Search

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as wombling boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the meshed Gaussian process (MGP). A major contribution is the development of an MGPs on tessellated domains, accompanied by a Gibbs sampler for the efficient recovery of spatial random effects. In particular, the cubic MGP (Q-MGP) can harness high-performance computing resources by executing all large-scale operations in parallel within the Gibbs sampler, improving mixing and computing time compared to sequential updating schemes. Unlike some existing models for large spatial data, a Q-MGP facilitates massive caching of expensive matrix operations, making it particularly apt in dealing with spatiotemporal remote-sensing data. We compare Q-MGPs with large synthetic and real world data against state-of-the-art methods. We also illustrate using Normalized Difference Vegetation Index data from the Serengeti park region to recover latent multivariate spatiotemporal random effects at millions of locations. The source code is available at github.com/mkln/meshgp. for this article are available online. [ABSTRACT FROM AUTHOR]

Let Graph HT ht be a dynamic spatial process denoting the energy consumption for household I i i within a geographically referenced "location" I s i on day I t i . Alternatively, if a joint spatial-temporal process for energy consumption Graph HT ht and nightlight data Graph HT ht is specified at every point-referenced location I s i , then model-based uncertainty quantification will be possible at arbitrary scales using either spatial interpolation or "kriging" (Stein [6]) or using stochastic sums or averaging over grid blocks as the case may be. [Extracted from the article]

Exposure assessment models are deterministic models derived from physical–chemical laws. In real workplace settings, chemical concentration measurements can be noisy and indirectly measured. In addition, inference on important parameters such as generation and ventilation rates are usually of interest since they are difficult to obtain. In this article, we outline a flexible Bayesian framework for parameter inference and exposure prediction. In particular, we devise Bayesian state space models by discretizing the differential equation models and incorporating information from observed measurements and expert prior knowledge. At each time point, a new measurement is available that contains some noise, so using the physical model and the available measurements, we try to obtain a more accurate state estimate, which can be called filtering. We consider Monte Carlo sampling methods for parameter estimation and inference under nonlinear and non-Gaussian assumptions. The performance of the different methods is studied on computer-simulated and controlled laboratory-generated data. We consider some commonly used exposure models representing different physical hypotheses. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider alternate formulations of recently proposed hierarchical nearest neighbor Gaussian process (NNGP) models for improved convergence, faster computing time, and more robust and reproducible Bayesian inference. Algorithms are defined that improve CPU memory management and exploit existing high-performance numerical linear algebra libraries. Computational and inferential benefits are assessed for alternate NNGP specifications using simulated datasets and remotely sensed light detection and ranging data collected over the U.S. Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska. The resulting data product is the first statistically robust map of forest canopy for the TIU. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations becomes large. There is a burgeoning literature on approaches for analyzing large spatial datasets. In this article, we propose a divide-and-conquer strategy within the Bayesian paradigm. We partition the data into subsets, analyze each subset using a Bayesian spatial process model, and then obtain approximate posterior inference for the entire dataset by combining the individual posterior distributions from each subset. Importantly, as often desired in spatial analysis, we offer full posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. We call this approach “spatial meta-kriging” (SMK). We do not need to store the entire data in one processor, and this leads to superior scalability. We demonstrate SMK with various spatial regression models including Gaussian processes with Matern and compactly supported correlation functions. The approach is intuitive, easy to implement, and is supported by theoretical results presented in the supplementary material available online. Empirical illustrations are provided using different simulation experiments and a geostatistical analysis of Pacific Ocean sea surface temperature data. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

In industrial hygiene, a worker’s exposure to chemical, physical, and biological agents is increasingly being modeled using deterministic physical models that study exposures near and farther away from a contaminant source. However, predicting exposure in the workplace is challenging and simply regressing on a physical model may prove ineffective due to biases and extraneous variability. A further complication is that data from the workplace are usuallymisaligned. This means that not all timepoints measure concentrations near and far from the source. We recognize these challenges and outline a flexible Bayesian hierarchical framework to synthesize the physical model with the field data. We reckon that the physical model, by itself, is inadequate for enhanced inferential and predictive performance and deploy (multivariate) Gaussian processes to capture uncertainties and associations. We propose rich covariance structures for multiple outcomes using latent stochastic processes. This article has supplementary material available online. [ABSTRACT FROM AUTHOR]

Results are presented from a study that investigated the effect of data interpretation training on exposure judgment accuracy of industrial hygienists across several companies in different industry sectors. Participating companies provided monitoring information on specific exposure tasks. Forty-nine hygienists from six companies participated in the study, and 22 industrial tasks were evaluated. The number of monitoring data points for individual tasks varied between 5 and 24. After reviewing all available basic characterization information for the job, task, and chemical, hygienists were asked to provide their judgment on the probability of the 95th percentile of the underlying exposure distribution being located in one of four exposure categories relative to the occupational exposure limit as outlined in the AIHA® exposure assessment strategy. Ninety-three qualitative judgments (i.e., without reviewing monitoring data) and 2142 quantitative judgments (i.e., those made after reviewing monitoring data) were obtained. Data interpretation training, with simple rules of thumb for estimating 95th percentiles, was provided to all hygienists. A data interpretation test was administered before and after training. All exposure task judgments were collected before and after training. Data interpretation test accuracy for the hygienists increased from 48% to 67% after training (p < 0.001) and a significant underestimation bias was removed. Hygienist quantitative task judgment accuracy improved from 46% to 69% (p < 0.001) post-training. Accuracy results showed good improvement in industrial hygienists’ quantitative judgments as a result of training. Hence, the use of statistical tools is promoted to improve judgments based on monitoring data and provide feedback and calibration to improve qualitative judgments. It may be worthwhile to develop standard training programs to improve exposure judgments. [ABSTRACT FROM AUTHOR]

This study examines the impact of several experience and education determinants on exposure judgment accuracy. The study used desktop assessments performed on several different tasks with different exposure profiles to identify correlations between determinants and judgment accuracy using logistic regression models. The exposure judgments were elicited from industrial hygienists with varying levels of experience, education, and training. Videos and written and oral information about the exposure tasks were presented to all participants as they documented a series of qualitative and quantitative exposure judgment probabilities in four exposure categories. Participants (n = 77) first documented their qualitative and then their quantitative exposure assessments after receiving the series of sampling data points. Data interpretation tests and training in simple rules-of-thumb for data interpretation were also given to each participant to investigate the impact of data interpretation skills on exposure judgment accuracy. Logistic regression analysis indicated “years of exposure assessment experience” (p < 0.05), “highest EHS degree” (p < 0.05), and a participant's “data interpretation test score” (p < 0.05) directly impacted qualitative exposure judgment accuracy. Logistic regression models of quantitative judgment accuracy showed positive correlation with “greater than 10 years of exposure assessment experience” (p < 0.05), “highest EHS degree” (p < 0.05), a participant's “data interpretation test score” (p < 0.001), rules-of-thumb data interpretation training (p < 0.001), and the number of sample data points available for a judgment (p < 0.005). Analyzing judgments in subsets for participants with less or more than 10 years’ experience indicated additional correlations with Certified Industrial Hygienist and Certified Safety Professional certifications, total number of task exposure assessments, and career number of air surveys. The correlation of qualitative and quantitative exposure judgment accuracy with “greater than 10 years experience” supports similar research findings from other fields. The results of this study indicate that several determinants of experience, education, and training, in addition to the availability of sampling data, significantly impact the accuracy of exposure assessments. The findings also suggest methods for enhancing exposure judgment accuracy through statistical tools, mathematical exposure modeling, and specific training. [ABSTRACT FROM PUBLISHER]

This paper draws on the experiences of Indian-origin groups in the USA and UK to examine transnational forms of ethnicity. It focuses specifically on ethnic organisations that are engaged in constructing transnational ethnic identities, using religion as a means for constructing new, virtually linked communities. Based on web-based data of Hindu student groups in the USA and UK, this study examines transnational ethnic identities these groups deploy on their websites, and to what extent these are similar across the USA and UK. As Hinduism is a religion with no uniform sets of practices (chosen religious texts, practices and beliefs are culturally, regionally and family dependent), it provides a good basis for examining whether the identities constructed by these groups are transnational, that is, the same elements are emphasised by groups in the two countries to construct ethnic identities that transcend the specificities of the national and local contexts. It also examines the structure of links between websites to show whether websites that appear to be nation-specific are actually linked to each other to create a transnational network. The findings of this study suggest that the study of transnationalism needs to be extended beyond the current focus on ‘home’ and ‘host’ countries to consider what happens in multiple ‘host’ countries. It also shows that organised groups promote homogenised versions of virtual ethnicity as they build transnational networks across countries. [ABSTRACT FROM PUBLISHER]

This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest. Direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several thousand iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negates the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects we discuss a multivariate predictive process that reduces the computational burden by projecting the original process onto a subspace generated by realizations of the original process at a specified set of locations (or knots). We illustrate the proposed methods using a synthetic dataset with multivariate additive and dominant genetic effects and anisotropic spatial residuals, and a large dataset from a scots pine ( Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability. [ABSTRACT FROM AUTHOR]

House dust samples were collected up to six times over a 1-year period to explore seasonal variability of individual fungal genera in inner-city households in Minneapolis, Minnesota. General linear mixed-effects models were used to explore the variability of 13 fungal genera (Cladosporium, yeasts, Aureobasidium, Alternaria, Penicillium, Epicoccum, Mucor, Rhodotorula, Aspergillus, sterile fungi, Phoma, Pithomyces, and Fusarium) found in more than 20% of total dust samples. The five most common fungi (% of samples detected) were Cladosporium (81%), yeasts (63%), Aureobasidium (57%), Alternaria (56%), and Penicillium (55%), with the remaining genera found in 20-50% of the samples. When expressed as frequency of occurrence (%), genus fraction of total fungal concentration (%), or concentration of individual genera (CFU/g), these five genera also varied substantially by season. In contrast, Aureobasidium, Fusarium, and Mucor levels remained relatively constant throughout the year. The observed concentrations of the five most common fungal genera were higher than levels associated with increased respiratory symptoms reported in previous studies. Our results indicate that seasonal variability in common fungal genera is large: within-home to between-home variance ratios of Penicillium (4.1), Alternaria (4.9), Cladosporium (7.1), and yeasts (20.3) were substantially larger than that observed for total fungi (2.5). These results suggest that future studies attempting to link individual fungal genera to health effects need to characterize and control for this seasonal variability. [ABSTRACT FROM AUTHOR]

With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, lbrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in Underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework's ability to distinguish among underlying mechanisms that lead to relapse and cure. [ABSTRACT FROM AUTHOR]

Large-scale inference for random spatial surfaces over a region using spatial process models has been well studied. Under such models, local analysis of the surface (e.g., gradients at given points) has received recent attention. A more ambitious objective is to move from points to curves, to attempt to assign a meaningful gradient to a curve. For a point, if the gradient in a particular direction is large (positive or negative), then the surface is rapidly increasing or decreasing in that direction. For a curve, if the gradients in the direction orthogonal to the curve tend to be large, then the curve tracks a path through the region where the surface is rapidly changing. In the literature, learning about where the surface exhibits rapid change is called wombling, and a curve such as we have described is called a wombling boundary. Existing wombling methods have focused mostly on identifying points and then connecting these points using an ad hoc algorithm to create curvilinear wombling boundaries. Such methods are not easily incorporated into a statistical modeling setting. The contribution of this article is to formalize the notion of a curvilinear wombling boundary in a vector analytic framework using parametric curves and to develop a comprehensive statistical framework for curvilinear boundary analysis based on spatial process models for point-referenced data. For a given curve that may represent a natural feature (e.g., a mountain, a river, or a political boundary), we address the issue of testing or assessing whether it is a wombling boundary. Our approach is applicable to both spatial response surfaces and, often more appropriately, spatial residual surfaces. We illustrate our methodology with a simulation study, a weather dataset for the state of Colorado, and a species presence/absence dataset from Connecticut. [ABSTRACT FROM AUTHOR]

A model is presented for applying Bayesian statistical techniques to the problem of determining, from the usual limited number of exposure measurements, whether the exposure profile for a similar exposure group can be considered a Category 0, 1, 2, 3, or 4 exposure. The categories were adapted from the AIHA exposure category scheme and refer to (0) negligible or trivial exposure (i.e., the true X 0.95 < 1%OEL), (1) highly controlled (i.e., X 0.95 < 10%OEL), (2) well controlled (i.e., X 0.95 < 50%OEL), (3) controlled (i.e., X 0.95 < 100%OEL), or (4) poorly controlled (i.e., X0.95 > 1%OEL) exposures. Unlike conventional statistical methods applied to exposure data, Bayesian statistical techniques can be adapted to explicitly take into account professional judgment or other sources of information. The analysis output consists of a distribution (i.e., set) of decision probabilities: e.g., 1%, 80%, 12%, 5%, and 2% probability that the exposure profile is a Category 0, 1, 2, 3, or 4 exposure. By inspection of these decision probabilities, rather than the often difficult to interpret point estimates (e.g., the sample 95th percentile exposure) and confidence intervals, a risk manager can be better positioned to arrive at an effective (i.e., correct) and efficient decision. Bayesian decision methods are based on the concepts of prior, likelihood, and posterior distributions of decision probabilities. The prior decision distribution represents what an industrial hygienist knows about this type of operation, using professional judgment; company, industry, or trade organization experience; historical or surrogate exposure data; or exposure modeling predictions. The likelihood decision distribution represents the decision probabilities based on an analysis of only the current data. The posterior decision distribution is derived by mathematically combining the functions underlying the prior and likelihood decision distributions, and represents the final decision probabilities. Advantages of Bayesian decision analysis include: (a) decision probabilities are easier to understand by risk managers and employees; (b) prior data, professional judgment, or modeling information can be objectively incorporated into the decision-making process; (c) decisions can be made with greater certainty; (d) the decision analysis can be constrained to a more realistic 'parameter space' (i.e., the range of plausible values for the true geometric mean and geometric standard deviation); and (e) fewer measurements are necessary whenever the prior distribution is well defined and the process is fairly stable. Furthermore, Bayesian decision analysis provides an obvious feedback mechanism that can be used by an industrial hygienist to improve professional judgment. For example, if the likelihood decision distribution is inconsistent with the prior decision distribution then it is likely that either a significant process change has occurred or the industrial hygienist's initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation. [ABSTRACT FROM AUTHOR]

For point-referenced spatial data, we often create explanatory models that introduce regression structure with error consisting of a spatial term and a white noise term. Here we consider more flexible regression structures that allow spatially varying regression coefficients. The resulting mean becomes a spatial response surface that is a linear combination of the components of the spatially varying coefficient vector. Of possible interest in this setting would be gradients associated with the coefficient surfaces as well as the mean surface. Gradients could be sought at arbitrary points and in arbitrary directions. Extending ideas developed in earlier work, we obtain a fully inferential approach within the Bayesian framework for examining such gradients. In particular, we can obtain posterior distributions for any such gradient, for the direction of maximal gradient, and for the magnitude of the maximal gradient. The motivation for our work is the desire to examine urban land value gradients. There is considerable literature in the real estate community on economic theory, modeling, and data analysis relating urban land values to distance from the city center. Here we focus on gradients to such surfaces. The flexibility of our approach allows for much richer insights into the behavior of such gradients than was available previously. We illustrate by fitting a portion of Olcott's classic Chicago land value data. [ABSTRACT FROM AUTHOR]

This article presents measurements of biological contaminants in two elementary schools that serve inner city minority populations. One of the schools is an older building; the other is newer and was designed to minimize indoor air quality problems. Measurements were obtained for airborne fungi, carpet loadings of dust mite allergens, cockroach allergens, cat allergens, and carpet fungi. Carbon dioxide concentrations, temperature, and relative humidity were also measured. Each of these measurements was made in five classrooms in each school over three seasons—fall, winter, and spring. We compared the indoor environments at the two schools and examined the variability in measured parameters between and within schools and across seasons. A fixed-effects, nested analysis was performed to determine the effect of school, season, and room-within-school, as well as CO2, temperature and relative humidity. The levels of all measured parameters were comparable for the two schools. Carpet culturable fungal concentrations and cat allergen levels in the newer school started and remained higher than in the older school over the study period. Cockroach allergen levels in some areas were very high in the newer school and declined over the study period to levels lower than the older school. Dust mite allergen and culturable fungal concentrations in both schools were relatively low compared with benchmark values. The daily averages for temperature and relative humidity frequently did not meet ASHRAE guidelines in either school, which suggests that proper HVAC and general building operation and maintenance procedures are at least as important as proper design and construction for adequate indoor air quality. The results show that for fungi and cat allergens, the school environment can be an important exposure source for children. [ABSTRACT FROM AUTHOR]

Focuses on spherical trigonometry with orthogonal projectors. Use of linear algebra; Two basic laws of a spherical angle; Properties of orthogonal projectors in Euclidean spaces; Derivations of the spherical laws of cosine and sine.

Spatial process models are now widely used for inference in many areas of application. In such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction. Examples include temperature or rainfall gradients in meteorology, pollution gradients for environmental data, and surface roughness assessment for digital elevation models. Because the spatial surface is viewed as a random realization, all such rates of change are random as well. We formalize the notions of directional finite difference processes and directional derivative processes building upon the concept of mean square differentiability as developed by Stein and Banerjee and Gelfand. We obtain complete distribution theory results under the assumptions of a stationary Gaussian process model either for the data or for spatial random effects. We present inference under a Bayesian framework which, in this setting, presents several advantages. Finally, we illustrate our methodology with a simulated dataset and also with a real estate dataset consisting of selling prices of individual homes. [ABSTRACT FROM AUTHOR]

In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly all of this work, the regression coefficients are assumed to be constant over the region. However, in some applications, coefficients are expected to vary at the local or subregional level. Here we focus on the local case. Although parametric modeling of the spatial surface for the coefficient is possible, here we argue that it is more natural and flexible to view the surface as a realization from a spatial process. We show how such modeling can be formalized in the context of Gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal setting. We illustrate both static and dynamic modeling with a dataset that attempts to explain (log) selling price of single-family houses. [ABSTRACT FROM AUTHOR]