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

Analysis of the pig genome for the identification of genomic regions affecting production traits

The aim of this work was to identify markers associated with production traits in the pig genome using different approaches. We focused the attention on Italian Large White pig breed using Genome Wide Association Studies (GWAS) and applying a selective genotyping approach to increase the power of the analyses. Furthermore, we searched the pig genome using Next Generation Sequencing (NSG) Ion Torrent Technology to combine selective genotyping approach and deep sequencing for SNP discovery. Other two studies were carried on with a different approach. Allele frequency changes for SNPs affecting candidate genes and at Genome Wide level were analysed to identify selection signatures driven by selection program during the last 20 years. This approach confirmed that a great number of markers may affect production traits and that they are captured by the classical selection programs. GWAS revealed 123 significant or suggestively significant SNP associated with Back Fat Thickenss and 229 associated with Average Daily Gain. 16 Copy Number Variant Regions resulted more frequent in lean or fat pigs and showed that different copies of those region could have a limited impact on fat. These often appear to be involved in food intake and behavior, beside affecting genes involved in metabolic pathways and their expression. By combining NGS sequencing with selective genotyping approach, new variants where discovered and at least 54 are worth to be analysed in association studies. The study of groups of pigs undergone to stringent selection showed that allele frequency of some loci can drastically change if they are close to traits that are interesting for selection schemes. These approaches could be, in future, integrated in genomic selection plans.