A multivariate prediction of spatial process with non-stationary covariance for Kuwait non-methane hydrocarbons levels

Predicting unmeasured realizations of multivariate spatial process responses is a fundamental problem in environmetrics. The study of levels of air pollutants is important for understanding and improving air quality in major urban areas. This research aims to handle the prediction in a Bayesian framework for non-methane hydrocarbons NMHC pollutant for the State of Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to study the distribution level of NMHC with respect to time and metreological parameters and space and use this distribution to predict the concentration of NMHC in other sites of Kuwait using the minimum amount of data (reducing the cost). We will implement a hierarchical Bayesian approach assuming Gaussian random field technique that allows us to pool the data from different sites in predicting the exposure of the non-methane hydrocarbons in different regions of Kuwait.     

燕山石化地区NMHC的特征研究

本文采用气相色谱－质谱联用方法，对燕山石化地区不同生产区域的大气样品，定量地进行非甲烷碳氢化合物（ＮＭＨＣ）的分类测定。本方法可以鉴定Ｃ２－Ｃ１１共六十多个色谱峰。实验表明，燕山石化地区烷烃、烯烃和芳香烃等各类碳氢化合物均具有较高浓度，是对ＮＭＨＣ有重要贡献的一个工业源。本文还参照各大气样品的不同来源，分析了ＮＭＨＣ的排放特征，从而确定了燕山石化区ＮＭＨＣ排放的典型物种。     

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.     

Hierarchical modeling of count data with application to nuclear fall-out

We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R². We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998).     

State space models with spatial deformation

Space deformation has been proposed to model space-time varying observation processes with non-stationary spatial covariance structure under the hypothesis of temporal stationarity. In real applications, however, the temporal stationarity assumption is inappropriate and unrealistic. In this work we propose a spatial-temporal model whose temporal trend is modeled through state space models and a spatially varying anisotropy is modeled through spatial deformation, under the Bayesian approach. A distinctive feature of our approach is the consideration of model uncertainty in an unified framework. Our model has a clear advantage over the ones proposed so far in the literature when the main objective of the study is to perform spatial interpolation for fixed points in time. Approximations of the posterior distributions of the model parameters are obtained via Markov chain Monte Carlo methods. This allows for prediction of the process values in space and time as well as handling of missing values. Two applications are presented: the first one to model concentrations of sulfur dioxide in the eastern United States and the second one to model monthly minimum temperatures in the State of Rio de Janeiro.     

An assessment of the air pollution data from two monitoring stations in Kuwait

This article assesses the air pollution data from two monitoring stations in Kuwait. The measurements cover major pollutants, i.e., CO, CO₂, methanated and non-methanated hydrocarbons, NO _x , SO₂, O₃, and particulate matter (PM10). The data also includes meteorological parameters, i.e., solar intensity, temperature, wind speed, and wind direction, and has been collected over a period 4 years, from 2001 to 2004. Data analysis includes the assessment of annual hourly averages and 1-h maxima. Typical pollutant concentration trends, similar to those previously reported for Kuwait and for other locations around the world, are observed except for particulate matter measurements, which have higher values because of proximity to the desert. Emissions of nitrogen oxides show a consistent increase over the years. This is caused by the increase in the number of motor vehicles and the expansion in power generation and industrial activities. The data collected is a subset of the air quality criteria, as defined by the US EPA (United States Environmental Protection Agency).     

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.     

Combining data and simulated data for space–time fields: application to ozone

This paper presents a theory for modeling random environmental spatial-temporal fields that allows simulated data (numerical-physical model output) to be combined with measurements made at fixed monitoring sites. That theory involves Bayesian hierarchical models that provide temporal forecasts and spatial predictions along with appropriate credibility intervals. A by-product is a method for re-calibrating the simulated data to bring it into line with the measurements for certain applications. While the approach covers a broad domain of potential applications, this paper addresses a field of particular importance, ground level ozone concentrations over the eastern and central USA. A univariate model is developed and illustrated with hourly ozone fields. A multivariate alternative is also provided and illustrated with daily concentration fields. The forecasts and predictions they provide are compared with those from other approaches.     

Major PM10 source location by a spatial multivariate receptor model

We present a multivariate receptor model for identifying the spatial location of major PM₁₀ pollution sources through the concentrations at multiple monitoring stations. We build on a mixed multiplicative log-normal factor model adjusting the source contributions for meteorological covariates and for temporal correlation and considering source profiles as compositional Gaussian random fields, to account for the variability induced by the spatial distribution of the monitoring sites. Taking a Bayesian approach to estimation, the proposed hierarchical model is implemented and used to analyze average daily PM₁₀ concentration measurements from 13 monitoring sites in Taranto, Italy, for the period April–December 2005. Three major sources of pollution are identified and characterized in terms of their spatial and temporal behavior and in relation to meteorological data.     

Analysis of air pollution at Shuaiba industrial area in Kuwait

A study has been conducted over a period of one year on measurements of air pollution in the Shuaiba Industrial Area (SIA) of Kuwait. The study included analysis of pollutant behaviour relative to the wind speed and direction. SIA comprises several large scale industries including three petroleum refineries, two power plants, two fertilizer plants, a cement plant, a chlorine and soda plant, a commercial harbour and two large oil loading terminals. Measurements of 15 parameters have been carried out every 5 minutes using a mobile laboratory fitted with an automatic calibrator and a data storage system. The pollutants studied include methane, non‐methane hydrocarbons (NMHC), carbon monoxide, carbon dioxide, nitrogen oxides (NO, NO₂, and NO _x ), sulphur dioxide, ozone and suspended dust. Meteorological parameters monitored simultaneously include wind speed and direction, air temperature, relative humidity, solar radiation, and barometric pressure. The air quality data collected using the mobile laboratory have been used to calculate the diurnal and monthly variations in the major primary and secondary pollutants. Distribution levels of these pollutants relative to wind direction and speed have also been used in the analysis. The results show large diurnal variations in some pollutant concentrations. Generally, two types of concentration variations have been found, depending on whether the species is a primary or a secondary pollutant. Diurnal variations with two maxima were observed in the concentrations of primary pollutants including NO, SO₂, NMHC, CO and suspended dust, whereas a single maximum was observed for secondary pollutants such as O₃and NO₂. The monthly variations of SO₂and NO _x showed maximum values during the warm months. However, ozone showed a quite marked seasonal variation with maxima during spring and late summer and a minimum during the early summer. The results also indicated a common source for NO _x , SO₂, NMHC, CO and suspended dust to the North‐West (NW) of the monitoring station. Moreover for NO _x and SO₂, another less significant source is to the South‐South‐West (SSW) and South‐West (SW) of the monitoring station.     

A pioneer validation of a state-space model of vessel trajectories (VMS) with observers’ data

In the context of the expansion of animal tracking and bio-logging, state-space models have been developed with the objective to characterise animals’ trajectories and to understand the factors controlling their behaviour. In the fisheries community, the electronic tagging of vessels commonly designated by Vessel Monitoring Systems (VMS) is developing and provides a new insight for the understanding, the analysis and the modelling of the trajectories of vessels and their prospecting behaviour. VMS data are thus a clue for the proper definition of fishing effort which remains a fundamental parameter of tuna stock assessments. In this context, we used the VMS (recording of hourly positions) of the French tropical tuna purse-seiners operating in the Indian Ocean to characterise three types of movement (states) on the VMS trajectories (stillness, tracking, and cruising). Based on empirical evidences, and on the regular frequency of VMS acquisition, this was achieved by the development of a Bayesian Hidden Markov model for the speeds and turning angles derived from the hourly steps of the trajectories. In a second phase, states were related to activities disentangling stillness into fishing or stop at sea. Finally the quality of the model performances was rigorously quantified thanks to observers’ data. Confronting model prediction and true activities allowed estimating that 10% of the hourly steps were misclassified. The assumptions and model’ choices are discussed, highlighting the fact that VMS data and observers’ data having different time resolutions, the effective use of validating data was troublesome. However, without validation, these analyses remain speculative. The validation part of this work represents an important step for the operational use of state-space models in ecology in the broad sense (predators’ tracking data, e.g. birds or mammals trajectories).     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Multimethod,multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves

In many cases, the first step in large‐carnivore management is to obtain objective, reliable, and cost‐effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical‐site‐occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost‐effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well‐coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population‐parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.     

Bayesian Small Area Models for Assessing Wildlife Conservation Risk in Patchy Populations

Abstract:  Species conservation risk assessments require accurate, probabilistic, and biologically meaningful maps of population distribution. In patchy populations, the reasons for discontinuities are not often well understood. We tested a novel approach to habitat modeling in which methods of small area estimation were used within a hierarchical Bayesian framework. Amphibian occurrence was modeled with logistic regression that included third-order drainages as hierarchical effects to account for patchy populations. Models including the random drainage effects adequately represented species occurrences in patchy populations of 4 amphibian species in the Oregon Coast Range (U.S.A.). Amphibian surveys from other locations within the same drainage were used to calibrate local drainage-scale effects. Cross-validation showed that prediction errors for calibrated models were 77% to 86% lower than comparable regionally constructed models, depending on species. When calibration data were unavailable, small area and regional models performed similarly, although poorly. Small area estimation models complement wildlife ecology and habitat studies, and can help managers develop a regional picture of the conservation status for relatively rare species.     

Tropical deforestation in Madagascar: analysis using hierarchical,spatially explicit,Bayesian regression models

Establishing cause–effect relationships for deforestation at various scales has proven difficult even when rates of deforestation appear well documented. There is a need for better explanatory models, which also provide insight into the process of deforestation. We propose a novel hierarchical modeling specification incorporating spatial association. The hierarchical aspect allows us to accommodate misalignment between the land-use (response) data layer and explanatory data layers. Spatial structure seems appropriate due to the inherently spatial nature of land use and data layers explaining land use. Typically, there will be missing values or holes in the response data. To accommodate this we propose an imputation strategy. We apply our modeling approach to develop a novel deforestation model for the eastern wet forested zone of Madagascar, a global rain forest “hot spot”. Using five data layers created for this region, we fit a suitable spatial hierarchical model. Though fitting such models is computationally much more demanding than fitting more standard models, we show that the resulting interpretation is much richer. Also, we employ a model choice criterion to argue that our fully Bayesian model performs better than simpler ones. To the best of our knowledge, this is the first work that applies hierarchical Bayesian modeling techniques to study deforestation processes. We conclude with a discussion of our findings and an indication of the broader ecological applicability of our modeling style.     

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.     

An application of Bayesian variable selection to spatial concurrent linear models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing.     

Efficient statistical mapping of avian count data

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.     

Field-scale roles of density, temperature, nitrogen, and predation on aphid population dynamics

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.