High-Resolution Space–Time Ozone Modeling for Assessing Trends

Sahu, Sujit K.; Gelfand, Alan E.; Holland, David M.

doi:10.1198/016214507000000031

Cited by 92 publications

(103 citation statements)

References 19 publications

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“…In practice, however, being a spatially coloured matrix, Q x will depend on several unknown parameters describing smoothness and rate of spatial decay. It is likely that Gaussian approximations for the posterior distributions of those parameters will be more challenging, since MCMC sampling algorithms often behave very poorly owing to weak identifiability; see for example Sahu et al (2007).…”

Section: Sujit K Sahu (University Of Southampton)mentioning

confidence: 99%

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Rue

Martino

Chopin

2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

4,206

4,451

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Summary. Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

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Section: Sujit K Sahu (University Of Southampton)mentioning

confidence: 99%

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Rue

Martino

Chopin

2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

4,206

4,451

View full text Add to dashboard Cite

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“…Here, we consider exponential correlation functions, which are used widely in applications (Sahu et al 2010;Berrocal et al 2010;Sahu et al 2007;Huerta et al 2004). We have that…”

Section: Effect Of Spatial Correlationmentioning

confidence: 99%

“…We let a 0 = a = 2 and b = b = 1, implying a prior mean of one and infinite prior variance for σ 2 0 and σ 2 . These are common hyperparameters for inverse gamma prior distributions, see Sahu et al (2007), Gelfand et al (2003. Figure 12 shows boxplots of the MPSRF M (1.1) (top row) and the ESS of θ 0 (bottom row) for the CP.…”

Section: A Simulation Studymentioning

confidence: 99%

“…We We begin by estimating the decay parameters using an empirical Bayes method by performing a grid search over a small number of values, then choosing those values that minimise some calibration criterion. This is a common approach adopted by many authors, e.g., Sahu et al (2011), Berrocal et al (2010, Sahu et al (2007) since Zhang (2004) showed that it is not possible to consistently estimate these in a model with Matérn covariance function in the presence of other unknown parameters. In our Bayesian inference setting, this will imply weak identifiability in the posterior distribution when non-informative prior distributions are assumed.…”

Section: Real-data Examplementioning

confidence: 99%

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A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC

Bass

2016

Stat Comput

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Markov chain Monte Carlo (MCMC) algorithms for Bayesian computation for Gaussian process-based models under default parameterisations are slow to converge due to the presence of spatial-and other-induced dependence structures. The main focus of this paper is to study the effect of the assumed spatial correlation structure on the convergence properties of the Gibbs sampler under the default non-centred parameterisation and a rival centred parameterisation (CP), for the mean structure of a general multi-process Gaussian spatial model. Our investigation finds answers to many pertinent, but as yet unanswered, questions on the choice between the two. Assuming the covariance parameters to be known, we compare the exact rates of convergence of the two by varying the strength of the spatial correlation, the level of covariance tapering, the scale of the spatially varying covariates, the number of data points, the number and the structure of block updating of the spatial effects and the amount of smoothness assumed in a Matérn covariance function. We also study the effects of introducing differing levels of geometric anisotropy in the spatial model. The case of unknown variance parameters is investigated using wellknown MCMC convergence diagnostics. A simulation study and a real-data example on modelling air pollution levels in London are used for illustrations. A generic pattern emerges that the CP is preferable in the presence of more spatial correlation or more information obtained through, for example, additional data points or by increased covariate variability.

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“…Zheng et al (2007) use a dynamic linear model and a generalized additive model to explain ozone trends. A recent paper by Sahu (2007) presents a very elegant approach, using ozone differentials to explain spatial temporal patterns for ozone in Ohio. In their model, the authors add a correlated error structure using a linear model of coregionalization that has a stationary covariance model.…”

Section: Introductionmentioning

confidence: 99%

A class of nonseparable and nonstationary spatial temporal covariance functions

2007

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SUMMARYSpectral methods are powerful tools to study and model the dependency structure of spatial temporal processes. However, standard spectral approaches as well as geostatistical methods assume separability and stationarity of the covariance function; these can be very unrealistic assumptions in many settings. In this work, we introduce a general and flexible parametric class of spatial temporal covariance models, that allows for lack of stationarity and separability by using a spectral representation of the process. This new class of covariance models has a unique parameter that indicates the strength of the interaction between the spatial and temporal components; it has the separable covariance model as a particular case. We introduce an application with ambient ozone air pollution data provided by the U.S. Environmental Protection Agency (U.S. EPA).

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High-Resolution Space–Time Ozone Modeling for Assessing Trends

Cited by 92 publications

References 19 publications

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC

A class of nonseparable and nonstationary spatial temporal covariance functions

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