A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Spatial and temporal characterisation of ground deformation recorded by geodetic techniques

A critical point in the analysis of ground displacements time series is the development of data driven methods that allow the different sources that generate the observed displacements to be discerned and characterised. A widely used multivariate statistical technique is the Principal Component Analysis (PCA), which allows reducing the dimensionality of the data space maintaining most of the variance of the dataset explained. Anyway, PCA does not perform well in finding the solution to the so-called Blind Source Separation (BSS) problem, i.e. in recovering and separating the original sources that generated the observed data. This is mainly due to the assumptions on which PCA relies: it looks for a new Euclidean space where the projected data are uncorrelated. The Independent Component Analysis (ICA) is a popular technique adopted to approach this problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, I use a variational bayesian ICA (vbICA) method, which models the probability density function (pdf) of each source signal using a mix of Gaussian distributions. This technique allows for more flexibility in the description of the pdf of the sources, giving a more reliable estimate of them. Here I present the application of the vbICA technique to GPS position time series. First, I use vbICA on synthetic data that simulate a seismic cycle (interseismic + coseismic + postseismic + seasonal + noise) and a volcanic source, and I study the ability of the algorithm to recover the original (known) sources of deformation. Secondly, I apply vbICA to different tectonically active scenarios, such as the 2009 L'Aquila (central Italy) earthquake, the 2012 Emilia (northern Italy) seismic sequence, and the 2006 Guerrero (Mexico) Slow Slip Event (SSE).