Comparing the performances of Diggle's tests of spatial randomness for small samples with and without edge-effect correction: application to ecological data

Diggle's tests of spatial randomness based on empirical distributions of interpoint distances can be performed with and without edge-effect correction. We present here numerical results illustrating that tests without the edge-effect correction proposed by Diggle (1979, Biometrics 35, 87-101) have a higher power for small sample sizes than those with correction. Ignoring the correction enables detection of departure from spatial randomness with smaller samples (down to 10 points vs. 30 points for the tests with correction). These results are confirmed by an example with ecological data consisting of maps of two species of trees in a West African savanna. Tree numbers per species per map were often less than 20. For one of the species, for which maps strongly suggest an aggregated pattern, tests without edge-effect correction enabled rejection of the null hypothesis on three plots out of five vs. on only one for the tests with correction.     

Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets

Summary .  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. Direct application of such models to large spatial datasets are, however, 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 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 negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein–Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, 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.     

Bayesian partitioning for estimating disease risk

This paper presents a Bayesian nonlinear approach for the analysis of spatial count data. It extends the Bayesian partition methodology of Holmes, Denison, and Mallick (1999, Bayesian partitioning for classification and regression, Technical Report, Imperial College, London) to handle data that involve counts. A demonstration involving incidence rates of leukemia in New York state is used to highlight the methodology. The model allows us to make probability statements on the incidence rates around point sources without making any parametric assumptions about the nature of the influence between the sources and the surrounding location.     

Proper multivariate conditional autoregressive models for spatial data analysis

In the past decade conditional autoregressive modelling specifications have found considerable application for the analysis of spatial data. Nearly all of this work is done in the univariate case and employs an improper specification. Our contribution here is to move to multivariate conditional autoregressive models and to provide rich, flexible classes which yield proper distributions. Our approach is to introduce spatial autoregression parameters. We first clarify what classes can be developed from the family of Mardia (1988) and contrast with recent work of Kim et al. (2000). We then present a novel parametric linear transformation which provides an extension with attractive interpretation. We propose to employ these models as specifications for second-stage spatial effects in hierarchical models. Two applications are discussed; one for the two-dimensional case modelling spatial patterns of child growth, the other for a four-dimensional situation modelling spatial variation in HLA-B allele frequencies. In each case, full Bayesian inference is carried out using Markov chain Monte Carlo simulation.     

Monte Carlo-based assessment of the trade-off between spatial resolution,field-of-view and scattered radiation in the variable resolution X-ray CT scanner

ObjectiveThe purpose of this work is to evaluate the impact of optimization of magnification on performance parameters of the variable resolution X-ray (VRX) CT scanner.MethodsA realistic model based on an actual VRX CT scanner was implemented in the GATE Monte Carlo simulation platform. To evaluate the influence of system magnification, spatial resolution, field-of-view (FOV) and scatter-to-primary ratio of the scanner were estimated for both fixed and optimum object magnification at each detector rotation angle. Comparison and inference between these performance parameters were performed angle by angle to determine appropriate object position at each opening half angle.ResultsOptimization of magnification resulted in a trade-off between spatial resolution and FOV of the scanner at opening half angles of 90°–12°, where the spatial resolution increased up to 50% and the scatter-to-primary ratio decreased from 4.8% to 3.8% at a detector angle of about 90° for the same FOV and X-ray energy spectrum. The disadvantage of magnification optimization at these angles is the significant reduction of the FOV (up to 50%). Moreover, magnification optimization was definitely beneficial for opening half angles below 12° improving the spatial resolution from 7.5 cy/mm to 20 cy/mm. Meanwhile, the FOV increased by more than 50% at these angles.ConclusionIt can be concluded that optimization of magnification is essential for opening half angles below 12°. For opening half angles between 90° and 12°, the VRX CT scanner magnification should be set according to the desired spatial resolution and FOV.     

Rank-based tests for dose finding in nonmonotonic dose-response settings

Lim and Wolfe (1997, Biometrics 53, 410-418) proposed rank-based multiple test procedures for identifying the dose levels that are more effective than the zero-dose control in randomized complete block designs when it can be assumed that the efficacy of the increasing dose levels is monotonically increasing up to a point, followed by a monotonic decrease. Modifications of the Lim-Wolfe tests are suggested that provide more practical and powerful alternatives. Two numerical examples are illustrated and the results of a Monte Carlo power study are presented.     

Emission sources and probabilistic health risk of volatile organic compounds emitted from production areas in a petrochemical refinery in Hainan,China

Abstract

The emission sources and health risks of volatile organic compounds (VOCs) were analyzed and evaluated in a typical petrochemical refinery in Hainan, China. The sources and levels of 9 VOCs in five production areas were identified and qualified, and the probabilistic risk assessment method was employed to obtain more reasonable and scientific outcomes specifically realized by inhalation risk model and Monte Carlo simulation. Sensitivity and uncertainty analysis were also conducted to determine the influential factors in the risk evaluation process. The results indicated that for the refinery benzene, toluene, ethyl benzene, and xylene were the primary pollutants in these production areas, where the aromatic hydrocarbon extraction device (AHED) and xylene fractionation device areas are main contributors. In terms of non-carcinogenic risk, the largest hazard index existed in AHED area. The non-carcinogenic risk values for all production areas were not more than 1. The risk value of substances such as benzene still exceed the carcinogenic risk value of 10^?6, indicating these substances existed potential carcinogenic risk to workers. Meanwhile, the findings can help to accumulate basic data for VOCs research in different installations of refineries, and provide evidence for VOCs pollution prevention and control.     

Bayesian detection and modeling of spatial disease clustering

Many current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about specific models for spatial clustering. The proposed methodology incorporates ideas from image analysis, from Bayesian model averaging, and from model selection. With our approach, we obtain estimates for disease rates and allow for greater flexibility in both the type of clusters and the number of clusters that may be considered. We illustrate the proposed procedure through simulation studies and an analysis of the well-known New York leukemia data.     

The use of score tests for inference on variance components

Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.     

A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking.In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level.The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.