Bayesian areal wombling via adjacency modeling

Recently, public health professionals and other geostatistical researchers have shown increasing interest in boundary analysis, the detection or testing of zones or boundaries that reveal sharp changes in the values of spatially oriented variables. For areal data (i.e., data which consist only of sums or averages over geopolitical regions), Lu and Carlin (Geogr Anal 37: 265–285, 2005) suggested a fully model-based framework for areal wombling using Bayesian hierarchical models with posterior summaries computed using Markov chain Monte Carlo (MCMC) methods, and showed the approach to have advantages over existing non-stochastic alternatives. In this paper, we develop Bayesian areal boundary analysis methods that estimate the spatial neighborhood structure using the value of the process in each region and other variables that indicate how similar two regions are. Boundaries may then be determined by the posterior distribution of either this estimated neighborhood structure or the regional mean response differences themselves. Our methods do require several assumptions (including an appropriate prior distribution, a normal spatial random effect distribution, and a Bernoulli distribution for a set of spatial weights), but also deliver more in terms of full posterior inference for the boundary segments (e.g., direct probability statements regarding the probability that a particular border segment is part of the boundary). We illustrate three different remedies for the computing difficulties encountered in implementing our method. We use simulation to compare among existing purely algorithmic approaches, the Lu and Carlin (2005) method, and our new adjacency modeling methods. We also illustrate more practical modeling issues (e.g., covariate selection) in the context of a breast cancer late detection data set collected at the county level in the state of Minnesota.     

Bayesian non-parametric detection heterogeneity in ecological models

Environmental and Ecological Statistics - Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or...     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

Hierarchical Bayesian modelling of early detection surveillance for plant pest invasions

Early detection surveillance programs aim to find invasions of exotic plant pests and diseases before they are too widespread to eradicate. However, the value of these programs can be difficult to justify when no positive detections are made. To demonstrate the value of pest absence information provided by these programs, we use a hierarchical Bayesian framework to model estimates of incursion extent with and without surveillance. A model for the latent invasion process provides the baseline against which surveillance data are assessed. Ecological knowledge and pest management criteria are introduced into the model using informative priors for invasion parameters. Observation models assimilate information from spatio-temporal presence/absence data to accommodate imperfect detection and generate posterior estimates of pest extent. When applied to an early detection program operating in Queensland, Australia, the framework demonstrates that this typical surveillance regime provides a modest reduction in the estimate that a surveyed district is infested. More importantly, the model suggests that early detection surveillance programs can provide a dramatic reduction in the putative area of incursion and therefore offer a substantial benefit to incursion management. By mapping spatial estimates of the point probability of infestation, the model identifies where future surveillance resources can be most effectively deployed.     

Flexible modeling for stock-recruitment relationships using Bayesian nonparametric mixtures

The stock and recruitment relationship is fundamental to the management of fishery natural resources. However, inferring stock-recruitment relationships is a challenging problem because of the limited available data, the collection of plausible models, and the biological characteristics that should be reflected in the model. Motivated by limitations of traditional parametric stock-recruitment models, we propose a Bayesian nonparametric approach based on a mixture model for the joint distribution of log-reproductive success and stock biomass. Flexible mixture modeling for this bivariate distribution yields rich inference for the stock-recruitment relationship through the implied conditional distribution of log-reproductive success given stock biomass. The method is illustrated with cod data from six regions of the North Atlantic, including comparison with simpler Bayesian parametric and semiparametric models.     

Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling

Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery et al. Mon Weather Rev 133:1155–1174, 2005) has recommended the Expectation–Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model streamflow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.     

无公害农业与合理施肥

滥施肥料是造成环境污染、农产品质量下降的原因。施用化肥与无公害农业并不矛盾，无公害农业更需要优质的化肥。化肥在无公害农业中的作用是不可替代的。只要科学地选择肥料和科学地施用肥料，使有机肥料与化肥有机地结合，使营养元素全面而平衡，不但不会对环境带来污染，而且能改善土壤微生态环境和人类的生存环境，提高农产品的产量和质量，有益于人类的健康。     

Bayesian Ecological Regression with Latent Factors: Atmospheric Pollutants Emissions and Mortality for Lung Cancer

In this work we propose a Bayesian ecological analysis in which a latent variable summarizes data on emissions of atmospheric pollutants. We specified a hierarchical Bayesian model with spatially structured and unstructured random terms with a nested latent factor model. This can be considered a combination of the convolution spatial model of Besag et al. (1991) and an ecological regression analysis in which a latent variable plays the role of the covariate. The unified approach allows to proper account for the uncertainty in the latent score estimation in the regression analysis. The Bayesian Latent Factor model is used to summarize the information on environmental pressure derived from three stressors: Carbon Monoxide, Nitrogen Oxides and Inhalable Particles. We found evidence of positive correlation between Lung cancer mortality and environmental pressure indicators, in males, Tuscany (Italy), 1995–1999. Environmental pressure seems to be restricted to fourteen municipalities (top 5% of the Latent Factor distribution). The model identified two areas with high point source emissions.     

Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach

Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.     

Predicting arsenic concentration in groundwater of Bangladesh using Bayesian geostatistical model

The pattern of the spatial variation in arsenic concentration in groundwater of Bangladesh is usually needed for the planning of safe drinking water. Often a model-based prediction is required for this purpose. In this paper, we fit a Bayesian hierarchical geostatistical model by utilizing data from the project, ‘Groundwater studies of arsenic concentration in Bangladesh’ conducted by the British Geological Survey and the Department of Public Health Engineering of Bangladesh. We also develop a predictive model for arsenic concentration at different levels of well-depth using the same approach. The resulting predictive model has been cross-validated by appropriate statistical tools. Finally, we obtained reliable spatially continuous predictive maps and predictive probability maps showing the areas with high probability of arsenic concentration for different levels of well-depth. Results indicate that our model fits the data well and captures a substantial amount of spatial variation. Moreover, well-depth is found to have a significant contribution in explaining the observed variation in arsenic concentration. The predictive maps that have been produced are observed to be different for various levels of well-depths and are expected to be helpful to the policy makers in preparing proper regional planning for safe drinking water.     

Bayesian estimation of species relative abundances and habitat preferences using opportunistic data

We develop a new statistical procedure to monitor relative species abundances and their respective preferences for different habitat types, using opportunistic data. Following Giraud et al. (Biometrics 72(2):649–658, 2015), we combine the opportunistic data with some standardized data in order to correct the bias inherent to the opportunistic data collection. Species observations are modeled by Poisson distributions whose parameters quantify species abundances and habitat preferences, and are estimated using Bayesian computations. Our main contributions are (i) to tackle the bias induced by habitat selection behaviors, (ii) to handle data where the habitat type associated to each observation is unknown, (iii) to estimate probabilities of selection of habitat for the species. As an illustration, we estimate common bird species habitat preferences and abundances in the region of Aquitaine (France).     

Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian kriged Kalman model

This article describes the hierarchical Bayesian approach for predicting average hourly concentrations of ambient non-methane hydrocarbons (NMHC) in Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to predict the concentration level of NMHC in unmonitored areas. Here an attempt is made for the prediction of unmeasured concentration of NMHC at two additional locations in Kuwait. We will implement a kriged Kalman filter (KKF) hierarchical Bayesian approach assuming a Gaussian random field, a technique that allows the pooling of data from different sites in order to predict the exposure of the NMHC in different regions of Kuwait. In order to increase the accuracy of the KKF we will use other statistical models such as imputation, regression, principal components, and time series analysis in our approach. We considered four different types of imputation techniques to address the missing data. At the primary level, the logarithmic field is modeled as a trend plus Gaussian stochastic residual model. The trend model depends on hourly meteorological predictors which are common to all sites. The residuals are then modeled using KKF, and the prediction equation is derived conditioned on adjoining hours. On this basis we developed a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales, we can impute Kuwait’s hourly non-methane hydrocarbons field.     

Modelling the dynamics of coral reef macroalgae using a Bayesian belief network approach

Macroalgae are a major benthic component of coral reefs and their dynamics influence the resilience of coral reefs to disturbance. However, the relative importance of physical and ecological processes in driving macroalgal dynamics is poorly understood. Here we develop a Bayesian belief network (BBN) model to integrate many of these processes and predict the growth of coral reef macroalgae. Bayesian belief networks use probabilistic relationships rather than deterministic rules to quantify the cause and effect assumptions. The model was developed using both new empirical data and quantified relationships elicited from previous studies. We demonstrate the efficacy of the BBN to predict the dynamics of a common Caribbean macroalgal genus Dictyota. Predictions of the model have an average accuracy of 55% (implying that 55% of the predicted categories of Dictyota cover were assigned to the correct class). Sensitivity analysis suggested that macroalgal dynamics were primarily driven by top–down processes of grazing rather than bottom–up nutrification. BBNs provide a useful framework for modelling complex systems, identifying gaps in our scientific understanding and communicating the complexities of the associated uncertainties in an explicit manner to stakeholders. We anticipate that accuracies will improve as new data are added to the model.     

Bayesian estimation of European sulphur emissions using monitoring data and an acid deposition model

A statistical method for estimating national emissions of acidifying air pollutants in Europe is presented. The method uses an acid deposition model to match official emissions data from European countries and measured depositions from a monitoring network. An application to 1990 sulphate data demonstrates the method and suggests some tendencies in the reported emissions. The proposed framework may prove useful for verifying national compliance with emissions standards, and the method should be applicable also to other substances than sulphur dioxide. The problem of designing an optimal monitoring network may also be assessed within the proposed statistical framework.     

Modelling cheetah relocation success in southern Africa using an Iterative Bayesian Network Development Cycle

Relocation is one of the strategies used by conservationists to deal with problem cheetahs in southern Africa. The success of a relocation event and the factors that influence it within the broader context of long-term viability of wild cheetah metapopulations was the focus of a Bayesian Network (BN) modelling workshop in South Africa. Using a new heuristics, Iterative Bayesian Network Development Cycle (IBNDC), described in this paper, several networks were formulated to distinguish between the unique relocation experiences and conditions in Botswana and South Africa. There were many common underlying factors, despite the disparate relocation strategies and sites in the two countries. The benefit of relocation BNs goes beyond the identification and quantification of the factors influencing the success of relocations and population viability. They equip conservationists with a powerful communication tool in their negotiations with land and livestock owners, which is key to the long-term survival of cheetahs in southern Africa. Importantly, the IBNDC provides the ecological modeller with a methodological process that combines several BN design frameworks to facilitate the development of a BN in a multi-expert and multi-field domain.     

Modelling dependence structures of extreme wind speed using bivariate distribution: a Bayesian approach

When investigating extremes of weather variables, it is seldom that a single weather station determines the damage, and extremes may be caused from the combined behaviour of several weather stations. To investigate joint dependence of extreme wind speed, a bivariate generalised extreme value distribution (BGEVD) was considered from frequentist and Bayesian approaches to analyse the extremes of component-wise monthly maximum wind speed at selected weather stations in South Africa. In the frequentist approach, the parameters of extreme value distributions (EVDs) were estimated with maximum likelihood, whereas in the Bayesian approach the Markov Chain Monte Carlo (MCMC) technique was used with the Metropolis–Hastings algorithm. The results showed that when fitted to component-wise maxima of extreme weather variables, the BGEVD provided apparent benefits over the univariate method, which allowed information to be pooled across stations and resulted in improved precision of the estimates for the parameters and return levels of the distributions. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from weather characteristics of four pairs of surrounding weather stations at various distances. The results from the Bayesian analysis showed that posterior inference might be affected by the choice of priors that were used to formulate the informative priors. From the results, it could be inferred that the Bayesian approach provides a satisfactory estimation strategy in terms of precision, compared with the frequentist approach, because it accounts for uncertainty in parameters and return level estimations.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Estimating metabolic rate for butadiene at steady state using a Bayesian physiologically-based pharmacokinetic model

In a study of 133 volunteer subjects, demographic, physiologic and pharmacokinetic data through exposure to 1,3-Butadiene (BD) were collected in order to estimate the percentage of BD concentration metabolized at steady state, and to determine whether this percentage varies across gender, racial, and age groups. During the 20 min of continuous exposure to 2 parts per million (ppm) of BD, five measurements of exhaled concentration were made on each subject. In the following 40 min washout period, another five measurements were collected. A Bayesian hierarchical compartmental physiologically-based pharmacokinetic model (PKPB) was used. Using prior information on the model parameters, Markov Chain Monte Carlo (MCMC) simulation was conducted to obtain posterior distributions. The overall estimate of the mean percent of BD metabolized at steady state was 12.7% (95% credible interval: 7.7–17.8%). There was no significant difference in gender with males having a mean of 13.5%, and females 12.3%. Among the racial groups, Hispanic (13.9%), White (13.0%), Asian (12.1%), and Black (10.9%), the significant difference came from the difference between Black and Hispanic with a 95% credible interval from −5.63 to −0.30%. Those older than 30 years had a mean of 12.2% versus 12.9% for the younger group; although this was not a statistically significant difference. Given a constant inhalation input of 2 ppm, at steady state, the overall mean exhaled concentration was estimated to be 1.75ppm (95% credible interval: 1.64–1.84). An equivalent parameter, first-order metabolic rate constant, was also estimated and found to be consistent with the percent of BD metabolized at steady state across gender, race, and age strata.     

Space-time Bayesian small area disease risk models: development and evaluation with a focus on cluster detection

This paper extends the spatial local-likelihood model and the spatial mixture model to the space-time (ST) domain. For comparison, a standard random effect space-time (SREST) model is examined to allow evaluation of each model’s ability in relation to cluster detection. To pursue this evaluation, we use the ST counterparts of spatial cluster detection diagnostics. The proposed criteria are based on posterior estimates (e.g., misclassification rate) and some are based on post-hoc analysis of posterior samples (e.g., exceedance probability). In addition, we examine more conventional model fit criteria including mean square error (MSE). We illustrate the methodology with a real ST dataset, Georgia throat cancer mortality data for the years 1994–2005, and a simulated dataset where different levels and shapes of clusters are embedded. Overall, it is found that conventional SREST models fair well in ST cluster detection and in goodness-of-fit, while for extreme risk detection the local likelihood ST model does best.     

Bayesian spatial prediction

This paper presents a complete Bayesian methodology for analyzing spatial data, one which employs proper priors and features diagnostic methods in the Bayesian spatial setting. The spatial covariance structure is modeled using a rich class of covariance functions for Gaussian random fields. A general class of priors for trend, scale, and structural covariance parameters is considered. In particular, we obtain analytic results that allow easy computation of the predictive distribution for an arbitrary prior on the parameters of the covariance function using importance sampling. The computations, as well as model diagnostics and sensitivity analysis, are illustrated with a set of precipitation data.