and a few assumptions. The relative fit of competing models is compared by Akaike Information Criterion. The spatial clustering pattern is well characterized by the model which gives the best fit to the data. A simulated aftershock sequence is generated by thinning algorithm and compared with the real seismicity.     

A deformation/blurring-based spatio-temporal model

A key objective in spatio-temporal modeling consists of providing an appropriate representation of complexity in interactive spatio-temporal dynamics inherent to real phenomena. Propagated effect of dynamical spatial deformation provides a meaningful way to describe certain forms of heterogeneous behaviour; in particular, in relation to processes evolving in unstable media, or to account for the possible effect of covariates, to mention some significant interpretations. In this paper, the formulation of a discrete time and continuous space spatio-temporal interaction model with autoregressive dynamics, incorporating the effect of continuous deformation of the spatial support over time, is studied. Among other fields, this approach provides a suitable representation for a variety of geophysical and environmental applications. In particular, a vast family of heterogeneous models is generated from models which display homogeneity in the absence of deformation. Structural characteristics and variability properties, as well as self-consistency conditions for a limiting continuous-time approximation, are analyzed.     

A spatio-temporal climate-based model of early dengue fever warning in southern Taiwan

Dengue Fever (DF) has been identified by the World Health organization (WHO) as one of the most serious vector-borne infectious diseases in tropical and sub-tropical areas. During 2007, in particular, there were over 2,000 DF cases in Taiwan, which was the highest number of cases in the recorded history of Taiwan epidemics. Most DF studies have focused mainly on temporal DF patterns and its close association with climatic covariates, whereas they have understated spatial DF patterns (spatial dependence and clustering) and composite space–time effects. The present study proposes a spatio-temporal DF prediction approach based on stochastic Bayesian Maximum Entropy (BME) analysis. Core and site-specific knowledge bases are considered, including climate and health datasets under conditions of uncertainty, space–time dependence functions, and a Poisson regression model of climatic variables contributing to DF occurrences in southern Taiwan during 2007. The results show that the DF outbreaks in the study area are highly influenced by climatic conditions. Furthermore, the analysis can provide the required “one-week-ahead” outbreak warnings based on spatio-temporal predictions of DF distributions. Therefore, the proposed approach can provide the Taiwan Disease Control Agency with a valuable tool to timely identify, control, and even efficiently prevent DF spreading across space–time.     

A spatio-temporal Poisson hurdle point process to model wildfires

Wildfires have been studied in many ways, for instance as a spatial point pattern or through modeling the size of fires or the relative risk of big fires. Lately a large variety of complex statistical models can be fitted routinely to complex data sets, in particular wildfires, as a result of widely accessible high-level statistical software, such as R. The objective in this paper is to model the occurrence of big wildfires (greater than a given extension of hectares) using an adapted two-part econometric model, specifically a hurdle model. The methodology used in this paper is useful to determine those factors that help any fire to become a big wildfire. Our proposal and methodology can be routinely used to contribute to the management of big wildfires.     

Incorporating the spatio-temporal distribution of rainfall and basin geomorphology into nonlinear analyses of streamflow dynamics

Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been given to the nonlinear dependencies of the two and especially on how the spatio-temporal distribution of rainfall affects the nonlinear dynamics of streamflow at flood time scales. In this paper, a methodology is presented which simultaneously considers streamflow series, spatio-temporal structure of precipitation and catchment geomorphology into a nonlinear analysis of streamflow dynamics. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic spatially extended system rather than a deterministic multivariate one. The methodology is applied to two basins in Central North America using 6-hour streamflow data and radar images for a period of 5 years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between streamflow dynamics and the spatio-temporal dynamics of precipitation; (b) study how streamflow predictability is affected by the trade-offs between the level of detail necessary to explain the spatial variability of rainfall and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) streamflow predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology.     

Monitoring global spatial statistics

The use of global statistics to assess spatial dependence and deviations from spatial randomness often is carried out on a single dataset. However, there are situations where new datasets become available periodically, and it is of interest to determine whether there has been a temporal change point, where a new regime of global spatial autocorrelation has been established. If the global test is simply repeated every time period, change will be often be found by chance alone, even when it has not occurred, due to the multiple hypothesis testing. Cumulative sum methods are introduced as a method for monitoring the global statistics; they address the problem of multiple testing, and are optimal for finding temporal changes in the global spatial statistics. The method is illustrated through an application to data on breast cancer mortality in the northeastern United States.     

Spatio-temporal variability of currents over a mobile dune field in the Dover Strait

A one month field campaign featuring two spring–neap tide cycles and three strong storms has been performed in a mobile dune area located in the central part of the Dover Strait. These dunes are known to move in a complex manner as their migration direction varies in space and time (Le Bot et al., 2000, Le Bot, 2001, Le Bot and Trentesaux, 2004). In order to gain some insights into the dune motion processes we present an analysis of the spatio-temporal variability of currents in the area emphasizing the relative influence of tides and storms. A total of eight different hydro-meteorological regimes have been distinguished during the experiment duration. The analysis of the currents measurements at five locations in the area shows that the eight hydro-meteorological regimes induce very different current responses at the bottom. The residual tidal currents exhibit a significant spatial variability both in direction and in intensity. A numerical model of tidal currents over the Dover Strait confirms the strong spatio-temporal variability of the residual tidal currents featuring three singular points. Amongst them, a saddle point is located just south of the I-dune at the convergence of opposite direction residual tidal currents. The wind-induced currents are almost uniform in space, their intensity and direction however strongly depends on the wind regime and thus on time. The mean total current feature a spatial pattern which can be tidal of wind-induced currents dominated, or either in balance, depending on the regime considered. At the PERMOD campaign time scale, the total current is dominated by the residual tidal current. These results proved to give valuable insights to explain the complex dynamics of dune motion observed in this area by Le Bot et al., 2000, Le Bot, 2001, Le Bot and Trentesaux, 2004 at short and long time scales.     

On some aspects of peaks-over-threshold modeling of floods under nonstationarity using climate covariates

This paper discusses some aspects of flood frequency analysis using the peaks-over-threshold model with Poisson arrivals and generalized Pareto (GP) distributed peak magnitudes under nonstationarity, using climate covariates. The discussion topics were motivated by a case study on the influence of El Niño–Southern Oscillation on the flood regime in the Itajaí river basin, in Southern Brazil. The Niño3.4 (DJF) index is used as a covariate in nonstationary estimates of the Poisson and GP distributions scale parameters. Prior to the positing of parametric dependence functions, a preliminary data-driven analysis was carried out using nonparametric regression models to estimate the dependence of the parameters on the covariate. Model fits were evaluated using asymptotic likelihood ratio tests, AIC, and Q–Q plots. Results show statistically significant and complex dependence relationships with the covariate on both nonstationary parameters. The nonstationary flood hazard measure design life level (DLL) was used to compare the relative performances of stationary and nonstationary models in quantifying flood hazard over the period of records. Uncertainty analyses were carried out in every step of the application using the delta method.     

Spatio-temporal filtering using wavelets

 In this paper, a class of spatio-temporal processes with first-order autoregressive temporal structure and functional spatio-temporal interaction is introduced. The spatial second-order regularity is allowed to change over time and is characterized in terms of fractional Sobolev spaces. The associated filtering problem is considered, assuming that observations are defined by spatial linear functionals of the process of interest, being affected by additive noise. Conditions under which a stable solution to this problem is obtained are studied. A functional least-squares linear estimate fusion method is derived to calculate this solution A multiscale finite-dimensional approximation to the problem is obtained from the wavelet-based orthogonal expansions of the time cross-section spatial processes, which allows the numerical inversion of the linear operator involved.     

Estimating Effective Porosity in Bedrock Aquifers

Flow in many bedrock aquifers is through fracture networks. Point to point tracer tests using applied tracers provide a direct measure of time of travel and are most useful for determining effective porosity. Calculated values from these tests are typically between 10⁻⁴ and 10⁻² (0.01% to 1%), with these low values indicating preferential flow through fracture and channel networks. Tracer tests are not commonly used in site investigations, and specific yield is often used as a proxy for effective porosity. The most popular methods have used centrifuge measurements, water table fluctuations, pumping tests, and packer tests. Specific yield varies substantially with the testing method. No method is as reliable as tracer testing for providing estimates of effective porosity, but all methods provide complementary insights on aquifer structure. Temporal and spatial scaling effects suggest that bedrock aquifers have hierarchical structures, with a network of more permeable fractures and channels, which are connected to less permeable fractures and to the matrix. Consequences of the low effective porosities include groundwater velocities that often exceed 100 m/d and more frequent microbial contamination than in aquifers in unconsolidated sediments. The large uncertainty over the magnitude of effective porosity in bedrock aquifers makes it an important parameter to determine in studies where time of travel is of interest.     

Aseismic base isolation: review and bibliography

The idea that a building can be uncoupled from the damaging effects of the ground movement produced by a strong earthquake has appealed to inventors and engineers for more than a century. Many ingenious devices have been proposed to achieve this result, but very few have been tried and the concept now generally referred to as base isolation or seismic isolation has yet to become acceptable to the engineering profession as a whole. Although most of the proposed systems are unacceptably complicated, in recent years a few practical systems have emerged and have been implemented. While some of these systems have been tested on large-scale shaking tables, none has to date been tested as built by a strong earth tremor. The shake testing and related static testing of full-scale components such as isolation bearings, however, has led to a certain degree of acceptance by the profession and it is possible that the number of practical implementations of base isolation will increase quite dramatically in the next few years.

This review summarizes much of the literature on theoretical aspects of seismic isolation, describes testing programmes and enumerates those isolation systems which have been used in buildings completed or under construction. It describes the characteristics of the various implemented systems with an indication of their range of applicability and some assessment of their development as backed by research. A bibliography of all papers published on the topic from 1900 to 1984 is included. The bibliography is as complete as possible, but, due to the rapid increase in research interest in the topic in the past few years, there may be a substantial degree of omission in the later years.     

Hierarchical spatial modeling of the presence of Chagas disease insect vectors in Argentina. A comparative approach

We modeled the spatial distribution of the most important Chagas disease vectors in Argentina, in order to obtain a predictive mapping method for the probability of presence of the vector species. We analyzed both the binary variable of presence-absence of Chagas disease and the vector species richness in Argentina, in combination with climatic and topographical covariates associated to the region of interest. We used several statistical techniques to produce distribution maps of presence–absence for the different insect species as well as species richness, using a hierarchical Bayesian framework within the context of multivariate geostatistical modeling. Our results show that the inclusion of covariates improves the quality of the fitted models, and that there is spatial interaction between neighboring cells/pixels, so mapping methods used in the past, which assumed spatial independence, are not adequate as they provide unreliable results.     

Pinpointing spatio-temporal interactions in wildfire patterns

The spatial and spatio-temporal patterns of wildfire incidence and their relationship to various geographical and environmental variables are analyzed. Such relationships may be treated as components in particular point process models for wildfire activity. We show some of the techniques for the analysis of point patterns that have become available due to recent developments in point process modeling software. These developments permit convenient exploratory data analysis, model fitting, and model assessment. The discussion of these techniques is conducted jointly with and in the context of the analyses of a collection of data sets which are of considerable interest in their own right. These data sets consist of the complete records of wildfires occurred in Catalonia (north-eastern Spain) during the years 2004–2008.     

Testing the type of non-separability and some classes of space-time covariance function models

In statistical space-time modeling, the use of non-separable covariance functions is often more realistic than separable models. In the literature, various tests for separability may justify this choice. However, in case of rejection of the separability hypothesis, none of these tests include testing for the type of non-separability of space-time covariance functions. This is an important and further significant step for choosing a class of models. In this paper a method for testing positive and negative non-separability is given; moreover, an approach for testing some well known classes of space-time covariance function models has been proposed. The performance of the tests has been shown using real and simulated data.     

Additive versus multiplicative models in ecologic regression

Much research in environmental epidemiology relies on aggregate-level information on exposure to potentially toxic substances and on relevant covariates. We compare the use of additive (linear) and multiplicative (log-linear) regression models for the analysis of such data. We illustrate how both additive and multiplicative models can be fit to aggregate-level data sets in which disease incidence is the dependent variable, and contrast these results with similar models fitted to individual-level data. We find (1) that for aggregate-level data, multiplicative models are more likely than additive models to introduce bias into the estimation of rates, an effect not found with individual-level data; and (2) that under many circumstances multiplicative models reduce the precision of the estimates, an effect also not found in individual-level models. For both additive and multiplicative models of aggregate-level data, we find that, in the presence of covariates, narrow confidence interval are obtained only when two or more antecedent factors are strongly related to the measured covariate and/or the exposure of primary substantive interest. We conclude that the equivalency of fitting additive versus multiplicative models in studies with individual-level binary data does not carry over to studies that analyze aggregate-level information. For aggregate data, we strongly recommend use of additive models. Supported by Grant #1 U19 EH000102 from the National Center for Environmental Health, Centers for Disease Control and Prevention, Atlanta, GA.     

Spatio-temporal modelling of hydro-meteorological derived risk using a Bayesian approach: a case study in Venezuela

Extreme environmental events have considerable impacts on society. Preparation to mitigate or forecast accurately these events is a growing concern for governments. In this regard, policy and decision makers require accurate tools for risk estimation in order to take informed decisions. This work proposes a Bayesian framework for a unified treatment and statistical modeling of the main components of risk: hazard, vulnerability and exposure. Risk is defined as the expected economic loss or population affected as a consequence of a hazard event. The vulnerability is interpreted as the loss experienced by an exposed population due to hazard events. The framework combines data of different spatial and temporal supports. It produces a sequence of temporal risk maps for the domain of interest including a measure of uncertainty for the hazard and vulnerability. In particular, the considered hazard (rainfall) is interpolated from point-based measured rainfall data using a hierarchical spatio-temporal Kriging model, whose parameters are estimated using the Bayesian paradigm. Vulnerability is modeled using zero-inflated distributions with parameters dependent on climatic variables at local and large scales. Exposure is defined as the total population settled in the spatial domain and is interpolated using census data. The proposed methodology was applied to the Vargas state of Venezuela to map the spatio-temporal risk for the period 1970–2006. The framework highlights both high and low risk areas given extreme rainfall events.