Fertility evolution in Italy has shown a deep drop in 1995, and up to now the fertility rate is considered among the lowest in the world. The empirical distribution of the age-specific fertility rates is characterized by a decreasing tendency of the maximum fertility rate and a simultaneous increase of the corresponding mother’s age. This tendency has been stimulating recent contributions in modelling and forecasting. The aim of this paper is to propose a dynamic model for describing and predicting the evolution of the Italian age-specific fertility rates over time. In particular, a well-documented model, such as a Gamma function, slightly modified in order to include time-varying stochastic parameters, is used to describe the systematic and macroscopic variations of the age-specific fertility rates over time, while a nonparametric geostatistical model is applied to describe the correlated residuals at microscopic level. Finally, predictions for the variable under study are provided and main empirical evidences of the temporal evolution for different mother’s ages are discussed.

In many environmental sciences, several correlated variables are observed at some locations of the domain of interest, then appropriate modeling and prediction techniques for multivariate spatial data are necessary. This paper aims to highlight the convenience of using multivariate geostatistical methods to study the spatial distribution of radon soil concentration, to map and assess high risk areas. Indeed, this soil gas, due its nature, is known to be carcinogen: many studies have demonstrated that risk of lung cancer increases substantially with the exposure to higher radon concentrations. In analyzing radon concentrations, it is relevant to consider the available data regarding the geology, geomorphology and soil type since this gas is released during the decay of some radioactive elements found in rocks and soil. Thus, the application of multivariate geostatistical techniques, such as indicator-cokriging and indicator kriging for conditional probability analysis, is convenient to classify areas according to radon levels and to provide probability maps of radon risk. Note that in this paper geostatistical bootstrap for quantifying spatial uncertainty has been performed. A case study on sample data concerning radon-222 concentrations, permeability, lithology, fault and polje in Lecce district (Southern Italy) is proposed. Radon risk prediction maps for the probability to exceed certain threshold values, conditioned to specific soil type, can be useful especially for regions with no or only few measurements of soil gas radon.

Sometimes, space-time covariance models can be derived as solutions of partial differential equations, for phenomena which can be described by physical laws. When the complexity of natural processes does not allow such a description, it would be useful to have a guide for selecting an appropriate class of space-time covariance models for a given data set, among the classes constructed in the last years. Thus, the main aim of this paper is to provide a general procedure for space-time modeling, where the first step to be made is not the choice of a particular covariance model but the choice of the class of covariance functions suitable for the variable under study. Hence, starting from a space-time data set, an adequate class of models will be properly chosen by considering the main characteristics, such as full symmetry, separability, behavior at the origin, anisotropy aspects, as well as type of non separability and asymptotic behavior. In the literature, these aspects have never been considered in a unified way; nevertheless, they can be relevant for selecting a suitable class of covariance models. The proposed procedure has been applied to both a simulated data set and an environmental case study.

Environmental data present nearly always a multivariate spatiotemporal structure. Simultaneous diagonalization of the sample matrix variogram is often convenient for isolating space and time correlation of complex latent components. This is also useful for modeling and prediction purposes.

Several studies have demonstrated that skilled human capital is a key resource for the economic growth of a territory, since it helps to increase productivity, competitiveness and sustainability over time. The aim of this paper is to model the probability of working for university graduates three years after degree, taking into account the effectiveness and coherence of a degree with respect to the labour market. Hence, first of all, a multilevel binary logit model for measuring the probability of working will be discussed. Then, a multilevel multinomial model suitable to predict the probability of the possible job status, such as unemployed/unsteady employed/steady employed, will be further proposed. The ISTAT microdata regarding the Italian survey on the graduates' employment conditions, will be used.

New classes of cross-covariance functions have been recently proposed, nevertheless the linear coregionalization model (LCM) is still of interest and widely applied. In this paper, a new fitting procedure of the space-time LCM (STLCM) using the generalized product-sum model is proposed. This procedure is based on the well known algorithm of matrix simultaneous diagonalization, applied on the sample matrix variograms computed for multiple spatial-temporal lags.

Multivariate analysis has been applied in order to assess the variables that influence behaviour and attitudes of visitors of a food and wine event. Stepwise logistic regression is also used and the most parsimonious set of predictors that are most effective in predicting the choice of purchase are considered

In the recent years, the interest in the quality measurement of a specific health care service has increased. In particular, patient satisfaction ratings are used as health care quality markers and then as profitable competitive tools for health care management. On the other hand, perceived quality of health care services has a great influence on patient behaviors. In this context, statistical tools and techniques for assessing patients satisfaction in hospitals and other health care organizations are very useful. In this paper, a case study on the service quality provided to the long-term cancer patients and the relationship between doctors and patients has been discussed. In particular, a questionnaire has been submitted to a sample of long-term cancer patients, who follow a therapy at some hospitals belonging to the district of Lecce (Apulia Region). Several dimensions of perceived service quality including tangible aspects, reliability, empathy (doctor-patient human relations) and hospital organization have been considered. Statistical methodologies for customer satisfaction have been used in order to identify the service quality factors that are important to patients. Moreover, multivariate statistical analysis has been performed in order to identify the service critical aspects to be improved and to determine significant associations between the selected dimensions and patients satisfaction.

Nel presente capitolo saranno illustrati i concetti di campo aleatorio spazio-temporale, separabilità, stazionarietà e completa simmetria. Successivamente, sar`a presentata una rassegna dei modelli di covarianza spazio-temporali disponibili in letteratura. Infine, dopo aver descritto le differenze tra modelli deterministici e stocastici, si illustrer`a il metodo del kriging per le previsioni spazio-temporali.

Nel presente capitolo saranno analizzati i decessi per tumori maligni nel periodo 1981- 2012, focalizzando l’attenzione dapprima sull’intera area del Grande Salento e, successivamente, sulle Province che lo compongono. Inoltre, sar`a condotta l’analisi statistica descrittiva del tasso di mortalità, rilevandone l’evoluzione temporale per l’intero periodo considerato. Successivamente, si fornir`a uno studio approfondito sulla mortalit`a per neoplasie all’apparato respiratorio e suoi annessi, che rappresenta una problematica sempre pi`u allarmante e significativamente correlata con differenti fattori di rischio (quali ad esempio, l’inquinamento atmosferico, le esposizioni sul luogo di lavoro o nel luogo di residenza). Tale analisi sar`a realizzata a scopi previsivi, avvalendosi di appropriate tecniche geostatistiche per il dominio temporale e spaziale. Le elaborazioni statistiche saranno effettuate sui dati forniti, a livello disaggregato, dall’ISTAT.

Abstract: The near simultaneous diagonalization of the sample space-time matrix covariances or variograms makes the fitting procedure of a space-time linear coregionalization model (ST-LCM) easier. The method is illustrated by a case study involving data on three environmental variables measured at some monitoring stations of the Puglia region, Italy. It is shown that the near diagonalization works very well for this data set and the cross validation results show that the fitted matrix variogram is appropriate for the data.

Although a wide list of classes of space–time covariance functions is nowavailable, selecting an appropriate class of models for a variable under study is still difficult and it represents a priority problem with respect to the choice of a particular model of a specified class.Then, knowing the characteristics of various classes of covariances, and their auxiliary functions,and matching those with the characteristics of the empirical space–time covariance surface might be helpful in the selection of a suitable class. In this paper some characteristics, such as behavior at the origin ,asymptotic behavior, non-separability and anisotropy aspects, are studied for some wellknown classes of covariance models of stationary space–time random fields.Moreover, some important issues related to modeling choices are described and a case study is presented

Complex-valued random fields represent a natural extension of real-valued random fields and can be useful for modeling vectorial data in two dimensions (i.e., a wind field). In such a case, some theoretical issues arise concerning generating and fitting complex covariance functions to be used for prediction purposes. In this paper, some general aspects and properties of complex-valued random fields are summarized and a procedure to fit complex stationary covariance functions is proposed. A case study for analyzing wind speed data is presented.

Tests on properties of space-time covariance functions. Tests on symmetry, separability and for assessing different forms of non-separability are available. Moreover tests on some classes of covariance functions, such that the classes of product-sum models, Gneiting models and integrated product models have been provided.

The aim of this paper is to investigate the service quality provided to the patients and the relationship between doctors and long-term cancer patients. Data have been collected during a survey conducted to long-term cancer patients, who follow a therapy at the Hospital Vito Fazzi, in Province of Lecce (located in the Southern region of Puglia, Italy). In particular, factor analysis and structural equation model are used to measure the relations among latent variables related to two aspects of the analyzed issue, such as service quality provided to the patient and the relationship between doctors and long-term cancer patients. The first model describes the perceived service quality provided to the patient, which is influenced by four important factors such as the tangible aspects, the reliability, the empathy (doctor-patient human relations) and the hospital organization. The second model describes the relationship between doctors and long-term cancer patients, which is influenced by three factors, such as the reliability, the empathy (doctor-patient human relations) and the hospital organization. The results are useful to investigate the strategies used to improve the quality service. Moreover, the analysis focuses on highlighting some empirical evidences in health risk through the use of a Geographical Information System (GIS). The advantages of implementing a GIS are related to the possibility to include different demographic databases, relate and analyze them as well as to detect and represent the areas in which there are high mortality rates. This tool, called GIS Cancer Screening, allows to process thematic maps using health data and support public health policies.

Sono anni che si discute sul cambiamento climatico, insieme alle tematiche riguardanti la disponibilità di acqua, la qualità ambientale (in particolare, la qualità dell’aria), l’energia rinnovabile e le dinamiche degli ecosistemi. Questi problemi, anche se sono di grande interesse, sono spesso scollegati dalla Fisica, dalla Chimica e dalla Matematica che risultano essere gli strumenti fondamentali per il loro studio e la loro comprensione. Questo volume è destinato a fornire una descrizione sintetica dei processi di base e dei fenomeni naturali che si registrano nell’area dello Ionio, così come alle tendenze climatiche e/o alle modifiche che sono state rilevate nei parametri critici, quale la pioggia. Pertanto, sono affrontati, a livello introduttivo, i temi delle dinamiche atmosferiche, meteorologiche e climatiche, delle dinamiche oceanografiche e della tettonica nell’area geografica del Mar Ionio (in particolare, nelle Isole Ioniche e nella Penisola della Puglia).

Environmental data is nearly always multivariate and often spatial–temporal. Thus to interpolate the data in space or to predict in space–time it is necessary to use a multivariate spatial–temporal method. Cokriging is easily extended to spatial–temporal data if there are valid space–time variograms or covariance functions. Various authors have proposed such models. In this paper, a generalized product–sum model is used with a linear coregionalization model for cokriging. The GSLib “COKB3D” program was modified to incorporate the space–time linear coregionalization model (ST-LCM), using the generalized product–sum variogram model. Hence, a new GSLib software, named “COK2ST”, is proposed. To demonstrate the use of the software, hourly measurements of carbon monoxide and nitrogen dioxide from the Puglia region in Italy are used.

La Geostatistica ed i sistemi informativi geografici, indicati con l’acronimo GIS (Geographic Information System), sono particolarmente diffusi nell’ambito del trattamento dei dati geografici ed ambientali, e rappresentano un valido supporto per garantire uno sviluppo sostenibile del territorio. Nel presente Capitolo, dopo aver descritto le potenzialità dei GIS per l’analisi dei dati ambientali e le possibilità di integrazione di tali sistemi con le tecniche geostatistiche, sarà presentato un progetto GIS, realizzato per l’archiviazione e l’analisi dei dati rilevati dalle stazioni di monitoraggio degli inquinanti e delle variabili meteo-climatiche, localizzate nel Grande Salento. Inoltre, saranno descritte le caratteristiche di un WebGIS per i dati ambientali del Grande Salento, in grado di rendere disponibili online le informazioni territoriali nonché i risultati dell’analisi geostatistica.

Abstract Chapter3: Exploratory data analysis and prediction in time series modeling are not typically based on geostatistical techniques, although in several cases applying these techniques might be convenient. This paper aims to illustrate the usefulness of using Geostatistics and its basic tool, such as the variogram, in time series, especially when an explicit model for the process is not an important goal of the analysis. Moreover, the main differences between the time-domain approach and Geostatistics are highlighted throughout the paper. In order to underline the role of the variogram for modeling and prediction purposes, several theoretical aspects, such as interpolation of missing values, temporal prediction, nonparametric estimation, and their computational problems, are faced through an extensive case study regarding an environmental time series. A modified version of GSLib routine for kriging is suitably developed in order to define appropriate temporal search neighborhoods for missing values treatment and prediction.

Non-separable models are receiving a lot of attention, since they are more flexible to handle empirical covariance functions showed up in applications. When phenomena can not be described by physical laws and their space-time covariance models can not be obtained as solutions of partial differential equations, it is advisable to choose an appropriate class of spacetime covariance models for the given data set, on the basis of the main characteristics, such as full symmetry, separability, behavior at the origin, anisotropy aspects, as well as type of non separability and asymptotic behavior of the empirical covariance function. In particular, a particular attention will be turned on the type of non separability of a space-time covariance function and variability along space and time exhibited by the spatial and temporal marginal covariances. Moreover, a technique for testing some classes of covariance functions, as well as applications to the classes of Rodrigues and Diggle models (Rodrigues and Diggle, 2010), product-sum models (De Iaco et al., 2001), Gneiting models (Gneiting, 2002), integrated product models (De Iaco et al., 2002; Ma, 2003) and Cressie-Huang models (Cressie and Huang, 1999) are also provided. A case study on an environmental variable is presented.

In questo volume si propongono i risultati di un’accurata indagine - finanziata nell’ambito del Programma delle Attività Culturali per il triennio 2013/2015 della Regione Puglia - svolta nel 2014 dal Gruppo di Ricerca di Statistica del Dipartimento di Scienze dell’Economia dell’Università del Salento. Attraverso la somministrazione di un questionario rivolto a cittadini pugliesi di varie fasce d’età e la successiva elaborazione dei risultati, sono stati analizzati i comportamenti e gli orientamenti dei salentini in tema di fruizione di concerti, preferenze rispetto al genere musicale, acquisto di dischi e merchandising, partecipazione a festival di breve e lunga durata, disponibilità a spostarsi fuori provincia per assistere ai vari eventi (live, raduni, fiere di settore, happening vari ...). Inoltre, sono stati evidenziati i punti di forza e criticità relativi alla fruizione dell’offerta musicale dal vivo nel nostro territorio, allo scopo di identificare le problematiche che ne ostacolano il consumo.

Il Mercatino del Gusto, manifestazione enogastronomica organizzata a Maglie (in Provincia di Lecce) dall’1 al 5 agosto 2012 e giunta alla XIII edizione, costituisce per la Regione Puglia un’occasione per i numerosi visitatori di scoprire i prodotti della tradizione alimentare pugliese ed apprezzare le bellezze architettoniche locali, nonchè una risorsa per lo sviluppo sia economico che socio-culturale del territorio. Nel presente lavoro, vengono analizzati i principali risultati conseguiti nell’ambito dell’indagine campionaria condotta al fine di valutare le opinioni, le abitudini ed il livello di soddisfazione dei visitatori e degli espositori presenti alla manifestazione. Inoltre, sono individuati gli strumenti di pubblicizzazione dell’evento ed i punti di forza e di debolezza della manifestazione, allo scopo di fornire, agli amministratori locali, gli elementi per porre in essere scelte volte a migliorare le successive edizioni dell’evento, nonché programmare interventi pubblici volti a rivalutare il territorio pugliese e promuovere le aziende che realizzano prodotti tipici di elevata qualità.

Assessing environmental quality usually requires the observation of two or more correlated variables, which are measured in several points of the study area. Sometimes, the characteristic of interest is sparsely sampled over the area, then it is convenient to incorporate some auxiliary variables, correlated with the variable of interest, into the estimation procedure. Indeed they carry relevant information for the variable being estimated, especially if they are more densely available over the domain. In this paper three different spatial interpolation approaches have been used in order to obtain spatial predictions of the variable of interest characterized by a severe lack of data.

The quality assessment is a relevant issue in the strategic management of public health sector. The goal of this analysis is to investigate about the perception of the health quality system for long-term cancer patients. The data of interest have been collected during a survey conducted to long-term cancer patients who follow an oncological therapy in a Public Hospital. Exploratory Factorial Analysis (EFA) is developed and a Structural Equation Model (SEM) is proposed. The model describes the service quality, as perceived by the patients, which is influenced by four important factors such as tangible aspects, reliability, empathy (doctor-patient human relations) and hospital organization.

An environmental data set often concerns different correlated variables measured at some locations of the study area and for several time points. In this case, the data set presents a multivariate spatio-temporal structure; therefore appropriate modeling techniques which take into account the spatio-temporal relationships among the variables are needed. The space-time LCM (ST-LCM) based on admissible spatiotemporal models may successfully capture the spatio-temporal behaviour of the phenomena under study and can be used for prediction purposes. After a brief presentation of the spatio-temporal multivariate geostatistical framework, a case study is proposed and the following aspects are considered: 1. estimating the spatio-temporal interrelationships among the variables of interest and, consequently, identifying the basic hidden components in space and in time which characterize the same variables; the simultaneous diagonalization-based method is applied to several matrix variograms in order to detect the basic independent components which contribute to define the multivariate correlation structure of the observed variables (De Iaco et al., 2013); 2. modeling the spatio-temporal correlation among the variables under study by using the ST-LCM (De Iaco et al., 2005); in this step, the basic models at the selected scales of spatio-temporal variability have been properly chosen after the inspection of the non separability index computed for the basic components (De Iaco and Posa, 2013); 3. spatio-temporal cokriging performed by a modified version of GSLib routine to obtain prediction, over the study area, for the variable of interest. Note that the ST-LCM used in this paper is based on mixture models, i.e. the ST-LCM has been fitted by selecting different classes of spatio-temporal correlation measures, related to different scales of spatiotemporal variability.

I modelli di covarianza spazio-temporali separabili, definiti come il prodotto di una covarianza puramente spaziale con una puramente temporale, sono ampiamente utilizzati nelle applicazioni; tuttavia, essi si basano su assunzioni eccessivamente semplificatrici. A tale tipologia di modelli di covarianza si contrappongono quelli non separabili, negli ultimi anni presi maggiormente in considerazione dal mondo accademico in quanto risultano essere pi`u flessibili nelle applicazioni. Recentemente, in letteratura sono state definite differenti forme di non separabilit`a per funzioni di covarianza spazio-temporale; in particolare, si `e passati dalle generiche definizioni di non separabilit` a positiva e negativa, alle pi`u specifiche nozioni di non separabilit`a puntuale ed uniforme. Nel presente capitolo, dopo aver illustrato e formalizzato le nozioni di non separabilit`a positiva e negativa, nonch´e quelle di non separabilit`a puntuale ed uniforme, si analizzeranno alcuni modelli di covarianza spazio-temporale. Inoltre, verranno descritti gli script predisposti per il calcolo dell’indice di non separabilità all’interno del software R.

Although positive definiteness is a sufficient condition for a function to be a covariance, the stronger strict positive definiteness is important for many applications, especially in spatial statistics, since it ensures that the kriging equations have a unique solution. In particular, spatial–temporal prediction has received a lot of attention, hence strictly positive definite spatial–temporal covariance models (or equivalently strictly conditionally negative definite variogram models) are needed. In this paper the necessary and sufficient condition for the product and the product–sum space–time covariance models to be strictly positive definite (or the variogram function to be strictly conditionally negative definite) is given. In addition it is shown that an example appeared in the recent literature which purports to show that product–sum covariance functions may be only semi-definite is itself invalid. Strict positive definiteness of the sum of products model is also discussed.

This article provides a review of recent advances in modeling spatio-temporal multivariate data. It focuses then on the linear coregionalization model (LCM) which is still widely used in geostatistics and on the choice of it starting from data. Advantages and drawbacks are highlighted and different tests for checking the LCM hypothesis are briefly discussed.

Nowadays, there is an increasing interest in multi-point models and their applications in Earth sciences. However, users not only ask for multi-point methods able to capture the uncertainties of complex structures and to reproduce the properties of a training image, but also they need quantitative tools for assessing whether a set of realizations have the properties required. Moreover, it is crucial to study the sensitivity of the realizations to the size of the data template and to analyze how fast realization-based statistics converge on average toward training-based statistics. In this paper, some similarity measures and convergence indexes, based on some physically measurable quantities and cumulants of high-order, are presented. In the case study, multi-point simulations of the spatial distribution of coarse-grained limestone and calcareous rock, generated by using three templates of different sizes, are compared and convergence toward training-based statistics is analyzed by taking into account increasing numbers of realizations.

Box-Jenkins methodology (1976) is commonly applied for time series analysis. Using this approach, sample autocorrelation and partial functions (ACF and PACF, respectively) are conventionally inspected in order to identify the most appropriate model which describes the temporal evolution of the process under study. The fitted model is subsequently used for prediction purposes. Opposite to the above ACF and PACF based-method, the variogram represents the basic tool in Linear Geostatistics to face a variety of inferential problems (Chilés and Delfiner, 1999; Journel and Huijbregts, 1981; Matheron, 1963). In this context, detection of a parametric model for the process under study gives way to the estimation and modeling of the variogram in order to perform predictions of the analyzed variable at unsampled points. This paper aims to illustrate the importance and convenience of variogram-based exploratory and prediction techniques to perform a complete analysis of a time series, even in presence of a periodic behaviour. In particular an extensive case study regarding the time series of PM10 daily concentrations registered at a monitoring station located in an area with high risk of particle pollution, is faced through the following steps: a) identification of trends and periodicity exhibited by data, b) estimation of missing values, c) predictions of the PM10 concentrations at time points following the last available observation, d) estimation of the distribution function. Regarding the computational aspects, a modified version of the GSLib kriging routine (Deutsch and Journel, 1998) has been used to define appropriate temporal search neighborhoods for interpolation and prediction purposes.

Separable spatio-temporal covariance models, defined as the product of purely spatial and purely temporal covariance functions, are often used in practice, but frequently they only represent a convenient assumption. On the other hand, non-separable models are receiving a lot of attention, since they are more flexible to handle empirical covariances showed up in applications. Different forms of non-separability for space–timecovariance functions have been recently defined in the literature. In this paper, the notion of positive and negativenon-separability is further formalized in order to distinguish between pointwise and uniform non-separability. Various well-known non-separable space–time stationary covariance models are analyzed and classified by using the new definition of non-separability. In particular, wide classes of non-separable spatio-temporal covariance functions, able to capture positive and negativenon-separability, are proposed and some examples of these classes are given. General results concerning the non-separability of spatial–temporal covariance functions obtained by a linear combination of spatial–temporal covariance functions and some stability properties are also presented. These results can be helpful to generate as well as to select appropriate covariance models for describing space–time data.

Modeling of spatio-temporal processes is critical in many fields such as environmental sciences, meteorology, hydrology and reservoir engineering. Nowadays spatio-temporal analysis cannot be adequately faced without considering important issues, such as: (a) modeling the spatio-temporal random field from which data might be reasonably derived, (b) choosing suitable covariance models which describe the spatio-temporal correlation of the variables of interest, (c) using adequate software packages which tackle different inferential problems. In this paper, the above aspects are properly analyzed. In particular, three different space–time random field decomposition choices are considered and the flexibility of using the generalized product–sum model is highlighted. A customized GSLib routine for kriging in space-time is proposed. This Fortran routine, named “K2ST”, is based on the use of the generalized product -sum model, with nested structures, and appropriate space-time search neighborhoods. An application to NO2 pollutant in an urban area is presented. In order to compare kriging results associated with three hypotheses of space–time random field decomposition, correlation coefficients and standardized errors between true values and predicted ones are computed. Moreover, nonparametric tests are applied to check the significance of the difference among the three approaches.

Vehicular traffic, industrial activity and street dust are important sources of atmospheric particles, which cause pollution and serious health problems, including respiratory illness. Hence, techniques for analyzing and modeling the spatio-temporal behavior of particulate matter (PM), in the recent statistical literature, represent an essential support for environmental and human health protection. In this paper, air pollution from particleswith diameters smaller than 10 μmand related meteorological variables, such as temperature and wind speed, measured during November 2009 in the south of Apulian region (Lecce, Brindisi, and Taranto districts) are studied. A thorough multivariate geostatistical analysis is proposed, where different tools for testing the symmetry assumption of the spatio-temporal linear coregionalizationmodel (ST-LCM) are considered, as well as a recent fitting procedure of the ST-LCM, based on the simultaneous diagonalization of symmetric real-valued matrix variograms, is adopted and two non-separable classes of variogram models, the product–sum and Gneiting classes, are fitted to the basic components. The most significant aspects of this study are (a) the quantitative assessment of the assumption of symmetry of the ST-LCM, (b) the use of different non-separable spatio-temporal models for fitting the basic components of a ST-LCM and, more importantly, (c) the application of the spatio-temporal multivariate geostatistical analysis to predict particle pollution in one of the most polluted geographical area. Prediction maps for particle pollution levels with the corresponding validation results are given.

Complex formalism is often convenient to describe, in a compact and unified way, a vectorial data set in two dimensions, such as wind field, electromagnetic field, as well as measurements out-coming from any two dimensional vectorial field. This representation is rarely considered in Geostatistics, although interesting applications can be found in environmental sciences and meteorology. In such a case, some practical issues related to the prediction step have to be faced. In this paper, some essential aspects on complex formalism, such as fitting a complex covariance function and predicting a complex-valued random field through an ad-hoc GSLib routine, are given. An environmental application to wind data has been furnished.

In questo lavoro, si intende ripercorrere i processi valutativi che hanno riguardato la ricerca italiana dell’Area 13, i criteri utilizzati e le ripercussioni sui contributi derivanti da specifici interessi di ricerca. Si conclude con una proposta di nuovi criteri di valutazione in grado di supportare processi valutativi trasparenti, basati su principi noti ex-ante, volti a valorizzare gli svariati interessi di ricerca, quelli di ampio respiro e quelli di nicchia.

Radon (Rn) is a colorless, odorless, tasteless, inert radioactive gas, and derives from the decay of uranium, which is a radioactive element that is found in small quantities in all sediments and rocks. The International Agency for Research on Cancer (IARC) and theWorld Health Organization (WHO) classify Rn pollution as the second leading cause of lung cancer after smoking. Since Rn is present, in the depths of the Earth, in gaseous phase, it reaches the surface because it interacts with other natural elements, such as uranium, thorium and radio (precursor elements); moreover other geo-lithological features, such as the mineralogical composition of the rocks, the underground permeability levels, the presence of faults, fractures and cavities, affect the transport of the Rn on the surface. In this paper, the spatial distribution of the Rn concentrations in soil gas over a survey area located in the South of Apulian Region (Italy) and its prediction at unsampled points have been discussed. In particular, Ordinary Kriging (OK), Log-Normal Kriging (LK), Cokriging with indicator variable (ICK) and Kriging with Varying Means (KVM) have been used to predict Rn concentrations over the study area. In this context, the integration of a Geographical Information System (GIS) and geostatistical tools can certainly support the evaluation of alternative scenarios, possible strategies for a sustainable development.

Radon (Rn) is a potentially toxic gas in soil which may affect human health. Assessing Rn levels in soil gas usually requires enormous efforts in terms of time and costs, since the sampling protocol is very complex. In most cases, the variable under study is sparsely sampled over the domain and this could affect the reliability of the spatial predictions. For this reason, it is useful to incorporate, into the estimation procedure, some auxiliary variables, correlated with the in soil gas Rn concentrations (primary variable) and more densely available over the domain. On the basis of this latter aspect, it is even better if the covariates are derived from a geographical information system (GIS). In this article, the Rn sampling protocol used during a measurement campaign planned over a risk area is described and the process of deriving GIS covariates considered as secondary information for predicting the primary variable is clarified. Then, multivariate modeling and prediction of the Rn concentrations over the domain of interest are discussed and a comparative study regarding the performance of the prediction procedures is presented. Rn prone areas are also analyzed with respect to urban and school density. All these aspects can clearly support decisions on environmental and human safeguard.

Non-separable models are receiving a lot of attention, since they are more flexible to handle empirical covariances showed up in applications. Most of the papers which develop space-time covariance functions end with a case study which tries to prove the adequacy of the proposed class of models to a specified data set. In literature it is not customary to follow the opposite path; in other words, starting from the data set, the problem is to look for the class of space-time covariance functions which is appropriate for data under study. This is the aim of this paper and it will be followed by utilizing several theoretical results found in the literature.

Il presente volume è il risultato finale di un'attività di ricerca svolta dal Gruppo di Statistica dell’Università del Salento, nell’ambito del Progetto “Sistema Informativo Statistico per le Aree Mercatali”, approvato dal Consorzio Universitario Interprovinciale Salentino (C.U.I.S.), co-finanziato dalla Camera di Commercio di Lecce, dal Consorzio Operatori su Aree Pubbliche di Lecce e dal Dipartimento di Scienze dell’Economia dell’Università del Salento. L’analisi statistica e l’utilizzo di un sistema informativo territoriale a supporto delle politiche di gestione strategica del territorio, quale il GIS (Geographic information system) e il WebGis, rappresentano il giusto approccio verso una modernizzazione dell’attività amministrativa locale.

Un sistema informativo geografico, pi`u comunemente noto con l’espressione anglosassone Geographic Information System (GIS), ha lo scopo di acquisire, gestire e analizzare dati in un contesto spaziale. Esso rappresenta un valido supporto alla pianificazione territoriale e alla gestione di informazioni quali-quantitative complesse caratterizzate da una componente geografica. L’esigenza di condividere ed utilizzare l’informazione geografica ed il crescente sviluppo delle tecnologie di comunicazione, hanno determinato negli ultimi anni l’evoluzione e l’utilizzo dei WebGIS, ovvero di GIS implementati sul web. Tale strumento rende semplice ed immediata la consultazione delle informazioni archiviate nel GIS, anche da parte di utenti non specializzati nell’utilizzo di tecnologie informatiche. In questo capitolo, vengono presentati gli avanzamenti del GIS integrato in un WebGIS per il monitoraggio ambientale, gi`a proposto a livello prototipale nell’ambito del Progetto Sviluppi della Geostatistica multivariata per l’analisi dei dati ambientali nello spazio e nello spazio-tempo realizzato nell’anno 2011. Inoltre, dopo aver identificato gli episodi di trasporto di polvere africana, mediante l’analisi delle traiettorie all’indietro delle masse d’aria provenienti dalle regioni desertiche ed aver verificato l’esistenza di scenari favorevoli per il trasporto di polveri, avvalendosi delle mappe aerosol e delle immagini satellitari, si fornirà una quantificazione del contributo netto dovuto agli episodi di polveri africane.

Gli aspetti computazionali connessi all’utilizzo di alcuni ben noti modelli di covarianza sono stati affrontati ricorrendo a semplici algoritmi implementati per risolvere specifici problemi. Si pensi, ad esempio, ad alcune routines del software GSLIB modificate da De Cesare et al. (2001) e da De Iaco e Posa (2012) oppure ad opportuni pacchetti del software statistico R, idonei a rappresentare e modellare fenomeni spazio-temporali, quali gstat (Pebesma, 2004; Graler et al., 2016) e spacetime (Pebesma, 2012; Bivand et al., 2013). Ciò nonostante, continua a persistere il problema riguardante la mancanza di un software dedicato all’analisi di dati spazio-temporali.

Space–time correlation modelling is one of the crucial steps of traditional structural analysis, since space–time models are used for prediction purposes. A comparative study among some classes of space–time covariance functions is proposed. The relevance of choosing a suitable model by taking into account the characteristic behaviour of the models is proved by using a space–time data set of ozone daily averages and the flexibility of the product-sum model is also highlighted through simulated data sets

In many environmental sciences, the available information concern several correlated variables observed at some locations of the domain of interest and over a certain period of time. In this context, multivariate spatial-temporal data might exhibit an spatial anisotropy and a temporal trend. Then appropriate modeling and prediction techniques for multivariate spatial-temporal data are necessary. In this paper, a case study with an anisotropic space-time coregionalization model is discussed. Some critical steps of the fitting procedure are highlighted

Fertility evolution in France shows a countertrend compared to the common pattern of fertility in Europe. Based on aggregate statistics, such as the Total Fertility Rate (TFR), the population of France, as compared to all the other European countries, has one of the highest levels of fertility. The TFR has increased in the last 15 years although the growth rate is decreasing. Indeed the TFR shows a tendency to stabilize at around 2.0, as confirmed, with small variability, for each region. The aim of the paper is to propose spatio-temporal geostatistical modeling for the French TFR. In particular, a stochastic method for spatio-temporal prediction is proposed. Although time series analysis has been widely used to describe the temporal evolution of various demographic variables, recently increasing attention has also been given to the study of the spatial distribution of these variables. Thus, in this paper, geostatistical spatio-temporal tools are appropri- ately used to study simultaneously both the spatial and the temporal behaviour of the regional TFR in France for prediction purposes.

Geostatistical modeling is often based on the use of covariance functions, i.e., positive definite functions. However, when interpolation problems have to be solved, it is advisable to consider the subset of strictly positive definite functions. Indeed, it will be argued that ensuring strict positive definiteness for a covariance function is convenient from a theoretical and practical point of view. In this paper, an extensive analysis on strictly positive definite covariance functions has been given. The closure of the set of strictly positive definite functions with respect to the sum and the product of covariance functions defined on the same Euclidean dimensional space or on factor spaces, as well as on partially overlapped lower dimensional spaces, has been analyzed. These results are particularly useful (a) to extend strict positive definiteness in higher dimensional spaces starting from covariance functions which are only defined on lower dimensional spaces and/or are only strictly positive definite in lower dimensional spaces, (b) to construct strictly positive definite covariance functions in space–time as well as (c) to obtain new asymmetric and strictly positive definite covariance functions.

Positive definiteness represents an admissibility condition for a function to be a covariance. Nevertheless, the more restricted condition of strict positive definiteness has received attention in literature, especially in spatial statistics, since it ensures that the kriging system has a unique solution. Most known covariance functions are isotropic but there are applications where isotropy is not appropriate, e.g., space-time covariance functions. One way to construct non-isotropic covariance functions is to use a product or a product-sum. In this article, it is given a necessary as well as a sufficient condition for a product of two covariance functions to be strictly positive definite. This result is extended to the well-known product-sum covariance model.

Nelle scienze ambientali l'evoluzione spazio-temporale di un fenomeno è spesso il risultato del comportamento simultaneo di diverse variabili correlate tra loro. In tale contesto è opportuno ricorrere ad adeguati modelli stocastici e ad appropriate tecniche di analisi geostatistica multivariata nello spazio e nello spazio-tempo per garantire previsioni attendibili. Nel volume sono introdotti i concetti fondamentali della Geostatistica multivariata spazio-temporale, i modelli di coregionalizzazione lineare, le tecniche di previsione spazio-temporale multivariata, nonché una nuova procedura di adattamento del modello di coregionalizzazione lineare spazio-temporale. Inoltre viene dedicata un’ampia discussione allo studio dell'inquinamento atmosferico nel Grande Salento. Infine, le potenzialità dei GIS per analisi di tipo ambientale e il legame di tali sistemi con la Geostatistica sono dimostrate mediante l’implementazione di un GIS per la rete di monitoraggio ambientale nel Grande Salento.

In letteratura sono stati proposti alcuni test per valutare l’ipotesi di separabilità, al fine di giustificare la scelta di modelli caratterizzati da tale caratteristica. Nel caso di rifiuto dell’ipotesi di separabilità, nessuno dei test disponibili consente di verificare il tipo di non-separabilità di funzioni di covarianza spazio-temporali. Risulta, pertanto, indispensabile l’implementazione di nuove metodologie e strumenti che consentano di selezionare un’opportuna classe di modelli. In questo capitolo, dopo aver introdotto i test di simmetria e separabilità presenti in letteratura, verrà illustrato un nuovo metodo per valutare il tipo di non separabilità (positiva o negativa) e sarà, infine, discusso un nuovo approccio per sottoporre a verifica alcune classi di modelli di covarianza spazio-temporali.

In statistical space-time modeling, the use of non-separable covariance functions is often more realistic than separable models. In the literature, various tests for separability may justify this choice. However, in case of rejection of the separability hypothesis, none of these tests include testing for the type of non-separability of space- time covariance functions. This is an important and further significant step for choosing a class of models. In this paper a method for testing positive and negative non-separability is given; moreover, an approach for testing some well known classes of space-time covariance function models has been proposed. The performance of the tests has been shown using real and simulated data.

Given a vectorial data set in two dimensions, a representation on a complex domain is often convenient. This representation is rarely considered in geostatistics, although interesting applications can be found in environmental sciences and meteorology (e.g., for wind fields). In such a case, some computational diculties are related to the lack of software for estimating and modeling a complex covariance function, for predicting complex variables as well as for representing the output results. In this paper, the new Fortran software cgeostat for geostatistical analysis of complex-valued random fields is presented and an application is demonstrated.

During the period of 2012 – 2015, a network of 15 permanent scientific Meteorological – Environmental stations established along the Ionian Islands (Greece) and the Salento peninsula (Puglia or Apulia, Italy). The network extends from the Adriatic-Ionian borders (Otranto station) to the southern tip of the Ionian Islands complex (Zakynthos), almost in parallel to the main orography of the Greek peninsula, within the southern extension of the Western Balkans wind convergence zone. Twelve of the stations have a 10 m height Meteorological mast architecture, while the rest three of them monitor the air suspended particulate matter mass concentration. The installlation locations were carefully selected (in remote areas in most of the cases) in order to ensure best exposure to the prevailing weather conditions at pre-specified wind sectors. The network construction was realized in the framework of the Interreg IV European Territorial Cooperation Programs “Greece-Italy 2007-2013”, under the acronym “the DEMSNIISI” Project. All stations are equipped with high quality scientific sensors, that measure ten, basic Meteorological parameters (namely, the wind vector at 10 m height from earth surface, the wind gust, the rain rate, the air temperature, the relative humidity, the barometric pressure, the Solar irradiance in the visible, and the UV-A -B bands, and the aerosols mass concentration) at one minute logging interval; 14 more parameters (Aeolic and Solar energy flow, among them) are computed per station and per minute. The measurements are real time published in graphical form through the web page http://ionianweather.gr, while the measurements numerical values are also accessible through the climatic database. Under the DEMSNIISI Project the number of ground based Meteorological stations in the Ionian Islands were over-doubled and a high quality Meteorological - Environmental network was added in the sensitive area of the Central Mediterranean. In this article, the main atmospheric processes and the climatic variability of the network physical environment (Ionian Sea) is reviewed, taking also into account the results of a number of studies performed in the Project’s framework. Furthermore, the technical specifications of the network stations is given along with a description of the communication methods, the data flow, the pre- and post-processing, and the web platform products.

In many environmental sciences, several correlated variables are observed at some locations of the domain of interest and over a certain period of time. In this context, appropriate modeling and prediction techniques for multivariate space–time data as well as interactive software packages are necessary. In this paper, a new automatic procedure for fitting the space–time linear coregionalization model (ST-LCM) using the product–sum variogram model is discussed. This procedure, based on the simultaneous diagonalization of the sample matrix variograms, allows the identification of the ST-LCM parameters in a very flexible way. The fitting process is analytically described by a main flow chart and all steps are specified by four subprocedures. An application of this procedure is illustrated through a case study concerning the daily concentrations of three air pollutants measured in an urban area. Then the fitted space–time coregionalization model is applied to predict the variable of interest using a recent GSLib routine, named “COK2ST.”

Although there are multiple methods for modeling matrix covariance functions and matrix variograms in the geostatistical literature, the linear coregionalization model is still widely used. In particular it is easy to check to ensure whether the matrix covariance function is positive definite or that the matrix variogram is conditionally negative definite. One of the difficulties in using a linear coregionalization model is in determining the number of basic structures and the corresponding covariance functions or variograms. In this paper, a new procedure is given for identifying the basic structures of the space–time linear coregionalization model and modeling the matrix variogram. This procedure is based on the near simultaneous diagonalization of the sample matrix variograms computed for a set of spatiotemporal lags. A case study using a multivariate spatiotemporal data set provided by the Environmental Protection Agency of Lombardy, Italy, illustrates how nearly simultaneous diagonalization of the empirical matrix variograms simplifies modeling of the matrix variograms. The new methodology is compared with a previous one by analyzing various indices and statistics.

Traditional simulation methods that are based on some form of kriging are not sensitive to the presence of strings of connectivity of low or high values. They are particularly inappropriate in many earth sciences applications, where the geological structures to be simulated are curvilinear. In such cases, techniques allowing the reproduction of multiple-point statistics are required. The aim of this paper is to point out the advantages of integrating such multiple-statistics in a model in order to allow shape reproduction, as well as heterogeneity structures, of complex geological patterns to emerge. A comparison between a traditional variogram-based simulation algorithm, such as the sequential indicator simulation, and a multiple-point statistics algorithm (e.g., the single normal equation simulation) is presented. In particular, it is shown that the spatial distribution of limestone with meandering channels in Lecce, Italy is better reproduced by using the latter algorithm. The strengths of this study are, first, the use of a training image that is not a fluvial system and, more importantly, the quantitative comparison between the two algorithms. The paper focuses on different metrics that facilitate the comparison of the methods used for limestone spatial distribution simulation: both objective measures of similarity of facies realizations and high-order spatial cumulants based on different third- and fourth-order spatial templates are considered.

The formalism of complex random fields is suitable for describing, in a compact and unified way, vectorial data sets in two dimensions, such as wind fields, electromagnetic fields, as well as measurements derived from any two dimensional vectorial field. This representation is rarely considered in Geostatistics, although interesting applications can be found in environmental sciences and meteorology. Moreover, the lack of procedures for modeling a complex covariance function as well as the lack of specialized routines for computing predictions in the complex case have considerably restricted the applications of these techniques. In this paper, some essential aspects of the complex formalism and some computational developments associated with fitting a complex covariance function and predicting a complex-valued random field through an ad-hoc routine are discussed. An environmental application to wind data is provided, moreover, the consistency of the proposed methodology is demonstrated through a numerical study.