Assessment of source-specific health effects associated with an unknown number of major sources of multiple air pollutants: A unified Bayesian approach

Cardiovascular mortality; Model uncertainty; Multipollutant approach; Multivariate receptor models; PM health effects; Source apportionmen

Bayesian variable selection in quantile regression using the Savage-Dickey density ratio

In this paper we propose a Bayesian variable selection method in quantile regression based on the Savage-Dickey density ratio of Dickey (1976). The Bayes factor of a model containing a subset of variables against an encompassing model is given as the ratio of the marginal posterior and the marginal prior density of the corresponding subset of regression coefficients under the encompassing model. Posterior samples are generated from the encompassing model via a Gibbs sampling algorithm and the Bayes factors of all candidate models are computed simultaneously using one set of posterior samples from the encompassing model. The performance of the proposed method is investigated via simulation examples and real data sets. © 2016

Bayesian Multidimensional Scaling and Choice of Dimension

Multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects. We deal with two major problems in metric multidimensional scaling - configuration of objects and determination of the dimension of object configuration - within a Bayesian framework. A Markov chain Monte Carlo algorithm is proposed for object configuration, along with a simple Bayesian criterion, called MDSIC, for choosing their dimension. Simulation results are presented, as are real data. Our method provides better results than does classical multidimensional scaling and ALSCAL for object configuration, and MDSIC seems to work well for dimension choice in the examples considered

Robust Bayesian multivariate receptor modeling

Multivariate receptor modeling aims to unfold the multivariate air pollution data into components associated with different sources of air pollution based on ambient measurements of air pollutants. It is now a widely accepted approach in source identification and apportionment. An evolving area of research in multivariate receptor modeling is to quantify uncertainty in estimated source contributions as well as model uncertainty caused by the unknown identifiability conditions, sometimes referred to as rotational ambiguity. Unlike the uncertainty estimates for the source composition profiles that have been available in commonly used receptor modeling tools such as positive matrix factorization, little research has been conducted on the uncertainty estimation for the source contributions or the identifiability conditions. Bayesian multivariate receptor modeling based on Markov chain Monte Carol methods is an attractive approach as it offers a great deal of flexibility in both modeling and estimation of parameter uncertainty and model uncertainty. In this paper, we propose a robust Bayesian multivariate receptor modeling approach that can simultaneously estimate uncertainty in source contributions as well as in compositions and uncertainty due to the unknown identifiability conditions by extending the previous Bayesian multivariate receptor modeling in two ways. First, we explicitly account for nonnegativity constraints on the source contributions, in addition to the nonnegativity constraints on the source compositions, in both parameter estimation and model uncertainty estimation. Second, we account for outliers that may often exist in the air pollution data in estimation by considering a heavy-tailed error distribution. The approach is illustrated with both simulated data and real PM2.5 speciation data from Phoenix, Arizona, USA. (C) 2015 Elsevier B.V. All rights reserved

Tests for seasonal unit roots in panels of cross-sectionally correlated time series

For panel models of cross-sectionally correlated time series, seasonal unit root tests are constructed for each seasonal frequency. The tests are based on instrumental variable estimators which are modifications of signs of the regressors. Cross-sectional correlation is controlled by rotating the system of time series using an estimated error covariance matrix. The limiting null distributions of the tests are chi-squared and are free from nuisance parameters arising from cross-sectional correlation. A Monte-Carlo experiment compares size and power performances of the proposed tests. © 2009 Taylor & Francis

Bayesian inference and model selection in latent class logit models with parameter constraints: An application to market segmentation

Latent class models have recently drawn considerable attention among many researchers and practitioners as a class of useful tools for capturing heterogeneity across different segments in a target market or population. In this paper, we consider a latent class logit model with parameter constraints and deal with two important issues in the latent class models - parameter estimation and selection of an appropriate number of classes - within a Bayesian framework. A simple Gibbs sampling algorithm is proposed for sample generation from the posterior distribution of unknown parameters. Using the Gibbs output, we propose a method for determining an appropriate number of the latent classes. A real-world marketing example as an application for market segmentation is provided to illustrate the proposed method

Bayesian quantile multivariate receptor modeling

Multivariate receptor modeling is a collection of methods used for identifying major pollution sources and estimating their impacts by resolving ambient measurements of air pollutants collected at a receptor (or receptors) into components associated with different sources of air pollution. Air pollution data are often right-skewed and contain several outliers. While the outliers resulting from a laboratory error or a contamination in the field are considered to be faulty observations and need to be removed, some outliers such as those resulting from extreme values in source contributions may be valid observations and convey important information. In some cases, the modeling of very high concentrations of air pollutants such as 95th percentiles or 99th percentiles and estimating the corresponding source contributions and compositions, which could be different from those for the mean concentrations, may be of specific interest, e.g., in setting the standards for pollution control. Thus, it would be beneficial to model both the center and the tails of the distribution of air pollution data so that source contributions for extreme observations as well as those for typical observations can be estimated in order to provide more comprehensive knowledge on air pollution and underlying sources. In this paper, we propose a new flexible source apportionment approach, Bayesian quantile multivariate receptor modeling, which can easily deal with the non-normality of air pollution data and outliers by extending the idea of quantile regression. Bayesian quantile multivariate receptor modeling can estimate the source contributions corresponding to any part of the data distribution including the tails and the center. It can also be easily implemented by JAGS, free software developed for the analysis of Bayesian models using the Markov chain Monte Carlo simulation. The proposed method is illustrated with simulated data and PM2.5 speciation data from El Paso, Texas, USA. © 2016 Elsevier B.V

A Gibbs sampling approach to Bayesian analysis of generalized linear models for binary data

A Monte Carlo Gibbs sampling approach is suggested for Bayesian posterior inference on unknown parameters in generalized linear models for binary data. This paper exploits the idea of Albert and Chib(1993), introducing normal latent variables into a model and connecting the binary response data with a normal linear model on continuous latent response data. Then all the full conditional distributions of unknown parameters are given by normal distributions with restrictions. Simple and accurate approximations to the restrictions are suggested so that the Gibbs sampler can be very easily implemented

Multivariate receptor models and model uncertainty

Estimation of the number of major pollution sources, the source composition profiles, and the source contributions are the main interests in multivariate receptor modeling. Due to lack of identifiability of the receptor model, however, the estimation cannot be done without some additional assumptions. A common approach to this problem is to estimate the number of sources, q, at the first stage, and then estimate source profiles and contributions at the second stage, given additional constraints (identifiability conditions) to prevent source rotation/transformation and the assumption that the q-source model is correct. These assumptions on the parameters (the number of sources and identifiability conditions) are the main source of model uncertainty in multivariate receptor modeling. In this paper, we suggest a Bayesian approach to deal with model uncertainties in multivariate receptor models by using Markov chain Monte Carlo (MCMC) schemes. Specifically, we suggest a method which can simultaneously estimate parameters (compositions and contributions), parameter uncertainties, and model uncertainties (number of sources and identifiability conditions). Simulation results and an application to air pollution data are presented. © 2002 Elsevier Science B.V. All rights reserved

A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling

Multidimensional scaling (MDS) is a technique which retrieves the locations of objects in a Euclidean space (the object configuration) from data consisting of the dissimilarities between pairs of objects. An important issue in MDS is finding an appropriate dimensionality underlying these dissimilarities. In this paper, we propose a simple and efficient Bayesian approach for selecting dimensionality in MDS. For each column (attribute) vector of an MDS configuration, we assume a prior that is a mixture of the point mass at 0 and a continuous distribution for the rest of the parameter space. Then the marginal posterior distribution of each column vector is also a mixture of the same form, in which the mixing weight of the continuous distribution is a measure of significance for the column vector. We propose an efficient Markov chain Monte Carlo (MCMC) method for estimating the mixture posterior distribution.The proposed method is fully Bayesian. It takes parameter estimation error into account when computing penalties for complex models and provides an uncertainty measure for the choice of dimensionality. Also, the MCMC algorithm is computationally very efficient since it visits various dimensional models in one MCMC procedure. A simulation study compares the proposed method with the Bayesian method of Oh and Raftery (2001). Three real data sets are analysed by using the proposed method. © 2012 Elsevier Inc