Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue

Vehicular traffic, industrial activity and street dust are important sources of atmospheric particles, which cause pollution and serious health problems, including respiratory illness. Hence, techniques for analyzing and modeling the spatio-temporal behavior of particulate matter (PM), in the recent statistical literature, represent an essential support for environmental and human health protection. In this paper, air pollution from particles with diameters smaller than 10  ${\rm \mu}$ m and related meteorological variables, such as temperature and wind speed, measured during November 2009 in the south of Apulian region (Lecce, Brindisi, and Taranto districts) are studied. A thorough multivariate geostatistical analysis is proposed, where different tools for testing the symmetry assumption of the spatio-temporal linear coregionalization model (ST-LCM) are considered, as well as a recent fitting procedure of the ST-LCM, based on the simultaneous diagonalization of symmetric real-valued matrix variograms, is adopted and two non-separable classes of variogram models, the product–sum and Gneiting classes, are fitted to the basic components. The most significant aspects of this study are (a) the quantitative assessment of the assumption of symmetry of the ST-LCM, (b) the use of different non-separable spatio-temporal models for fitting the basic components of a ST-LCM and, more importantly, (c) the application of the spatio-temporal multivariate geostatistical analysis to predict particle pollution in one of the most polluted geographical area. Prediction maps for particle pollution levels with the corresponding validation results are given.     

交通拥堵与雾霾污染的因果关系——基于收敛交叉映射技术的经验研究

交通拥堵与雾霾污染是制约现代城市发展的两大顽疾,准确识别交通拥堵与雾霾污染之间的交互影响,有助于城市管理者重新审视现行治堵与治霾政策的合理性。本文借助大数据平台采集了我国99个城市的高德拥堵延迟指数（CDI）、空气质量指数（AQI）及六种分项空气污染物浓度日报数据,首次采用收敛交叉映射（CCM）方法实证考察了交通拥堵与雾霾污染之间的因果关系。研究发现,CDI与AQI以及CDI与分项污染物组成的动态系统均呈现明显的非线性与弱耦合特征。基于CCM检验结果,大多数城市的CDI与AQI之间不存在显著的因果关系;从分项空气污染物的角度,大多数城市的CDI与主要空气污染物之间不存在显著因果关系,但与次要空气污染物之间却存在显著的单向或双向因果关系。上述结果表明,尽管交通拥堵与雾霾污染之间有一定关联,但在因果关系上现有的经验证据并不支持两者相互影响,治堵和治霾不能“一箭双雕”而必须“双管齐下”。本文的研究在经验上丰富了关于交通拥堵与雾霾污染交互影响的讨论,对城市管理者更加谨慎与合理地制定治堵政策与治霾政策有重要现实意义。     

Nonparametric smoothing in the analysis of air pollution and respiratory illness

While most of epidemiology is observational, rather than experimental, the culture of epidemiology is still derived from agricultural experiments, rather than other observational fields, such as astronomy or economics. The mismatch is made greater as focus has turned to continue risk factors, multifactorial outcomes, and outcomes with large variation unexplainable by available risk factors. The analysis of such data is often viewed as hypothesis testing with statistical control replacing randomization. However, such approaches often test restricted forms of the hypothesis being investigated, such as the hypothesis of a linear association, when there is no prior empirical or theoretical reason to believe that if an association exists, it is linear. In combination with the large nonstochastic sources of error in such observational studies, this suggests the more flexible alternative of exploring the association. Conclusions on the possible causal nature of any discovered association will rest on the coherence and consistency of multiple studies. Nonparametric smoothing in general, and generalized additive models in particular, represent an attractive approach to such problems. This is illustrated using data examining the relationship between particulate air pollution and daily mortality in Birmingham, Alabama; between particulate air pollution, ozone, and SO₂ and daily hospital admissions for respiratory illness in Philadelphia; and between ozone and particulate air pollution and coughing episodes in children in six eastern U.S. cities. The results indicate that airborne particles and ozone are associated with adverse health outcomes at very low concentrations, and that there are likely no thresholds for these relationships.     

Spatial generalized linear mixed models in small area estimation

In survey sampling, policy decisions regarding the allocation of resources to sub‐groups of a population depend on reliable predictors of their underlying parameters. However, in some sub‐groups, called small areas due to small sample sizes relative to the population, the information needed for reliable estimation is typically not available. Consequently, data on a coarser scale are used to predict the characteristics of small areas. Mixed models are the primary tools in small area estimation (SAE) and also borrow information from alternative sources (e.g., previous surveys and administrative and census data sets). In many circumstances, small area predictors are associated with location. For instance, in the case of chronic disease or cancer, it is important for policy makers to understand spatial patterns of disease in order to determine small areas with high risk of disease and establish prevention strategies. The literature considering SAE with spatial random effects is sparse and mostly in the context of spatial linear mixed models. In this article, small area models are proposed for the class of spatial generalized linear mixed models to obtain small area predictors and corresponding second‐order unbiased mean squared prediction errors via Taylor expansion and a parametric bootstrap approach. The performance of the proposed approach is evaluated through simulation studies and application of the models to a real esophageal cancer data set from Minnesota, U.S.A. The Canadian Journal of Statistics 47: 426–437; 2019 © 2019 Statistical Society of Canada     

Competing risks model for clustered data based on the subdistribution hazards with spatial random effects

In some applications, the clustered survival data are arranged spatially such as clinical centers or geographical regions. Incorporating spatial variation in these data not only can improve the accuracy and efficiency of the parameter estimation, but it also investigates the spatial patterns of survivorship for identifying high-risk areas. Competing risks in survival data concern a situation where there is more than one cause of failure, but only the occurrence of the first one is observable. In this paper, we considered Bayesian subdistribution hazard regression models with spatial random effects for the clustered HIV/AIDS data. An intrinsic conditional autoregressive (ICAR) distribution was employed to model the areal spatial random effects. Comparison among competing models was performed by the deviance information criterion. We illustrated the gains of our model through application to the HIV/AIDS data and the simulation studies.KEYWORDS: Competing risks, subdistribution hazard, cumulative incidence function, spatial random effect, Markov chain Monte Carlo     

基于半参数空间模型的空气污染与经济增长关系再检验

选取2001-2014年中国30个省份数据作为样本,考虑空气污染的空间自相关性,采用空间杜宾滞后模型（SDM）和半参数空间滞后模型实证检验经济发展与空气污染的非线性关系。结果表明：①中国空气污染存在显著的空间正相关性,高空气污染水平集聚地随时间推移呈现出“由西向东”的转移特征。②空气污染与经济增长存在一种震荡曲线形式的关系,并不完全吻合传统的EKC倒U型曲线形状,但震荡关系也符合EKC所描述的环境污染与经济发展的关系将长期存在的特征,说明了经济增长并不能自发解决空气污染问题。③半参数空间滞后模型的拟合优度高于普通参数模型,其刻画的空气污染与经济增长的非线性特征验证了前人对二者震荡关系的猜想,结果更为稳健、准确与有效。     

Nonlinear models for ground-level ozone forecasting

One of the main concerns in air pollution is excessive tropospheric ozone concentration. The aim of this work is to develop statistical models giving shortterm forecasts of future ground-level ozone concentrations. Since there are few physical insights about the dynamic relationship between ozone, precursor emissions and/or meteorological factors, a nonparametric and nonlinear approach seems promising in order to specify the forecast models. First, we apply four nonparametric procedures to forecast daily maximum 1-hour and maximum 8-hour averages of ozone concentrations in an urban area. Then, in order to improve the forecast performances, we combine the time series of the forecasts. This idea seems to give encouraging results. This work was supported by a MURST grant. The authors would like to thank two anonymous referees for their helpful comments.     

行驶里程数对环境、交通和能源的影响——基于外部性视角的省际面板数据研究

近年来,机动车污染日趋成为中国空气污染的重要来源.选取2006-2010年中国30个省、市、自治区的面板数据,运用单位根检验、协整检验和面板数据模型等方法来研究行驶里程数对环境、交通和能源的影响.结论认为公路交通氮氧化物排放量、汽油消耗量、交通事故数与公路里程数之间存在显著的相关关系,为将行驶里程数纳入车险费率改革、开发绿色低碳车险产品提供参考.     

Place of living and health inequality: a study for elderly Italians

The aim of this study is to explore if the context matters in explaining socioeconomic inequality in the self-rated health of Italian elderly people. Our hypothesis is that health status perception is associated with existing huge imbalances among Italian areas. A multilevel approach is applied to account for the natural hierarchical structure, as individuals nested in geographical regions. Multilevel logistic regression models are performed including both individual and contextual variables, using data from 2005 Italian Health survey. We prove that individual factors (compositional effect), even representing the most important correlates of health, do not completely explain intra-regional heterogeneity, confirming the existence of an autonomous contextual effect. These territorial differences are present among both Regions and large areas, two geographical aggregations relevant in the domain of health. Moreover, for some Regions, the account for contextual factors explains variations in perceived health, leading to an overthrow of the initial situation: these Regions perform better than expected in the field of health. For other Regions, the contextual elements introduced do not catch the milieu heterogeneity. In this regard, we expect, and solicit, a major effort toward data availability, qualitatively and quantitatively, that might help in explaining residual territorial heterogeneity in health perception, a fundamental starting point for targeting specific policy interventions.     

Inference for the Hyperparameters of Structural Models Under Classical and Bayesian Perspectives: A Comparison Study

Structural models—or dynamic linear models as they are known in the Bayesian literature—have been widely used to model and predict time series using a decomposition in non observable components. Due to the direct interpretation of the parameters, structural models are a powerful and simple methodology to analyze time series in several areas, such as economy, climatology, environmental sciences, among others. The parameters of such models can be estimated either using maximum likelihood or Bayesian procedures, generally implemented using conjugate priors, and there are plenty of works in the literature employing both methods. But are there situations where one of these approaches should be preferred? In this work, instead of conjugate priors for the hyperparameters, the Jeffreys prior is used in the Bayesian approach, along with the uniform prior, and the results are compared to the maximum likelihood method, in an extensive Monte Carlo study. Interval estimation is also evaluated and, to this purpose, bootstrap confidence intervals are introduced in the context of structural models and their performance is compared to the asymptotic and credibility intervals. A real time series of a Brazilian electric company is used as illustration.     

Analyzing space-time sensor network data under suppression and failure in transmission

In this paper we present a fully model-based analysis of the effects of suppression and failure in data transmission with sensor networks. Sensor networks are becoming an increasingly common data collection mechanism in a variety of fields. Sensors can be created to collect data at very high temporal resolution. However, during periods when the process is following a stable path, transmission of such high resolution data would carry little additional information with regard to the process model, i.e., all of the data that is collected need not be transmitted. In particular, when there is cost to transmission, we find ourselves moving to consideration of suppression in transmission. Additionally, for many sensor networks, in practice, we will experience failures in transmission—messages sent by a sensor but not received at the gateway, messages sent but arriving corrupted. Evidently, both suppression and failure lead to information loss which will be reflected in inference associated with our process model. Our effort here is to assess the impact of such information loss under varying extents of suppression and varying incidence of failure. We consider two illustrative process models, presenting fully model-based analyses of suppression and failure using hierarchical models. Such models naturally facilitate borrowing strength across nodes, leveraging all available data to learn about local process behavior.     

Bivariate multilevel models for the analysis of mathematics and reading pupils' achievements

The purpose of this paper is to identify a relationship between pupils' mathematics and reading test scores and the characteristics of students themselves, stratifying for classes, schools and geographical areas. The data set of interest contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013, provided by the Italian Institute for the Evaluation of Educational System. The innovation of this work is in the use of multivariate multilevel models, in which the outcome is bivariate: reading and mathematics achievement. Using the bivariate outcome enables researchers to analyze the correlations between achievement levels in the two fields and to predict statistically significant school and class effects after adjusting for pupil's characteristics. The statistical model employed here explicates account for the potential covariance between the two topics, and at the same time it allows the school effect to vary among them. The results show that while for most cases the direction of school's effect is coherent for reading and mathematics (i.e. positive/negative), there are cases where internal school factors lead to different performances in the two fields.     

Frequency Domain Log-linear Models; Air Pollution and Mortality

Motivated by a study of the association between counts of daily mortality and air pollution, we present a frequency domain estimation approach for log-linear models that accounts for both overdispersion and autocorrelation. The methods also allow for the discounting or downweighting of information at particular frequencies at which, for example, confounding variables are likely to have greatest influence. This allows flexible sensitivity analyses to be carried out to assess the possible effect of confounders on the estimated effect. We apply the methods to estimate the association between counts of mortality and the concentration of airborne particles in Philadelphia, USA, for the years 1974–1988. We obtain an estimated effect of particulate air pollution on mortality that is significantly greater than zero but less than that obtained by a standard log-linear analysis.     

An objective stepwise Bayes approach to small area estimation

The term ‘small area’ or ‘small domain’ is commonly used to denote a small geographical area that has a small subpopulation of people within a large area. Small area estimation is an important area in survey sampling because of the growing demand for better statistical inference for small areas in public or private surveys. In small area estimation problems the focus is on how to borrow strength across areas in order to develop a reliable estimator and which makes use of available auxiliary information. Some traditional methods for small area problems such as empirical best linear unbiased prediction borrow strength through linear models that provide links to related areas, which may not be appropriate for some survey data. In this article, we propose a stepwise Bayes approach which borrows strength through an objective posterior distribution. This approach results in a generalized constrained Dirichlet posterior estimator when auxiliary information is available for small areas. The objective posterior distribution is based only on the assumption of exchangeability across related areas and does not make any explicit model assumptions. The form of our posterior distribution allows us to assign a weight to each member of the sample. These weights can then be used in a straight forward fashion to make inferences about the small area means. Theoretically, the stepwise Bayes character of the posterior allows one to prove the admissibility of the point estimators suggesting that inferential procedures based on this approach will tend to have good frequentist properties. Numerically, we demonstrate in simulations that the proposed stepwise Bayes approach can have substantial strengths compared to traditional methods.     

Discrimination between nested two- and three-parameter air pollutant frequency distributions

The purpose of this paper is to consider methods which discriminate between 2- and 3-parameter nested alternatives for the gamma, Weibull and log-normal distributions, and to investigate their utility in representing frequency distributions of air pollutant measurements. Monte Carlo experiments are conducted to evaluate the likelihood ratio test, Akaike's information criterion, Schwarz's information criterion, the Chi-square test and the Kolmogorov-Smirnov test. The performance of the tests and criteria depends on the types of nested distributions under consideration, the parametric values of the parent distributions, the confidence levels used (if applicable) and the sample sizes. The practical usefulness of the techniques is illustrated by observing the errors of the models in fitting the upper percentiles of the parent distribution. Two sets of air pollution data, namely hourly pollutant observations of B-scattering and nitrogen dioxide, from an urban airshed are used to examine the similarities and differences in fitting 2- and 3-parameter distributions where historical practice suggests there is a preference for the more parsimonious model.     

Spatiotemporal prediction for log-Gaussian Cox processes

Space–time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space–time point processes. Our models are Cox processes whose stochastic intensity is a space–time Ornstein–Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.     

Spatial robust small area estimation

The accuracy of recent applications in small area statistics in many cases highly depends on the assumed properties of the underlying models and the availability of micro information. In finite population sampling, small sample sizes may increase the sensitivity of the modeling with respect to single units. In these cases, area-specific sample sizes tend to be small such that normal assumptions, even of area means, seem to be violated. Hence, applying robust estimation methods is expected to yield more reliable results. In general, two robust small area methods are applied, the robust EBLUP and the M-quantile method. Additionally, the use of adequate auxiliary information may further increase the accuracy of the estimates. In prediction based approaches where information is needed on universe level, in general, only few variables are available which can be used for modeling. In addition to variables from the dataset, in many cases further information may be available, e.g. geographical information which could indicate spatial dependencies between neighboring areas. This spatial information can be included in the modeling using spatially correlated area effects. Within the paper the classical robust EBLUP is extended to cover spatial area effects via a simultaneous autoregressive model. The performance of the different estimators are compared in a model-based simulation study.     

Multistate recapture models: Modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.     

Multistate recapture models: modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.