Michela Cameletti

Spatial and spatio-temporal models with R-INLA.

During the last three decades, Bayesian methods have developed greatly in the field of epidemiology. Their main challenge focusses around computation, but the advent of Markov Chain Monte Carlo methods (MCMC) and in particular of the WinBUGS software has opened the doors of Bayesian modelling to the wide research community. However model complexity and database dimension still remain a constraint. Recently the use of Gaussian random fields has become increasingly popular in epidemiology as very often epidemiological data are characterised by a spatial and/or temporal structure which needs to be taken into account in the inferential process. The Integrated Nested Laplace Approximation (INLA) approach has been developed as a computationally efficient alternative to MCMC and the availability of an R package (R-INLA) allows researchers to easily apply this method. In this paper we review the INLA approach and present some applications on spatial and spatio-temporal data.

The EM algorithm in a distributed computing environment for modelling environmental space-time data

Statistical models for spatio-temporal data are increasingly used in environmetrics, climate change, epidemiology, remote sensing and dynamical risk mapping. Due to the complexity of the relationships among the involved variables and dimensionality of the parameter set to be estimated, techniques for model definition and estimation which can be worked out stepwise are welcome. In this context, hierarchical models are a suitable solution since they make it possible to define the joint dynamics and the full likelihood starting from simpler conditional submodels. Moreover, for a large class of hierarchical models, the maximum likelihood estimation procedure can be simplified using the Expectation-Maximization (EM) algorithm. In this paper, we define the EM algorithm for a rather general three-stage spatio-temporal hierarchical model, which includes also spatio-temporal covariates. In particular, we show that most of the parameters are updated using closed forms and this guarantees stability of the algorithm unlike the classical optimization techniques of the Newton-Raphson type for maximizing the full likelihood function. Moreover, we illustrate how the EM algorithm can be combined with a spatio-temporal parametric bootstrap for evaluating the parameter accuracy through standard errors and non-Gaussian confidence intervals. To do this a new software library in form of a standard R package has been developed. Moreover, realistic simulations on a distributed computing environment allow us to discuss the algorithm properties and performance also in terms of convergence iterations and computing times.

A Unified Statistical Approach for Simulation, Modeling, Analysis and Mapping of Environmental Data

In this paper, hierarchical models are proposed as a general approach for spatio-temporal problems, including dynamical mapping, and the analysis of the outputs from complex environmental modeling chains. In this frame, it is easy to define various model components concerning both model outputs and empirical data and to cover with both spatial and temporal correlation. Moreover, special sensitivity analysis techniques are developed for understanding both model components and mapping capability. The motivating application is the dynamical mapping of airborne particulate matters for risk monitoring using data from both a monitoring network and a computer model chain, which includes an emission, a meteorological and a chemical-transport module. Model estimation is determined by the Expectation-Maximization (EM) algorithm associated with simulation-based spatio-temporal parametric bootstrap. Applying sensitivity analysis techniques to the same hierarchical model provides interesting insights into the computer model chain.

Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions

Exposure to high levels of air pollutant concentration is known to be associated with respiratory problems which can translate into higher morbidity and mortality rates. The link between air pollution and population health has mainly been assessed considering air quality and hospitalisation or mortality data. However, this approach limits the analysis to individuals characterised by severe conditions. In this paper we evaluate the link between air pollution and respiratory diseases using general practice drug prescriptions for chronic respiratory diseases, which allow to draw conclusions based on the general population. We propose a two-stage statistical approach: in the first stage we specify a space-time model to estimate the monthly NO2 concentration integrating several data sources characterised by different spatio-temporal resolution; in the second stage we link the concentration to the β2-agonists prescribed monthly by general practices in England and we model the prescription rates through a small area approach.

An ordered probit model for seismic intensity data

Seismic intensity, measured through the Mercalli–Cancani–Sieberg (MCS) scale, provides an assessment of ground shaking level deduced from building damages, any natural environment changes and from any observed effects or feelings. Generally, moving away from the earthquake epicentre, the effects are lower but intensities may vary in space, as there could be areas that amplify or reduce the shaking depending on the earthquake source geometry, geological features and local factors. Currently, the Istituto Nazionale di Geofisica e Vulcanologia analyzes, for each seismic event, intensity data collected through the online macroseismic questionnaire available at the web-page www.haisentitoilterremoto.it. Questionnaire responses are aggregated at the municipality level and analyzed to obtain an intensity defined on an ordinal categorical scale. The main aim of this work is to model macroseismic attenuation and obtain an intensity prediction equation which describes the decay of macroseismic intensity as a function of the magnitude and distance from the hypocentre. To do this we employ an ordered probit model, assuming that the intensity response variable is related through the link probit function to some predictors. Differently from what it is commonly done in the macroseismic literature, this approach takes properly into account the qualitative and ordinal nature of the macroseismic intensity as defined on the MCS scale. Using Markov chain Monte Carlo methods, we estimate the posterior probability of the intensity at each site. Moreover, by comparing observed and estimated intensities we are able to detect anomalous areas in terms of residuals. This kind of information can be useful for a better assessment of seismic risk and for promoting effective policies to reduce major damages.

Species distribution modeling: a statistical review with focus in spatio-temporal issues

The use of complex statistical models has recently increased substantially in the context of species distribution behavior. This complexity has made the inferential and predictive processes challenging to perform. The Bayesian approach has become a good option to deal with these models due to the ease with which prior information can be incorporated along with the fact that it provides a more realistic and accurate estimation of uncertainty. In this paper, we first review the sources of information and different approaches (frequentist and Bayesian) to model the distribution of a species. We also discuss the Integrated Nested Laplace approximation as a tool with which to obtain marginal posterior distributions of the parameters involved in these models. We finally discuss some important statistical issues that arise when researchers use species data: the presence of a temporal effect (presenting different spatial and spatio-temporal structures), preferential sampling, spatial misalignment, non-stationarity, imperfect detection, and the excess of zeros.

An analysis of temporal and spatial patterns in Italian hospitalization rates for multiple diagnosis

In this paper, the Italian hospitalization database provided by the Ministry of Health is analyzed in terms of the temporal and spatial patterns of the hospitalization rates. The database covers the period 2010-2012 and the rates are evaluated for 110 Italian provinces and 18 diagnosis groups as defined by the ICD-9 classification. The analysis is based on a novel model-based clustering approach which enables clustering of spatially registered time series with respect to latent temporal patterns. The clustering result is analyzed to study the spatial distribution of the latent temporal patterns and their trend in order to identify possible critical areas in terms of increasing rates. Additionally, emerging spatial patterns may help common causes driving the hospitalization rates to be identified.

A GPU Software Library for Likelihood-Based Inference of Environmental Models with Large Datasets

Statistical environmental models are computationally intensive due to the high dimension of the data, both in space and time, and due to the inferential techniques required for parameter estimation and spatial prediction. In particular, the computational complexity of these techniques is related to matrix operations (inversion, solution of linear systems, factorization) involving large dense matrices. Recently, much attention has been paid around the possibility of taking advantage of graphics processing units (GPUs) for mathematical computation. GPUs provide a high degree of parallelism at a reasonable cost and may represent a viable alternative compared to the classic computer cluster configurations. In this work, we develop the shared library GPU4GL implementing ad-hoc linear-algebra functions running on GPUs and compare them with the standard algorithms for CPU. As an example, we apply the GPU functions of GPU4GL to make inference on a non-separable space–time model for air quality data.