The statistical analysis of compositional data

Noel Cressie and Christopher WikleHardcover: 624 pagesYear: 2011Publisher: John WileyISBN-13: 978-0471692744Here is the new reference book about spatial and spatio-temporal statistical modeling! No...

Statistics for Spatio-Temporal Data

/pdf/spatial-and-spatio-temporal-models-with-r-inla-29eh5lqe7n.pdf

Spatial and spatio-temporal models with R-INLA

In this work, we consider a hierarchical spatio-temporal model for particulate matter (PM) concentration in the North-Italian region Piemonte. The model involves a Gaussian Field (GF), affected by a measurement error, and a state process characterized by a first order autoregressive dynamic model and spatially correlated innovations. This kind of model is well discussed and widely used in the air quality literature thanks to its flexibility in modelling the effect of relevant covariates (i.e. meteorological and geographical variables) as well as time and space dependence. However, Bayesian inference—through Markov chain Monte Carlo (MCMC) techniques—can be a challenge due to convergence problems and heavy computational loads. In particular, the computational issue refers to the infeasibility of linear algebra operations involving the big dense covariance matrices which occur when large spatio-temporal datasets are present. The main goal of this work is to present an effective estimating and spatial prediction strategy for the considered spatio-temporal model. This proposal consists in representing a GF with Matern covariance function as a Gaussian Markov Random Field (GMRF) through the Stochastic Partial Differential Equations (SPDE) approach. The main advantage of moving from a GF to a GMRF stems from the good computational properties that the latter enjoys. In fact, GMRFs are defined by sparse matrices that allow for computationally effective numerical methods. Moreover, when dealing with Bayesian inference for GMRFs, it is possible to adopt the Integrated Nested Laplace Approximation (INLA) algorithm as an alternative to MCMC methods giving rise to additional computational advantages. The implementation of the SPDE approach through the R-library INLA (
 www.r-inla.org
 ) is illustrated with reference to the Piemonte PM data. In particular, providing the step-by-step R-code, we show how it is easy to get prediction and probability of exceedance maps in a reasonable computing time.

/pdf/spatio-temporal-modeling-of-particulate-matter-concentration-y4zaswgved.pdf

Spatio-temporal modeling of particulate matter concentration through the SPDE approach

Sources of high PM2.5 concentrations in Milan, Northern Italy: Molecular marker data and CMB modelling

. Vertical aerosol profiles were directly measured over the city of Milan during three years (2005–2008) of field campaigns. An optical particle counter, a portable meteorological station and a miniaturized cascade impactor were deployed on a tethered balloon. More than 300 vertical profiles were measured, both in winter and summer, mainly in conditions of clear, dry skies. The mixing height was determined from the observed vertical aerosol concentration gradient, and from potential temperature and relative humidity profiles. Results show that inter-consistent mixing heights can be retrieved highlighting good correlations between particle dispersion in the atmosphere and meteorological parameters. Mixing height growth speed was calculated for both winter and summer showing the low potential atmospheric dispersion in winter. Aerosol number size distribution and chemical composition profiles allowed us to investigate particle behaviour along height. Aerosol measurements showed changes in size distribution according to mixing height. Coarse particle profiles (dp>1.6 μm) were distributed differently than the fine ones (dp

/pdf/vertically-resolved-particle-size-distribution-within-and-5eu5kss982.pdf

Vertically-resolved particle size distribution within and above the mixing layer over the Milan metropolitan area

https://cab.unime.it/mus/384/1/Hierarchical_Space-time_Modelling_of_PM10_Pollution_in_the_Emilia-Romagna_Region.pdf

Hierarchical space-time modelling of PM10 pollution

Rainfall is a phenomenon difficult to model and predict, for the strong spatial and temporal heterogeneity and the presence of many zero values. We deal with hourly rainfall data provided by rain gauges, sparsely distributed on the ground, and radar data available on a fine grid of pixels. Radar data overcome the problem of sparseness of the rain gauge network, but are not reliable for the assessment of rain amounts. In this work we investigate how to calibrate radar measurements via rain gauge data and make spatial predictions for hourly rainfall, by means of Monte Carlo Markov Chain algorithms in a Bayesian hierarchical framework. We use zero-inflated distributions for taking zero-measurements into account. Several models are compared both in terms of data fitting and predictive performances on a set of validation sites. Finally, rainfall fields are reconstructed and standard error estimates at each prediction site are shown via easy-to-read spatial maps.

Spatial reconstruction of rainfall fields from rain gauge and radar data

Disease mapping studies have been widely performed at univariate level, that is considering only one disease in the estimated models. Nonetheless, simultaneous modelling of different diseases can be a valuable tool both from the epidemiological and from the statistical point of view. In this paper we propose a model for multivariate disease mapping that generalizes the univariate conditional auto-regressive distribution. The proposed model is proven to be an effective alternative to existing multivariate models, mainly because it overcome some restrictive hypotheses underlying models previously proposed in this context. Model performances are checked via a simulation study and via application to a case study.

/pdf/a-multivariate-car-model-for-improving-the-estimation-of-28qk7rl2wv.pdf

A multivariate CAR model for improving the estimation of relative risks.

Ecological regression studies are widely used in geographical epidemiology to assess the relationships between health hazard and putative risk factors. Very often, health data are measured at an aggregate level because of confidentiality restrictions, while putative risk factors are measured on a different grid, i.e., independent (exposure) variable and response (counts) variable are spatially misaligned. To perform a regression of risk on exposure, one needs to realign the spatial support of the variables. Bayesian hierarchical models constitute a natural approach to the problem because of their ability to model the exposure field and the relationship between exposure and relative risk at different levels of the hierarchy, taking proper account of the variability induced by the covariate estimation. In the current paper, we propose two fully Bayesian solutions to the problem. The first one is based on the kernel-smoothing technique, while the second one is built on the tessellation of the study region. We illustrate our methods by assessing the relationship between exposure to uranium in drinkable waters and cancer incidence, in South Carolina (USA).

Fedele Pasquale Greco

Papers

Vertically-resolved particle size distribution within and above the mixing layer over the Milan metropolitan area

Hierarchical space-time modelling of PM10 pollution

Spatial reconstruction of rainfall fields from rain gauge and radar data

A multivariate CAR model for improving the estimation of relative risks.

Some Interpolation Estimators in Environmental Risk Assessment for Spatially Misaligned Health Data