Regional source apportionment of PM2.5 in Seoul using Bayesian multivariate receptor model

Seoul, the capital city of Korea with over 10 million residents, has been experiencing serious air pollution problems. Previous studies on source apportionment of PM2.5 in Seoul are based on measurements of chemical compositions of PM2.5 from a single monitoring site. In this paper, we analyse PM2.5 concentration data collected from multiple sites in 24 districts of Seoul and estimate regional source profiles using Bayesian multivariate receptor model. The regional source profiles provide information for the identification of major PM2.5 sources as well as the regions relatively more seriously affected by each source than other regions. These regional characteristics relevant to PM2.5 can help establish effective, customised, region-specific PM2.5 control strategies for each region rather than general strategies that apply to every region of Seoul.     

Maximum likelihood estimation of bivariate circular hidden Markov models from incomplete data

In this paper, we propose a hidden Markov model for the analysis of the time series of bivariate circular observations, by assuming that the data are sampled from bivariate circular densities, whose parameters are driven by the evolution of a latent Markov chain. The model segments the data by accounting for redundancies due to correlations along time and across variables. A computationally feasible expectation maximization (EM) algorithm is provided for the maximum likelihood estimation of the model from incomplete data, by treating the missing values and the states of the latent chain as two different sources of incomplete information. Importance-sampling methods facilitate the computation of bootstrap standard errors of the estimates. The methodology is illustrated on a bivariate time series of wind and wave directions and compared with popular segmentation models for bivariate circular data, which ignore correlations across variables and/or along time.     

A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models

Hierarchical spatio-temporal models allow for the consideration and estimation of many sources of variability. A general spatio-temporal model can be written as the sum of a spatio-temporal trend and a spatio-temporal random effect. When spatial locations are considered to be homogeneous with respect to some exogenous features, the groups of locations may share a common spatial domain. Differences between groups can be highlighted both in the large-scale, spatio-temporal component and in the spatio-temporal dependence structure. When these differences are not included in the model specification, model performance and spatio-temporal predictions may be weak. This paper proposes a method for evaluating and comparing models that progressively include group differences. Hierarchical modeling under a Bayesian perspective is followed, allowing flexible models and the statistical assessment of results based on posterior predictive distributions. This procedure is applied to tropospheric ozone data in the Italian Emilia–Romagna region for 2001, where 30 monitoring sites are classified according to environmental laws into two groups by their relative position with respect to traffic emissions.     

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.     

Model-based clustering of multivariate skew data with circular components and missing values

Motivated by classification issues that arise in marine studies, we propose a latent-class mixture model for the unsupervised classification of incomplete quadrivariate data with two linear and two circular components. The model integrates bivariate circular densities and bivariate skew normal densities to capture the association between toroidal clusters of bivariate circular observations and planar clusters of bivariate linear observations. Maximum-likelihood estimation of the model is facilitated by an expectation maximization (EM) algorithm that treats unknown class membership and missing values as different sources of incomplete information. The model is exploited on hourly observations of wind speed and direction and wave height and direction to identify a number of sea regimes, which represent specific distributional shapes that the data take under environmental latent conditions.     

Multimodal exponential families of circular distributions with application to daily peak hours of PM2.5 level in a large city

In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between.     

Maximum likelihood estimation for generalized conditionally autoregressive models of spatial data

Conditionally autoregressive (CAR) models are often used to analyze a spatial process observed over a lattice or a set of irregular regions. The neighborhoods within a CAR model are generally formed deterministically using the inter-distances or boundaries between the regions. To accommodate directional and inherent anisotropy variation, a new class of spatial models is proposed that adaptively determines neighbors based on a bivariate kernel using the distances and angles between the centroid of the regions. The newly proposed model generalizes the usual CAR model in a sense of accounting for adaptively determined weights. Maximum likelihood estimators are derived and simulation studies are presented for the sampling properties of the estimates on the new model, which is compared to the CAR model. Finally the method is illustrated using a data set on the elevated blood lead levels of children under the age of 72 months observed in Virginia in the year of 2000.     

Approximating the projection depth median of dimensions p ⩾ 3

As a multivariate generalization of the univariate median, projection depth median (PM) is unique, and enjoys a very high breakdown point, much higher than its affine equivariant competitors such as halfspace depth median. Nevertheless, its computation is challenging. Until now PM can only be exactly computed efficiently for bivariate data. In this article, we develop an algorithm to approximate PM in higher dimensions. Some data examples indicate that the proposed algorithm performs well in terms of both accuracy and efficiency. As an application, we investigate the finite sample relative efficiency of PM by utilizing the Matlab implementation of this algorithm.     

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.     

Optimal designs for contingent response models with application to toxicity–efficacy studies

We describe a general family of contingent response models. These models have ternary outcomes constructed from two Bernoulli outcomes, where one outcome is only observed if the other outcome is positive. This family is represented in a canonical form which yields general results for its Fisher information. A bivariate extreme value distribution illustrates the model and optimal design results. To provide a motivating context, we call the two binary events that compose the contingent responses toxicity and efficacy. Efficacy or lack thereof is assumed only to be observable in the absence of toxicity, resulting in the ternary response (toxicity, efficacy without toxicity, neither efficacy nor toxicity). The rate of toxicity, and the rate of efficacy conditional on no toxicity, are assumed to increase with dose. While optimal designs for contingent response models are numerically found, limiting optimal designs can be expressed in closed forms. In particular, in the family of four parameter bivariate location-scale models we study, as the marginal probability functions of toxicity and no efficacy diverge, limiting D optimal designs are shown to consist of a mixture of the D optimal designs for each failure (toxicity and no efficacy) univariately. Limiting designs are also obtained for the case of equal scale parameters.     

Some alternative bivariate Kumaraswamy models

In this article we discuss various strategies for constructing bivariate Kumaraswamy distributions. As alternatives to the Nadarajah et al. (2011) bivariate model, four different models are introduced utilizing a conditional specification approach, a conditional survival function approach, and an Arnold–Ng bivariate beta distribution construction approach. Distributional properties for such bivariate distributions are investigated. Parameter estimation strategies for the models are discussed, as are the consequences of fitting two of the models to a particular data set involving the proportion of foggy days at two different airports in Colombia.     

A bivariate generalized linear model with an application to meteorological data analysis

A bivariate generalized linear model is developed as a mixture distribution with one component of the mixture being discrete with probability mass only at the origin. The use of the proposed model is illustrated by analyzing local area meteorological measurements with constant correlation structure that incorporates predictor variables. The Monte Carlo study is performed to evaluate the inferential efficiency of model parameters for two types of true models. These results suggest that the estimates of regression parameters are consistent and the efficiency of the inference increases for the proposed model for ρ≥0.50 especially in larger samples. As an illustration of a bivariate generalized linear model, we analyze a precipitation monitoring data of adjacent local stations for Tokyo and Yokohama.     

Comparisons of some bivariate regression models

The bivariate negative binomial regression (BNBR) and the bivariate Poisson log-normal regression (BPLR) models have been used to describe count data that are over-dispersed. In this paper, a new bivariate generalized Poisson regression (BGPR) model is defined. An advantage of the new regression model over the BNBR and BPLR models is that the BGPR can be used to model bivariate count data with either over-dispersion or under-dispersion. In this paper, we carry out a simulation study to compare the three regression models when the true data-generating process exhibits over-dispersion. In the simulation experiment, we observe that the bivariate generalized Poisson regression model performs better than the bivariate negative binomial regression model and the BPLR model.     

Multivariate spatial interpolation and exposure to air pollutants

We develop and apply an approach to the spatial interpolation of a vector-valued random response field. The Bayesian approach we adopt enables uncertainty about the underlying models to be représentés in expressing the accuracy of the resulting interpolants. The methodology is particularly relevant in environmetrics, where vector-valued responses are only observed at designated sites at successive time points. The theory allows space-time modelling at the second level of the hierarchical prior model so that uncertainty about the model parameters has been fully expressed at the first level. In this way, we avoid unduly optimistic estimates of inferential accuracy. Moreover, the prior model can be upgraded with any available new data, while past data can be used in a systematic way to fit model parameters. The theory is based on the multivariate normal and related joint distributions. Our hierarchical prior models lead to posterior distributions which are robust with respect to the choice of the prior (hyperparameters). We illustrate our theory with an example involving monitoring stations in southern Ontario, where monthly average levels of ozone, sulphate, and nitrate are available and between-station response triplets are interpolated. In this example we use a recently developed method for interpolating spatial correlation fields.     

Large-scale Bayesian spatial modelling of air pollution for policy support

The potential effects of air pollution are a major concern both in terms of the environment and in relation to human health. In order to support environmental policy, there is a need for accurate measurements of the concentrations of pollutants at high geographical resolution over large regions. However, within such regions, there are likely to be areas where the monitoring information will be sparse and so methods are required to accurately predict concentrations. Set within a Bayesian framework, models are developed which exploit the relationships between pollution and geographical covariate information, such as land use, climate and transport variables together with spatial structure. Candidate models are compared based on their ability to predict a set of validation sites. The chosen model is used to perform large-scale prediction of nitrogen dioxide at a 1×1 km resolution for the entire EU. The models allow probabilistic statements to be made with regard to the levels of air pollution that might be experienced in each area. When combined with population data, such information can be invaluable in informing policy by indicating areas for which improvements may be given priority.     

Non-mixture cure correlated frailty models in Bayesian approach

In this article, we develop a Bayesian approach for the estimation of two cure correlated frailty models that have been extended to the cure frailty models introduced by Yin [34]. We used the two different type of frailty with bivariate log-normal distribution instead of gamma distribution. A likelihood function was constructed based on a piecewise exponential distribution function. The model parameters were estimated by the Markov chain Monte Carlo method. The comparison of models is based on the Cox correlated frailty model with log-normal distribution. A real data set of bilateral corneal graft rejection was used to compare these models. The results of this data, based on deviance information criteria, showed the advantage of the proposed models.     

Construction of bivariate and multivariate weighted distributions via conditioning

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this article, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter, and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real-life data set is used to show the applicability of these bivariate weighted distributions.     

Identifying radon-prone building typologies by marginal modelling

Radon is a naturally occurring decay product of uranium known to be the main contributor to natural background radiation exposure. It has been established that the health risk related to radon exposure is lung cancer. In fact, radon is considered to be a major leading cause of lung cancer, second only to smoking. In this paper, we identified building typologies that affect the probability of detecting indoor radon concentration above reference values, using the data collected within two monitoring campaigns recently conducted in Northern Italy. This information is fundamental both in prevention, i.e. when the construction of a new building is planned and in mitigation, i.e. when a high concentration detected inside buildings has to be reduced. A spatial regression approach for binary data was adopted for this goal where some relevant covariates on the soil were retrieved by linking external spatial databases.     

Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.     

Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.