Lara Fontanella

Optimal spatial sampling schemes for environmental surveys

A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring network. This paper presents a fractal-based criterion for the construction of coverage designs to optimize the location of sampling points. The algorithm does not depend on the covariance structure of the process and provides desirable results for situations in which a poor prior knowledge is available. The statistical characteristics of the method are explored by a simulation study while a design exercise concerning the Pescara area monitoring network is used to demonstrate potential designs under realistic assumptions.

Hierarchical generalised latent spatial quantile regression models with applications to indoor radon concentration

Radon-222 is a noble gas arising naturally from decay of uranium-238 present in the earth’s crust. In confined spaces, high concentrations of radon can become a serious health concern. Hence, experts widely agree that prolonged exposure to this gas can significantly increase the risk of lung cancer. A range of variables, such as geological factors, soil properties, building characteristics, the living habits of dwellers and meteorological parameters, might have a significant impact on indoor radon concentration and its variability. In this paper, the effect of various factors that are believed to influence the indoor radon concentrations is studied at the municipal level of L’Aquila district (Abruzzo region, Italy). The statistical analysis is carried out through a hierarchical Bayesian spatial quantile regression model in which the matrix of explanatory variables is partially defined through a set of spatial common latent factors. The proposed model, here referred to as the Generalized latent-spatial-quantile regression model, is thus appropriate when some covariates are indicators of latent factors that can be used as predictors in the quantile regression and the variables are supposed to be spatially correlated. It is shown that the model has an intuitive appeal and that it is preferable when the interest is in studying the effects of covariates on one or both the tails of the response distribution, as in the case of indoor radon concentrations. Full probabilistic inference is performed by applying Markov chain Monte Carlo techniques.

Interpolation of spatial and spatio-temporal Gaussian fields using Gaussian Markov random fields

This paper considers interpolation on a lattice of covariance-based Gaussian Random Field models (Geostatistics models) using Gaussian Markov Random Fields (GMRFs) (conditional autoregression models). Two methods for estimating the GMRF parameters are considered. One generalises maximum likelihood for complete data, and the other ensures a better correspondence between fitted and theoretical correlations for higher lags. The methods can be used both for spatial and spatio-temporal data. Some different cross-validation methods for model choice are compared. The predictive ability of the GMRF is demonstrated by a simulation study, and an example using a real image is considered.

Dynamic models for space-time prediction via Karhunen-Loève expansion

The paper is concerned with the spatio-temporal prediction of spacetime processes. By combining the state-space model with the kriging predictor and Karhunen-Loève Expansion, we present a parsimonious space-time model which is spatially descriptive and temporally dynamic. We consider the difficulties of applying principal component analysis of stochastic processes observed on an irregular network. Using the Voronoi tessellation we make adjustments to the Fredholm integral equation to avoid distorted loading patterns and derive an “adjusted” kriging spatial predictor. This allows for the specification of a space-time model which achieves dimension reduction in the analysis of large spatial and spatio-temporal data sets. As a practical example, the model is applied to study the evolution of the Nitrogen Dioxide (NO2) measurements recorded in the Milan district.

Space-time texture analysis in thermal infrared imaging for classification of Raynaud’s Phenomenon

This paper proposes a supervised classification approach for the differential diagnosis of Raynaud’s Phenomenon on the basis of functional infrared imaging (IR) data. The segmentation and registration of IR images are briefly discussed and two texture analysis techniques are introduced in a spatio-temporal framework to deal with the feature extraction problem. The classification of data from healthy subjects and from patients suffering from primary and secondary Raynaud’s Phenomenon is performed by using Stepwise Linear Discriminant Analysis (LDA) on a large number of features extracted from the images. The results of the proposed methodology are shown and discussed for a temporal sequence of images related to 44 subjects.

Spectral Analysis in Frequency and Time Domain for Noisy Time Series

In this paper the orthogonal decomposition is used in order to reconstruct the noiseless component of a temporal stochastic process. For weakly stationary processes, the proposed methodology is based on the joint application of the spectral analysis in the frequency domain (Fourier analysis) and in the time domain (Karhunen Loeve expansion). For non stationary processes the orthogonal decomposition is realized in the wavelet domain.

Nonparametric combination-based tests in dynamic shape analysis

Landmark-based geometric morphometric methods are probably the most widely used approaches for shape analysis. Much work has been done for static or cross-sectional shape analysis while considerably less research has focused on dynamic or longitudinal shapes. The question of analysing shape changes over time is a fundamental issue in many research fields. In this paper, as a motivating example, we consider the problem of describing the dynamics of facial expressions for which medical and sociological studies call for a proper differential analysis to distinguish their different characteristics. We address the problem from an inferential point of view testing whether landmark positions change over time, within each facial expression, and whether these changes are different between different expressions. As the shape changes over time completely depend on geometrical landmarks, part of the problem becomes finding the subset of landmarks which best describes the dynamics of the expressions. In this paper, we show by means of a motivating example related to the analysis of the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions and emotions from the Technical University Munich [Wallhoff, F. (2006), ‘Database with Facial Expressions and Emotions from Technical University of Munich (FEEDTUM)’], that NonParametric Combination (NPC) tests can be effective tools when testing whether there is a difference between dynamics of facial expressions or testing which of the landmarks are more informative in explaining their dynamics. In particular, we start analysing data by means of bivariate linear mixed-effects models and then we improve inferential results using the NPC methodology.

A Functional Spatio-Temporal Model for Geometric Shape Analysis

In this chapter we consider a functional spatio-temporal model for shape objects represented by landmark data. The model describes a time-varying deformation of the ambient space in which the objects of interest lie. The use of basis functions, defined by principal warps in space and time, facilitates both the model specification and the fitting of the data in Procrustes tangent coordinates. The fitted model can be interpreted either just in terms of the finite set of landmarks at the given set of time points, or in terms of a deformation of the space which varies continuously in time. The method is illustrated on a facial expression dataset.

Parametric estimation for ARFIMA models via spectral methods

Given a fractional integrated, autoregressive, moving average,ARFIMA (p, d, q) process, the simultaneous estimation of the short and long memory parameters can be achieved by maximum likelihood estimators. In this paper, following a two-step algorithm, the coefficients are estimated combining the maximum likelihood estimators with the general orthogonal decomposition of stochastic processes. In particular, the principal component analysis of stochastic processes is exploited to estimate the short memory parameters, which are plugged into the maximum likelihood function to obtain the fractional differencingd.

Parametric and Non-parametric Testing of Mean Shapes

This chapter deals with inferential aspects in shape analysis. At first we review inferential methods known in the shape analysis literature, highlighting some drawbacks of using Hotelling’s T2 test statistic. Then we present an extension of the NonParametric Combination (NPC) methodology to compare shape configurations of landmarks. NPC tests represent an appealing alternative since they are distribution-free and allow for quite efficient solutions when the number of cases is lower than the number of variables (i.e., (semi)landmarks coordinates). This allows to obtain better representations of shapes even in presence of small sample size. NPC methodology enables to provide global as well as local evaluation of shapes: it is then possible to establish whether in general two shapes are different and which landmark/subgroup of landmarks mainly contributes to differentiate shapes under study. NPC tests enjoy the finite-sample consistency property hence, in this nonparametric framework, it is possible to obtain efficient solutions for multivariate small sample problems, like those encountered in the shape analysis field. We finally present a NPC solution for longitudinal data.