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Forest and land fires often occur on the island of Kalimantan and have a widespread impact on neighboring countries. One indicator of forest and land fires is hotspot. Climate factors play an important role in determining hotspot patterns and trends in a location, which often fluctuate and are difficult to predict. This research aims to predict the number of hotspot spatially and temporally in the next month on Kalimantan Island and analyze the influence of local climate on hotspot events. The Bayesian Conditional Autoregressive method with Integrated Nested Laplace Approximation and optimal weight selection using Getis-Ord G are used to increase prediction accuracy. The distribution of hotspot is assumed to follow the Negative Binomial distribution. The research results show that the best model uses an additive approach and interaction with explanatory variables with a Deviance Information Criterion value of 97,799.8. Predictions from this model have a Root Mean Square Prediction Error of 7.08 and an Average Absolute Prediction Error of 0.63. However, the model still has limitations in predicting extreme events. Climatic factors such as low rainfall, long days without rain, high air temperatures, and low humidity contribute significantly to the increase in the number of hotspot in Kalimantan.

The generalized Ridge penalty is a powerful tool for dealing with multicollinearity and high‐dimensionality in regression problems. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given covariance matrix. The covariance matrix controls the structure of the coefficients, which depends on the particular application. For example, it is appropriate to assume that the coefficients have a spatial structure when the covariates are spatially correlated. This study proposes an Expectation‐Maximization algorithm for estimating generalized Ridge parameters whose covariance structure depends on specific parameters. We focus on three cases: diagonal (when the covariance matrix is diagonal with constant elements), Matérn, and conditional autoregressive covariances. A simulation study is conducted to evaluate the performance of the proposed method, and then the method is applied to predict ocean wave heights using wind conditions. [ABSTRACT FROM AUTHOR]

Abstract Background Malaria and anaemia contribute substantially to child morbidity and mortality. In this study, we sought to jointly model the residual spatial variation in the likelihood of these two correlated diseases, while controlling for individual-level, household-level and environmental characteristics. Methods A child-level shared component model was utilised to partition shared and disease-specific district-level spatial effects. Results The results indicated that the spatial variation in the likelihood of malaria was more prominent compared to that of anaemia, for both the shared and specific spatial components. In addition, approximately 30% of the districts were associated with an increased likelihood of anaemia but a decreased likelihood of malaria. This suggests that there are other drivers of anaemia in children in these districts, which warrants further investigation. Conclusions The maps of the shared and disease-specific spatial patterns provide a tool to allow for more targeted action in malaria and anaemia control and prevention, as well as for the targeted allocation of limited district health system resources.

We developed spatial Bayesian hierarchical models to assess potential climate change impacts on suitable habitat for five important tree species in the Pacific northwestern United States (California, Oregon, and Washington). Individual‐species models were fit with presence–absence data from forest inventory field plots and spatial relationships were specified through a conditional autoregressive model. This modeling approach allowed us to visualize uncertainty in response curves, map current and future prediction uncertainty, and provide interval estimates for change. Upward elevational or northward latitudinal shifts in climatically suitable habitat were projected for all species. Climate change impacts were the most damaging for noble fir (Abies procera), for which 79%–100% of the current range was projected to become climatically unsuitable by the 2080s. Although coastal Douglas‐fir (Pseudotsuga menziesii var. menziesii) has been projected by others to gain habitat in Canada, within our study area we projected a net loss of climatically suitable habitat (ca. 8000–31,400 km2) under three of four future climate scenarios. A net loss in habitat was also projected for Oregon white oak (Quercus garryana) under three of four scenarios, with 40%–60% of the current range becoming unsuitable. Although there was no net loss of habitat for forest land blue oak under any scenario, other factors like competition may inhibit blue oak (Quercus douglasii) and white oak from occupying areas projected to increase in climatic suitability. Additionally, between 13% and 32% of blue oak's current range was projected to become unsuitable; some of these areas aligned with dieback following the 2012–2015 California drought, which our data set predates. Unlike the other four species, we projected a 17%–25% increase in climatically suitable habitat for California black oak (Quercus kelloggii), although 1%–20% of the current range was still projected to become unsuitable. Our findings indicate that, although some species will face more pressure in tracking climatically suitable habitat than others, climate change will impact the location of suitable habitat for many species. [ABSTRACT FROM AUTHOR]

Abstract We developed spatial Bayesian hierarchical models to assess potential climate change impacts on suitable habitat for five important tree species in the Pacific northwestern United States (California, Oregon, and Washington). Individual‐species models were fit with presence–absence data from forest inventory field plots and spatial relationships were specified through a conditional autoregressive model. This modeling approach allowed us to visualize uncertainty in response curves, map current and future prediction uncertainty, and provide interval estimates for change. Upward elevational or northward latitudinal shifts in climatically suitable habitat were projected for all species. Climate change impacts were the most damaging for noble fir (Abies procera), for which 79%–100% of the current range was projected to become climatically unsuitable by the 2080s. Although coastal Douglas‐fir (Pseudotsuga menziesii var. menziesii) has been projected by others to gain habitat in Canada, within our study area we projected a net loss of climatically suitable habitat (ca. 8000–31,400 km2) under three of four future climate scenarios. A net loss in habitat was also projected for Oregon white oak (Quercus garryana) under three of four scenarios, with 40%–60% of the current range becoming unsuitable. Although there was no net loss of habitat for forest land blue oak under any scenario, other factors like competition may inhibit blue oak (Quercus douglasii) and white oak from occupying areas projected to increase in climatic suitability. Additionally, between 13% and 32% of blue oak's current range was projected to become unsuitable; some of these areas aligned with dieback following the 2012–2015 California drought, which our data set predates. Unlike the other four species, we projected a 17%–25% increase in climatically suitable habitat for California black oak (Quercus kelloggii), although 1%–20% of the current range was still projected to become unsuitable. Our findings indicate that, although some species will face more pressure in tracking climatically suitable habitat than others, climate change will impact the location of suitable habitat for many species.

Abstract With the advent of technology for data gathering and storage, opportunistic citizen science data are proliferating. Species distribution models (SDMs) aim to use species occurrence or abundance for ecological insights, prediction and management. We analysed a massive opportunistic dataset with over 100,000 records of incidental shipboard observations of marine mammals. Our overall goal was to create maps of species density from massive opportunistic data by using spatial regression for count data with an effort offset. We illustrate the method with two marine mammals in the Gulf of Alaska and Bering Sea. We counted the total number of animals in 11,424 hexagons based on presence‐only data. To decrease bias, we first estimated a spatial density surface for ship‐days, which was our proxy variable for effort. We used spatial considerations to create pseudo‐absences, and left some hexagons as missing values. Next, we created SDMs that used modelled effort to create pseudo‐absences, and included the effort surface as an offset in a second stage analysis of two example species, northern fur seals and Steller sea lions. For both effort and species counts, we used spatial count regression with random effects that had a multivariate normal distribution with a conditional autoregressive (CAR) covariance matrix, providing 2.5 million Markov chain Monte Carlo (MCMC) samples (1,000 were retained) from the posterior distribution. We used a novel MCMC scheme that maintained sparse precision matrices for observed and missing data when batch sampling from the multivariate normal distribution. We also used a truncated normal distribution to stabilize estimates, and used a look‐up table for sampling the autocorrelation parameter. These innovations allowed us to draw several million samples in just a few hours. From the posterior distributions of the SDMs, we computed two functions of interest. We normalized the SDMs and then applied an overall abundance estimate obtained from the literature to derive spatially explicit abundance estimates, especially within subsetted areas. We also created ‘certain hotspots’ that scaled local abundance by standard deviation and using thresholds. Hexagons with values above a threshold were deemed as hotspots with enough evidence to be certain about them.

With the advent of technology for data gathering and storage, opportunistic citizen science data are proliferating. Species distribution models (SDMs) aim to use species occurrence or abundance for ecological insights, prediction and management. We analysed a massive opportunistic dataset with over 100,000 records of incidental shipboard observations of marine mammals. Our overall goal was to create maps of species density from massive opportunistic data by using spatial regression for count data with an effort offset. We illustrate the method with two marine mammals in the Gulf of Alaska and Bering Sea.We counted the total number of animals in 11,424 hexagons based on presence‐only data. To decrease bias, we first estimated a spatial density surface for ship‐days, which was our proxy variable for effort. We used spatial considerations to create pseudo‐absences, and left some hexagons as missing values. Next, we created SDMs that used modelled effort to create pseudo‐absences, and included the effort surface as an offset in a second stage analysis of two example species, northern fur seals and Steller sea lions.For both effort and species counts, we used spatial count regression with random effects that had a multivariate normal distribution with a conditional autoregressive (CAR) covariance matrix, providing 2.5 million Markov chain Monte Carlo (MCMC) samples (1,000 were retained) from the posterior distribution. We used a novel MCMC scheme that maintained sparse precision matrices for observed and missing data when batch sampling from the multivariate normal distribution. We also used a truncated normal distribution to stabilize estimates, and used a look‐up table for sampling the autocorrelation parameter. These innovations allowed us to draw several million samples in just a few hours.From the posterior distributions of the SDMs, we computed two functions of interest. We normalized the SDMs and then applied an overall abundance estimate obtained from the literature to derive spatially explicit abundance estimates, especially within subsetted areas. We also created 'certain hotspots' that scaled local abundance by standard deviation and using thresholds. Hexagons with values above a threshold were deemed as hotspots with enough evidence to be certain about them. [ABSTRACT FROM AUTHOR]

Objective: To understand the spatial pattern of dengue fever (DF) patients’ survival and investigated factors influencing DF patients’ survival. Method: A Bayesian spatial survival method via a conditional autoregressive approach was used to analyze the factors that influence DF patients’ survival in 14 sub-districts from January 2015 to May 2017 in Makassar city, Indonesia. Bayesian spatial and a non-spatial model were compared by using deviance information criterion. Results: The spatial model was more suitable than a non-spatial model. Under the Bayesian spatial model, there was a substantive relationship between age, grade and DF patients’ survival time. Conclusions: The relative risk map and related factors of DF patients’ survival can indicate the health policy makers to give special attention to the high risk areas in order to faster and more targeted treatment.

Spatial autoregressive in ecological studies are often modeled using the simultaneous autoregressive (SAR) and conditional autoregressive (CAR) models. Both models are known as network-based or graphical models. SAR and CAR models have been developed to analyse spatially autocorrelated data based on neighborhood proximity. The models have different conceptual concepts with the equivalent objectives. In practice, selecting which model should be used becomes a crucial issue since there are no standard criteria for comparing SAR and CAR models. We evaluate the similarity and differences between SAR and CAR modes based on the Monte Carlo simulation study and real application on diarrhea data. The evaluations of both models are essential in regression modelling to get more reliable result. In general, the smallest of bias parameter estimates and the smallest differences in estimated spatial autoregressive parameters between SAR and CAR models were found for weak and strong spatial dependencies. For medium spatial dependence, the differences estimated spatial autoregressive between SAR and CAR model relatively large. [ABSTRACT FROM AUTHOR]

Malnutrition is a condition of serious nutritional disorders that occurs when food intake does not match the amount of nutrients needed. This nutritional disorder is fatal to a toddler's health if not treated immediately. For this reason, the purposes of this study are to model and map malnutrition cases by taking into account regional aspects using the Bayes spatial analysis whose inference uses INLA (integrated nested Laplace approximation). The spatial Bayes model used is a generalized linear mixed model, by including random effects in the form of conditional autoregressive spatial structured components. The response variable is the number of cases of malnutrition in 22 city districts in Indonesia's East Nusa Tenggara province, which is assumed to have a Poisson distribution. In spatial modeling, the fixed effects as the explanatory variables are included, i.e. the number of children under five given complete immunization, the poverty depth index, the number of maternal and child health services, population density and the average duration of breastfeeding. The results of spatial modeling show that the poverty depth index is the main variable that has a significant effect on the number of malnutrition cases. From the results of spatial mapping, it can be seen that there are regional links that affect the number of malnutrition cases, including in Sumba Barat Daya, Sumba Barat and Sumba Utara which have a high probability of malnutrition risk rather than in Sumba Timur. [ABSTRACT FROM AUTHOR]

Sparsity inducing priors are widely used in Bayesian regression analysis, and seek dimensionality reduction to avoid unnecessarily complex models. An alternative to sparsity induction are discrete mixtures, such as spike and slab priors. These ideas extend to selection of random effects, either i ⁢ i ⁢ d or structured (e.g. spatially structured). In contrast to sparsity induction in mixed models with i ⁢ i ⁢ d random effects, in this paper we apply sparsity priors to spatial regression for area units (lattice data), and to spatial random effects in conditional autoregressive priors. In particular, we consider the use of global-local shrinkage to distinguish areas with average predictor effects from areas where the predictor effect is amplified or diminished because the response-predictor pattern is distinct from that of most areas. The operation and utility of this approach is demonstrated using simulated data, and in a real application to diabetes related deaths in New York counties. [ABSTRACT FROM AUTHOR]

Spatial autoregressive in ecological studies are often modeled using the simultaneous autoregressive (SAR) and conditional autoregressive (CAR) models. Both models are known as network-based or graphical models. SAR and CAR models have been developed to analyse spatially autocorrelated data based on neighborhood proximity. The models have different conceptual concepts with the equivalent objectives. In practice, selecting which model should be used becomes a crucial issue since there are no standard criteria for comparing SAR and CAR models. We evaluate the similarity and differences between SAR and CAR modes based on the Monte Carlo simulation study and real application on diarrhea data. The evaluations of both models are essential in regression modelling to get more reliable result. In general, the smallest of bias parameter estimates and the smallest differences in estimated spatial autoregressive parameters between SAR and CAR models were found for weak and strong spatial dependencies. For medium spatial dependence, the differences estimated spatial autoregressive between SAR and CAR model relatively large. [ABSTRACT FROM AUTHOR]

Health departments are seeking new ways to determine when and where limited resources should be allocated to achieve maximum benefit for the population. In this work, we demonstrate how one state health department worked to create relative risk measures of cancer incidence, late-stage cancer incidence and mortality incidence displayed in an easy to read map using spatio-temporal statistical tools. The data included age, sex, cancer type and stage, and ZIP Code Tabulation Area (ZCTA) for every incidence and death from 2004 to 2015. Eight types of cancer were selected for analysis: breast, cervical, colorectal, liver, lung, non-Hodgkin lymphoma (NHL), prostate, and melanoma. The risk maps were designed to illustrate areas of the state where risk for developing or dying from certain cancers was higher than the state average, and to show how trends are evolving over time. A hierarchical Bayesian log-normal Poisson regression model, with effects for ZCTA, time period, and a space-time interaction was implemented. The spatial effects accounted for spatial correlation using an intrinsic conditional auto-regressive model, and the time effects used an autoregressive model. Through the model, we were able to achieve reliable estimates of relative risk per ZCTA and time period, even for small population ZCTAs with few, if any, cases during the time period. Furthermore, we calculated a measure of risk probability for each ZCTA, relative to the state average. Results from two cancers are discussed in this manuscript, but all 24 results are available on the project website. [ABSTRACT FROM AUTHOR]

The term low birth weight refers an event where a newborn baby has a weight that is less than 2500 g. This is an essential indicator while the interest is in public health issues such as infant mortality, maternal complications, and antenatal care, etc. of a country, particularly, for a developing country like Bangladesh. The regional development programs are in the current priority list of Bangladesh government and other policy makers. Many of such regional development programs may need the spatial distribution of relative risk for low birth weight that can be obtained by mapping the risks over small area domains like the districts of Bangladesh. This study aims to find whether is there any spatial dependence among the relative risks of low birth weight for the districts of Bangladesh. This has been investigated using Moran's I statistic and a significant spatial dependence in the relative risks was found. Then, attempt has been made to rediscover the spatial distribution based on the idea of spatial smoothing. A Bayesian hierarchical model is used considering percent received antenatal care and female labor force participation as covariates to smooth the observed relative risks of low birth weight in 64 districts of Bangladesh. Revised spatial distribution taking the spatial dependence under consideration through intrinsic conditional autoregressive model is derived and showed in choropleth map along with its different behaviors. [ABSTRACT FROM AUTHOR]

In the recent decade, walking has been encouraged as an active mode of transportation, which could reduce congestion and air pollution and also improve community health. However, pedestrians are more vulnerable to traffic crashes compared with other road users, especially in developing countries such as Saudi Arabia. This paper examines the association among traffic volume, land-use, socio-demographic and roadway characteristics factors, and the frequency of pedestrian crashes based on macro-level safety analysis using data from Riyadh, the Capital of Saudi Arabia. Two Bayesian spatial Poisson-lognormal models for total and severe pedestrian crashes are developed in this study. The results show that the factors that affect total pedestrian crash occurrence are different from those affecting severe pedestrian crash. Several implications for pedestrian safety policies in Riyadh are suggested based on the results. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. However, choosing appropriate prior distributions for the parameters in these models is necessary and sometimes challenging. In particular, an intrinsic conditional autoregressive (CAR) hierarchical component is often used to account for spatial association. Vague proper prior distributions have frequently been used for this type of model, but this requires the careful selection of suitable hyperparameters. In this paper, we derive several objective priors for the Gaussian hierarchical model with an intrinsic CAR component and discuss their properties. We show that the independence Jeffreys and Jeffreys-rule priors result in improper posterior distributions, while the reference prior results in a proper posterior distribution. We present results from a simulation study that compares frequentist properties of Bayesian procedures that use several competing priors, including the derived reference prior. We demonstrate that using the reference prior results in favorable coverage, interval length, and mean squared error. Finally, we illustrate our methodology with an application to 2012 housing foreclosure rates in the 88 counties of Ohio. [ABSTRACT FROM AUTHOR]

Performance of environmental justice models depends on the level of accuracy in measuring or estimating the health of the environment. In the past decades, and especially in the area of stream health modeling, significant improvement has been observed. However, the impacts of these improvements on the robustness of environmental justice models have not been evaluated. Therefore in this study, the relative importance of parameter estimation in stream health based environmental justice modeling was evaluated. The Saginaw River Basin in Michigan was considered as the study area, and four major ecological indices evaluating the response of fish and macroinvertebrates to instream stressors were used for stream health assessment. Seventeen socioeconomic and physiographic indices were evaluated at three census levels of county, census tract, and block group. Then the ecological, socioeconomic, and physiographic indices were used in the development of stream health based environmental justice models. Results showed that incorporating ecologically relevant indices and a using two-phase modeling approach not only improved the performance of stream health predictive models but also reduced the sensitivity of environmental justice models to aggregation at different census levels. In addition, using improved stream health indices reduced the redundancy of the independent variables (socioeconomic and physiographic indices), where the total number of significant parameters was reduced from 171 to 115. Besides that, more robust and meaningful spatial dependencies were observed among stream health measures and environmental justice parameters at different spatial levels. In summary having a reliable stream health information is the key for development of robust environmental justice models as evidence by improving model predictability and eliminating contradictory results compared to previous studies. [ABSTRACT FROM AUTHOR]

We propose a formal specification for sum-zero constrained intrinsic conditional autoregressive (ICAR) models. Our specification first projects a vector of proper conditional autoregressive spatial random effects onto a subspace where the projected vector is constrained to sum to zero, and after that takes the limit when the proper conditional autoregressive model approaches the ICAR model. As a result, we show that the sum-zero constrained ICAR model has a singular Gaussian distribution with zero mean vector and a unique covariance matrix. Previously, sum-zero constraints have typically been imposed on the vector of spatial random effects in ICAR models within a Markov chain Monte Carlo (MCMC) algorithm in what is known as centering-on-the-fly. This mathematically informal way to impose the sum-zero constraint obscures the actual joint density of the spatial random effects. By contrast, the present work elucidates a unique distribution for ICAR random effects. The explicit expressions for the resulting unique covariance matrix and density function are useful for the development of Bayesian methodology in spatial statistics which will be useful to practitioners. We illustrate the practical relevance of our results by using Bayesian model selection to jointly assess both spatial dependence and fixed effects. [ABSTRACT FROM AUTHOR]

Abstract: Ecological data often exhibit spatial pattern, which can be modeled as autocorrelation. Conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models are network‐based models (also known as graphical models) specifically designed to model spatially autocorrelated data based on neighborhood relationships. We identify and discuss six different types of practical ecological inference using CAR and SAR models, including: (1) model selection, (2) spatial regression, (3) estimation of autocorrelation, (4) estimation of other connectivity parameters, (5) spatial prediction, and (6) spatial smoothing. We compare CAR and SAR models, showing their development and connection to partial correlations. Special cases, such as the intrinsic autoregressive model (IAR), are described. Conditional autoregressive and SAR models depend on weight matrices, whose practical development uses neighborhood definition and row‐standardization. Weight matrices can also include ecological covariates and connectivity structures, which we emphasize, but have been rarely used. Trends in harbor seals (Phoca vitulina) in southeastern Alaska from 463 polygons, some with missing data, are used to illustrate the six inference types. We develop a variety of weight matrices and CAR and SAR spatial regression models are fit using maximum likelihood and Bayesian methods. Profile likelihood graphs illustrate inference for covariance parameters. The same data set is used for both prediction and smoothing, and the relative merits of each are discussed. We show the nonstationary variances and correlations of a CAR model and demonstrate the effect of row‐standardization. We include several take‐home messages for CAR and SAR models, including (1) choosing between CAR and IAR models, (2) modeling ecological effects in the covariance matrix, (3) the appeal of spatial smoothing, and (4) how to handle isolated neighbors. We highlight several reasons why ecologists will want to make use of autoregressive models, both directly and in hierarchical models, and not only in explicit spatial settings, but also for more general connectivity models. [ABSTRACT FROM AUTHOR]

The Current Employment Statistics (CES) survey, administered by the US Bureau of Labor Statistics, publishes total employment estimates for thousands of domains at detailed geographical and industrial levels. Some of these domains do not have adequate sample size for the direct probability sample-based estimates to be reliable. Small area estimation methods are used to integrate information from historical sources and correlated domains to improve estimation efficiency. In this article, we explore alternatives to the Fay-Herriot two-stage hierarchical model that relax distributional and independence assumptions among random effects indexed by domain and month in order to more fully borrow strength to improve the efficiency of published employment estimates. We compare the performances of our alternative models on both synthetic data and in application to estimates from the CES survey. [ABSTRACT FROM AUTHOR]

To assess the importance of variation in observer effort between and within bird atlas projects and demonstrate the use of relatively simple conditional autoregressive ( CAR) models for analyzing grid-based atlas data with varying effort. Pennsylvania and West Virginia, United States of America. We used varying proportions of randomly selected training data to assess whether variations in observer effort can be accounted for using CAR models and whether such models would still be useful for atlases with incomplete data. We then evaluated whether the application of these models influenced our assessment of distribution change between two atlas projects separated by twenty years (Pennsylvania), and tested our modeling methodology on a state bird atlas with incomplete coverage (West Virginia). Conditional Autoregressive models which included observer effort and landscape covariates were able to make robust predictions of species distributions in cases of sparse data coverage. Further, we found that CAR models without landscape covariates performed favorably. These models also account for variation in observer effort between atlas projects and can have a profound effect on the overall assessment of distribution change. Accounting for variation in observer effort in atlas projects is critically important. CAR models provide a useful modeling framework for accounting for variation in observer effort in bird atlas data because they are relatively simple to apply, and quick to run. [ABSTRACT FROM AUTHOR]

• Monitoring PFAS in drinking water has increased due to health concerns. • Built models to detect & estimate PFAS in drinking water wells. • Random forest & autoregressive models enhance PFAS detection & estimation. • PFAS drivers include pollution sources, soil, geology, groundwater, & demography. The monitoring of Per and Polyfluoroalkyl substances (PFAS) in drinking water sources has significantly increased due to their recognition as a major public health concern. This information has been utilized to assess the importance of potential explanatory variables in determining the presence and concentration of PFAS in different regions. Nevertheless, the significance of these variables and the reliability of the methods in regions beyond where they were initially tested is still uncertain. Hence, our research pursues two main objectives: 1) to evaluate the validity of the aforementioned variables and methods for several PFAS species in a different area and 2) to build on existing modeling work; a new PFAS predictive model is introduced which is more reliable in determining the presence and concentration of PFAS at a regional level. To achieve these goals, we reconstructed four state-of-the-art models using a statewide dataset available for Michigan. These models involve spatial regression techniques, classification and regression random forest algorithms, and boosted regression trees. They also include numerous explanatory variables, such as features of local soil and hydrology and the number of nearby contamination sources. Then, we use a Bayesian selection approach to find the most relevant among these variables. Finally, we employ the most relevant covariates to assess PFAS occurrence and estimate their concentration using a novel combination of machine learning algorithms and conditional autoregressive (CAR) modeling. In the first case, PFAS occurrence was assessed with an accuracy comparable to the reconstructed models (>90%) while using significantly fewer variables. In the second case, by maintaining low data requirements, the estimated concentrations of most PFAS compounds were more closely aligned with available observations compared to previous methods, with correlation coefficients ρ > 0.90 and R 2 > 0.77. [ABSTRACT FROM AUTHOR]

Variation in disease risk underlying observed disease counts is increasingly a focus for Bayesian spatial modelling, including applications in spatial data mining. Bayesian analysis of spatial data, whether for disease or other types of event, often employs a conditionally autoregressive prior, which can express spatial dependence commonly present in underlying risks or rates. Such conditionally autoregressive priors typically assume a normal density and uniform local smoothing for underlying risks. However, normality assumptions may be affected or distorted by heteroscedasticity or spatial outliers. It is also desirable that spatial disease models represent variation that is not attributable to spatial dependence. A spatial prior representing spatial heteroscedasticity within a model accommodating both spatial and non-spatial variation is therefore proposed. Illustrative applications are to human TB incidence. A simulation example is based on mainland US states, while a real data application considers TB incidence in 326 English local authorities. [ABSTRACT FROM AUTHOR]

Summary This study evaluated the effects of spatial resolution on environmental justice analysis concerning stream health. The Saginaw River Basin in Michigan was selected since it is an area of concern in the Great Lakes basin. Three Bayesian Conditional Autoregressive (CAR) models (ordinary regression, weighted regression and spatial) were developed for each stream health measure based on 17 socioeconomic and physiographical variables at three census levels. For all stream health measures, spatial models had better performance compared to the two non-spatial ones at the census tract and block group levels. Meanwhile no spatial dependency was found at the county level. Multilevel Bayesian CAR models were also developed to understand the spatial dependency at the three levels. Results showed that considering level interactions improved models’ prediction. Residual plots also showed that models developed at the block group and census tract (in contrary to county level models) are able to capture spatial variations. [ABSTRACT FROM AUTHOR]