Alessandro Fasso

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 model-based framework for air quality indices and population risk evaluation, with an application to the analysis of Scottish air quality data

The paper is devoted to the development of a statistical framework for air quality assessment at the country level and for the evaluation of the ambient population exposure and risk with respect to airborne pollutants. The framework is based on a multivariate space–time model and on aggregated indices defined at different levels of aggregation in space and time. The indices are evaluated, uncertainty included, by considering both the model outputs and the information on the population spatial distribution. The framework is applied to the analysis of air quality data for Scotland for 2009 referring to European and Scottish air quality legislation.

A comparison of clustering approaches for the study of the temporal coherence of multiple time series

Two approaches for clustering of time series have been considered. The first is a novel approach based on a modification of classic state-space modelling while the second is based on functional clustering. For the latter, both k-means and complete-linkage hierarchical clustering algorithms are adopted. The two approaches are compared using a simulation study, and are applied to lake surface water temperature for 256 lakes globally for 5 years of data, to investigate information obtained from each approach.

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.

Modelling collocation uncertainty of 3D atmospheric profiles

Atmospheric thermodynamic data are gathered by high technology remote instruments such as radiosondes, giving rise to profiles that are usually modelled as functions depending only on height. The radiosonde balloons, however, drift away in the atmosphere resulting in not necessarily vertical but three-dimensional trajectories. To model this kind of functional data, we introduce a “point based” formulation of an heteroskedastic functional regression model that includes a trivariate smooth function and results to be an extension of a previously introduced unidimensional model. Functional coefficients of both the conditional mean and variance are estimated by reformulating the model as a standard generalized additive model and subsequently as a mixed model. This reformulation leads to a double mixed model whose parameters are fitted by using an iterative algorithm that allows to adjust for heteroskedasticity. The proposed modelling approach is applied to describe collocation mismatch when we deal with couples of balloons launched at two different locations. In particular, we model collocation error of atmospheric pressure in terms of meteorological covariates and space and time mismatch. Results show that model fitting is improved once heteroskedasticity is taken into account.

Statistical assessment of air quality interventions

This paper presents a general spatio-temporal model for assessing the air quality impact of environmental policies which are introduced as abrupt changes. The estimation method is based on the EM algorithm and the model allows to estimate the impact on air quality over a region and the reduction of human exposure following the considered environmental policy. Moreover, impact testing is proposed as a likelihood ratio test and the number of observations after intervention is computed in order to achieve a certain power for a minimal reduction. An extensive case study is related to the introduction of the congestion charge in Milan city. The consequent estimated reduction of airborne particulate matters and total nitrogen oxides motivates the methods introduced while its derivation illustrates both implementation and inferential issues.

Covariance tapering for multivariate Gaussian random fields estimation

In recent literature there has been a growing interest in the construction of covariance models for multivariate Gaussian random fields. However, effective estimation methods for these models are somehow unexplored. The maximum likelihood method has attractive features, but when we deal with large data sets this solution becomes impractical, so computationally efficient solutions have to be devised. In this paper we explore the use of the covariance tapering method for the estimation of multivariate covariance models. In particular, through a simulation study, we compare the use of simple separable tapers with more flexible multivariate tapers recently proposed in the literature and we discuss the asymptotic properties of the method under increasing domain asymptotics.

GCOS reference upper air network (GRUAN): Steps towards assuring future climate records

The observational climate record is a cornerstone of our scientific understanding of climate changes and their potential causes. Existing observing networks have been designed largely in support of operational weather forecasting and continue to be run in this mode. Coverage and timeliness are often higher priorities than absolute traceability and accuracy. Changes in instrumentation used in the observing system, as well as in operating procedures, are frequent, rarely adequately documented and their impacts poorly quantified. For monitoring changes in upper-air climate, which is achieved through in-situ soundings and more recently satellites and ground-based remote sensing, the net result has been trend uncertainties as large as, or larger than, the expected emergent signals of climate change. This is more than simply academic with the tropospheric temperature trends issue having been the subject of intense debate, two international assessment reports and several US congressional hearings. For more than a decade the international climate science community has been calling for the instigation of a network of reference quality measurements to reduce uncertainty in our climate monitoring capabilities. This paper provides a brief history of GRUAN developments to date and outlines future plans. Such reference networks can only be achieved and maintained with strong continuing input from the global metrological community.

Residual Autocorrelation Distribution in the Validation Data Set

Testing model performance on a data set other than the data set used for estimation is common practice in econometrics, technological stochastic modelling and environmetrics. In this paper, using an ARMAX model, the asymptotic distribution of the residual autocorrelations in the validation data set is given and a χ2 test for overall residual incorrelation is considered.

Functional Control Charts and Health Monitoring of Steam Sterilizers

In this paper, motivated by a multiple profile monitoring problem, we introduce general functional exponentially weighted moving average (EWMA) control charts. When functional data to be monitored are smooth enough to be representable by a finite dimensional basis, a particular version of these functional EWMAs is shown to be a multivariate EWMA applied to basis coefficients. Hence, it is called f-EWMA for monitoring single profiles and f-MEWMA for multiple profiles. The use of f-MEWMA is illustrated in connection to health monitoring of a steam sterilizer during its life cycle. Indeed, each sterilization run gives several profiles related to machine health, and degradation of the steam sterilizer during its life cycle modifies profile curvature in an unpredictable way. Hence, a control chart capable to monitor multiple sterilization profiles during the sterilizer life cycle is needed. The f-EWMA thresholds or control limits have been computed using Monte Carlo simulations. Moreover, the f-EWMA performance has been assessed using experimental data generated in laboratory according to anomalies considered relevant to the sterilizer maintenance program. Consequently, the average run length for these anomalies has been computed applying Monte Carlo simulation to experimental results. Copyright