I am a Professor of Statistics at the Department of Economics, University G. d’Annunzio of Chieti Pescara, Italy.
My main area of research is the development of statistical methodology in highly-structured data analysis, including complex environmental data, images, shapes, and functional data. My research aims to tackle environmental and medical problems by developing cutting edge statistical methods implemented through user friendly software packages. The methodology is mainly based on Bayesian spatial and spatio-temporal hierarchical models and Statistical and Machine Learning models. The research is developed within a broad network of collaborations with experts in environmental and health disciplines, and long-standing collaborations with important stakeholders, such as national and regional Environmental Protection Agencies, ISPRA and National Health Service. Most of the research colleagues are involved in the GRASPA-SIS group (the permanent research group of the Italian Statistical Society devoted to environmental research) and are also members of TIES, The International Environmetrics Society.
Specific research-topics of interests are:
1) Optimal spatial designs for environmental analysis and graph label propagation: monitoring networks are important to provide information on several environmental aspects such as air pollution, acid rain, water quality, earthquakes etc. For most environmental applications, we also require a prior mapping of the target pollutant agents over the study region so that the construction of an optimal monitoring network becomes a common problem with spatial dependence playing a crucial role. When a new network is to be constructed, or an existing one augmented or modified, it is important that the monitoring sites are optimally allocated across space to maximize the information available, which can then be used to make reliable and credible inferences about a variable of interest. When geostatistical data are considered, the monitoring network can be constructed to emphasize the utility of designs for interpolation. Assuming the second-order dependence is known, optimal interpolators (in the sense of minimum mean squared error) are jointly used with design criteria generally expressed as a function of the prediction variance. The specification of the variance matrix, and the use of Gaussian Random Fields (GRFs), define an optimal interpolator known in geostatistics as kriging (Cressie, 1993). An alternative approach is to specify a Gaussian Markov Random Field (GMRF), or Gaussian conditional autoregression (Cressie, 1993), which essentially is based on the specification of the precision matrix (i.e., the inverse covariance matrix). The purpose of this project is twofold. Firstly, it aims at providing a framework for the optimal spatial interpolator in which the two forms of kriging and GMRFs can be used as well as to provide new objective functions to be used for designing optimal sampling schemes for spatial predictions. Secondly, it attempts to extend results achieved in the field of environmental monitoring to the field of semi-supervised learning on graphs where label propagation and graph neural networks rely on Markov random field models. The papers Fontanella L. et al. (2022), Ippoliti et al (2018), Fontanella S. et al. (2015), Ippoliti et al (2013), Ippoliti et al (2011), Bhansali and Ippoliti (2005), Di Zio et al. (2004) and Dryden et al. (2002) serves as a rigorous statistical framework for understanding sampling issues on a network and creates a testbed for evaluating inductive learning performance, and provides a way to sample graph attributes.
2) Hierarchical Bayesian spatio-temporal models: the aim is to develop explanatory and predictive hierarchical spatio-temporal models for the study of complex phenomena. Particular attention is devoted to the development of Bayesian Factor models and the related issues pertaining to the study of the relationships existing between groups of variables showing either short or long range correlations both in space and time. Current interest also rests on modeling ideas that engender parsimonious structures and, in particular, on approaches to inducing data-informed sparsity via full shrinkage to zero of (many) latent time-varying loadings. Bayesian sparsity modeling ideas are well-developed in static models, such as sparse latent factor and regression models, but mapping over to time series raises new challenges of defining general approaches to dynamic sparsity. In health care research, important results have been achieved in the recently published paper Gamerman et al. (2022) which studies the effect of multiple air pollutants on multiple diseases in a space-time context. This paper provides new methodological and practical results in a field where, given the complexity of the problem, the literature is very sparse and most of the studies are focused on the effect of one single air pollutant (e.g., PM10) on one single disease (eg, respiratory disease). This paper also extends previous studies published in Di Battista et al. (2003), Fontanella L. et al. (2003), Fontanella L. et al. (2007), Ippoliti et al. (2012), Valentini et al. (2013) and Fontanella L. et al. (2015).
3) Image processing and functional data analysis: the aim is to work with data which are in the form of images or multiple time-dynamic processes naturally described as functional. Gauss Markov Random fields are commonly used in the field of image analysis and here we consider issues concerned with parameter estimation, both for univariate and multivariate processes. As for functional data, we consider curves that show different degrees of complexity as for example, those that: a) have a natural hierarchical structure, b) appear as spatially dependent, c) show complex connections in the form of graphs. Data showing a hierarchical structure are common, for example, in electro-encephalography, magneto-encephalography and thermal infrared imaging studies. Examples of functional graphs can be found in brain network analysis where, for example, EEG activity is measured at number of locations on the scalp and the objective is to estimate the network between the nodes/electrodes to show possible connections between different areas. Functional graphs and spatially dependent functional time series can also be found in many environmental applications. Former papers in this research field are represented by Arestusi et al. (2011), Fontanella L. et al. (2012), Fontanella and Ippoliti (2012) and Fontanella L. et al. (2019). Recent papers for images and functional data showing more complex structures are Pronello et al. (2022), Ferretti et al. (2022) and Schmidt et al. (2022).
4) Dynamic Shape analysis: the shape of an object is the geometrical information remaining after the effects of changes in location, scale and orientation have been removed. Statistical analysis of dynamic shapes is a problem with significant challenges due to the difficulty in providing a description of the shape changes over time, across subjects and over groups of subjects. Recent attempts to study the shape change in time are based on the Procrustes tangent coordinates or spherical splines in Kendall shape spaces. In this framework we investigate the use of basis functions, defined by principal warps in space and time, to facilitate the development of a spatio-temporal model which is able to describe the time-varying deformation of the ambient space in which the objects of interest lie. For this project, we also deal with the statistical analysis of a temporal sequence of landmark data using the exact distribution theory for the shape of planar correlated Gaussian configurations. Specifically, we aim at extending the theory of the offset-normal distribution to a dynamic framework and discuss its use for the description of time-varying shapes. Modeling the temporal correlation structure of the dynamic process is a complex task, in general. For two time points, Mardia and Walder (1994) have shown that the density function of the offset-normal distribution has a rather complicated form and discussed the difficulty of extending their results to more than two time points. The paper Fontanella L., Ippoliti L. and Kume (2019) has shown that it is possible to calculate the closed form expression of the offset-normal distribution for a general number of time points (though its calculation can be computationally expensive) and also provides a likelihood approach to perform inference under Gaussian mixture models in dynamic shape analysis. Further relevant papers with application on facial expression recognition are Brombin et al. (2015) and Kent et al. (2021) which has been included as invited paper in a volume dedicated to CR Rao’s 100th birthday.
5) Statistical Learning and deep models in Machine Learning: more recent works have been started by integrating deep neural network and more classical statistical modelling (see points 2 and 3 above) approaches to model spatial and spatio-temporal data. Multi-levels and nested Gaussian processes and Gaussian Markov random fields will be considered to develop deep kriging and deep GMRF models for general (e.g., nonstationary, non Gaussian) spatial processes. We will explore the performance of deep models as powerful prediction tools for a wide range of applications, with a specific focus to the recently funded project Big Earth data and Artificial Intelligence in environmental epidemiology for exposure prediction in Abruzzo region. Further developments are concerning with the application of deep neural networks and deep models to functional data.
Recent published papers:
Bucci A., Ippoliti L., Valentini P. (2022) Comparing unconstrained parametrization methods for return covariance matrix prediction. Statistics and Computing, 32:90, https://doi.org/10.1007/s11222-022-10157-4
Bucci A., Ippoliti L., Valentini P. (forthcoming). Analysing spatio-temporal patterns of COVID-19 confirmed deaths at the NUTS-2 regional level. REGIONAL STATISTICS
Gamerman D., Ippoliti L., Valentini P. (2022) Dynamic generalized structural equation modeling, with application to the effect of pollution on health. Journal of the Royal Statistical Society, Series C, 61, 175-200
Bucci A., Ippoliti L., Fontanella S., Valentini P (2022). Clustering spatio-temporal series of confirmed COVID-19 deaths in Europe. SPATIAL STATISTICS, 49:100543, doi: 10.1016/j.spasta.2021.100543, ISSN: 2211-6753
Uncini A., Aretusi G., Manganelli F., Sekiguchi Y., Magy L., Tozza S., Tsuneyama A., Lefour S., Kuwabara S., Santoro L., Ippoliti L. (2020) Electrodiagnostic accuracy in polyneuropathies: supervised learning algorithms as a tool for practitioners. Neurological Sciences. https://doi.org/10.1007/s10072-020-04499-y
Fontanella, Lara, Ippoliti, Luigi, Kume, Alfred (2019). The Offset Normal Shape Distribution for Dynamic Shape Analysis. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, vol. -28, p. 374-385, ISSN: 1061-8600, doi: 10.1080/10618600.2018.1530118
Fontanella, Lara, Ippoliti, Luigi, Valentini, Pasquale (2019). Predictive functional ANOVA models for longitudinal analysis of mandibular shape changes. BIOMETRICAL JOURNAL, vol. 61, p. 918-933, ISSN: 0323-3847, doi: 10.1002/bimj.201800228
Fontanella, Lara, Ippoliti, Luigi, Sarra, Annalina, Nissi, Eugenia, Palermi, Sergio (2019). Investigating the association between indoor radon concentrations and some potential influencing factors through a profile regression approach. ENVIRONMENTAL AND ECOLOGICAL STATISTICS, vol. 26, p. 185-216, ISSN: 1352-8505, doi: 10.1007/s10651-019-00424-5
Ippoliti L., Martin R.J., Romagnoli L. (2018) Efficient likelihood computations for some multivariate Gaussian Markov random fields. JOURNAL OF MULTIVARIATE ANALYSIS, vol. 168, p. 185-200, doi:https://doi.org/10.1016/j.jmva.2018.07.007