Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM<sub>2.5</sub>Exposure

Kibria, B. M. Golam; Sun, Li; Zidek, James V.; Le, Nhu D.

doi:10.1198/016214502753479275

Cited by 50 publications

(25 citation statements)

References 18 publications

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“…In fact, the generalized inverted Wishart prior in Kibria, Sun, Zidek and Le (2002) is to define each ii as an inverted Wishart distribution and each i as matrix-variate normal distribution. Moreover, the decomposition (30) may be viewed as a block counterpart of the decomposition considered by Pourahmadi (1999Pourahmadi ( , 2000, and Daniels and Pourahmadi (2002), etc.…”

Section: Bartlet Decompositionmentioning

confidence: 99%

“…Jinadasa and Tracy (1992) obtain a complicated form for the maximum likelihood estimators of the unknown mean and the covariance matrix in terms of some sufficient statistics, which extends the work of Anderson and Olkin (1985). Recently, Kibria, Sun, Zidek and Le (2002) discussed estimating using a generalized inverted Wishart (GIW) prior and applied the result to mapping PM 2.5 exposure. Other related references may include Liu (1999), Little and Rubin (1987), and Brown, Le and Zidek (1994).…”

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confidence: 96%

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Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Sun

2006

AISM

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Section: Bartlet Decompositionmentioning

confidence: 99%

mentioning

confidence: 96%

Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Sun

2006

AISM

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“…The method of moments developed by (Kibria et al, 2002) is used to estimate the model parameters. The estimate of the degrees of freedom is Ã ¼ 298:6 or the estimated is ¼ 298:6À 240 þ 1 ¼ 59:6.…”

Section: Giw Model With Kronecker Structurementioning

confidence: 99%

Contending with space–time interaction in the spatial prediction of pollution: Vancouver's hourly ambient PM₁₀ field

Zidek

Sun

et al. 2002

Environmetrics

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SUMMARYIn this article we describe an approach for predicting average hourly concentrations of ambient PM 10 in Vancouver. We know our solution also applies to hourly ozone fields and believe it may be quite generally applicable. We use a hierarchical Bayesian approach. At the primary level we model the logarithmic field as a trend model plus Gaussian stochastic residual. That trend model depends on hourly meteorological predictors and is common to all sites. The stochastic component consists of a 24-hour vector response that we model as a multivariate AR(3) temporal process with common spatial parameters. Removing the trend and AR structure leaves 'whitened' time series of vector series. With this approach (as opposed to using 24 separate univariate time series models), there is little loss of spatial correlation in these residuals compared with that in just the detrended residuals (prior to removing the AR component). Moreover our multivariate approach enables predictions for any given hour to 'borrow strength' through its correlation with adjoining hours. On this basis we develop a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales we can impute Vancouver's hourly PM 10 field.

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“…Several recent papers (Brown et al, 1994;Li et al, 1999;Golam Kibria et al, 2002) consider spatio-temporal modeling and interpolation for air pollutants such as ozone, while others (Zidek et al, 1998;Dominici et al, 2002) extend to investigating the relationship between pollutants and mortality or other adverse health effects. While this work is Bayesian, spatio-temporal, and often accommodates missing data, it does not seem to handle the sort of spatial data misalignment that we face.…”

Section: Introductionmentioning

confidence: 98%

Hierarchical regression with misaligned spatial data: relating ambient ozone and pediatric asthma ER visits in Atlanta

2003

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SUMMARYRecent work by the authors enabled a hierarchical modeling solution to the general change of support problem (COSP), where they seek to make inferences about the values of a variable at either points or regions different from those at which it has been observed. The approach presumes an underlying continuous stationary spatial process XðsÞ for locations s 2 D, a region of interest. It is straightforwardly extended to the spatio-temporal setting by assuming a space-time separable covariance function for the Xðs; tÞ process, t 2 T and again s 2 D. In this article they take up the associated misaligned regression problem, where, for example, the explanatory variable is envisioned from the Xðs; tÞ process, while the response is available only as areal summaries over a particular grid at particular times. They illustrate using a dataset relating several air quality indicators (ozone, particulate matter, nitrogen oxides, etc.) and a range of sociodemographic variables (age, gender, race, and a socioeconomic status surrogate) to the response, pediatric emergency room (ER) visit counts for asthma in Atlanta, Georgia. Here the air quality data is collected at fixed monitoring stations (point locations) while the sociodemographic covariates and response variable is collected by zip code (areal summaries). In fact, the air quality data are available as daily averages at each monitoring station, and the response is available as daily counts of visits in each zip code. As is now common in hierarchical Bayesian spatial applications, computing is implemented via a carefully tailored Metropolis-Hastings algorithm, with map summaries created using a geographic information system (GIS). Like many recent investigations of the ozone-asthma link, our results suggest a small positive association, though our data can permit this conclusion only for those children living in the city of Atlanta who use the ER to manage their asthma.

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Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM_2.5Exposure

Cited by 50 publications

References 18 publications

Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Contending with space–time interaction in the spatial prediction of pollution: Vancouver's hourly ambient PM₁₀ field

Hierarchical regression with misaligned spatial data: relating ambient ozone and pediatric asthma ER visits in Atlanta

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Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM2.5Exposure

Cited by 50 publications

References 18 publications

Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data

Contending with space–time interaction in the spatial prediction of pollution: Vancouver's hourly ambient PM10 field

Hierarchical regression with misaligned spatial data: relating ambient ozone and pediatric asthma ER visits in Atlanta

Contact Info

Product

Resources

About

Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM_2.5Exposure

Contending with space–time interaction in the spatial prediction of pollution: Vancouver's hourly ambient PM₁₀ field