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Let X andY be two independent continuous random variables. Three techniques to obtain confidence intervals for \rho=PrY >X are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for \rho; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study.An illustration is given using a data set on the detection of carriers of Duchenne Muscular Dystrophy.

In this paper, we develop nonparametric modelling of zero-in°ated Pois- son (ZIP) data. We model the nonparametric components of the regressors using penalized regression splines, so that inference can be accomplished by making use of the EM algorithm. The algorithm is illustrated by using an example from the literature.

The stress-strength model is considered in the case of skew-normal variates. Some exact probability results are given. For the case that either the stress or the strength has a skew-normal distribution, inferential issues are considered in a likelihood context, and simulation results provided which indicate a satisfactory agreement of nominal and actual confidence level for interval estimation.

Despite a long tradition in the study of graphs and relational data, for decades the analysis of complex networks was limited by difficulties in data collection and computational burdens. The advent of new technologies in life sciences, as well as in our daily life, has suddenly shed light on the many interconnections that our world features, from friendships and collaborations between individuals or organizations, to functional couplings between cellular molecules. This has highly facilitated the collection of relational data, fostering an unprecedented interest in network science. Understanding relations encoded in complex networks, however, still represents a challenging task, and statistical methods that can help to summarize and simplify complex networks are needed. In this thesis we show that often one can gain a deep insight of a network by focusing their attention on communities, i.e. on clusters of nodes, and on the relations that exist between them. We begin by presenting NEAT, a network-based test that allows to assess relations between gene sets in a gene interaction network. NEAT extends traditional gene enrichment analysis tests by incorporating information on interactions between genes and it overcomes some limitations of existing network enrichment analysis approaches. Then, we propose two extended stochastic blockmodels that allow to infer the relations that exist between communities from relations between pairs of individuals in a social network. We advocate the use of penalized inference to estimate these models, with the aim of deriving a sparse reduced graph between communities. Application of these models to bill cosponsorship networks in the Italian Chamber of Deputies allows us to reconstruct the pattern of collaborations between Italian political parties from 2001 to 2015. Finally, we propose a novel clustering strategy for sequences of graphs, based on mixtures of generalized linear models. We show that the proposed clustering method not only is capable to retrieve subpopulations of networks within a cross-sectional or longitudinal sequence of networks, but it also allows to directly characterize them by considering each of the components that form the mixture model.

Background: Time-course gene expression experiments are useful tools for exploring biological processes. In this type of experiments, gene expression changes are monitored along time. Unfortunately, replication of time series is still costly and usually long time course do not have replicates. Many approaches have been proposed to deal with this data structure, but none of them in the field of pathway analysis. Pathway analyses have acquired great relevance for helping the interpretation of gene expression data. Several methods have been proposed to this aim: from the classical enrichment to the more complex topological analysis that gains power from the topology of the pathway. None of them were devised to identify temporal variations in time course data. Results: Here we present timeClip, a topology based pathway analysis specifically tailored to long time series without replicates. timeClip combines dimension reduction techniques and graph decomposition theory to explore and identify the portion of pathways that is most time-dependent. In the first step, timeClip selects the time-dependent pathways; in the second step, the most time dependent portions of these pathways are highlighted. We used timeClip on simulated data and on a benchmark dataset regarding mouse muscle regeneration model. Our approach shows good performance on different simulated settings. On the real dataset, we identify 76 time-dependent pathways, most of which known to be involved in the regeneration process. Focusing on the ‘mTOR signaling pathway’ we highlight the timing of key processes of the muscle regeneration: from the early pathway activation through growth factor signals to the late burst of protein production needed for the fiber regeneration. Conclusions: timeClip represents a new improvement in the field of time-dependent pathway analysis. It allows to isolate and dissect pathways characterized by time-dependent components. Furthermore, using timeClip on a mouse muscle regeneration dataset we were able to characterize the process of muscle fiber regeneration with its correct timing.

Combining statistical models is an useful approach in all the research area where a global picture of the problem needs to be constructed by binding together evidence from different sources [M.S. Massa and S.L. Lauritzen Combining Statistical Models, M. Viana and H. Wynn, eds., American Mathematical Society, Providence, RI, 2010, pp. 239-259]. In this paper, we investigate the effectiveness of combining a fixed number of Gaussian graphical models respecting some consistency assumptions in problems of model building. In particular, we use the meta-Markov combination of Gaussian graphical models as detailed in Massa and Lauritzen and compare model selection results obtained by combining selections over smaller sets of variables with selection results over all variables of interest. In order to do so, we carry out some simulation studies in which different criteria are considered for the selection procedures. We conclude that the combination performs, generally, better than global estimation, is computationally simpler by virtue of having fewer and simpler models to work on, and has an intuitive appeal to a wide variety of contexts. © 2013 Copyright Taylor and Francis Group, LLC.

Gene set analysis using biological pathways has become a widely used statistical approach for gene expression analysis. A biological pathway can be represented through a graph where genes and their interactions are, respectively, nodes and edges of the graph. From a biological point of view only some portions of a pathway are expected to be altered; however, few methods using pathway topology have been proposed and none of them tries to identify the signal paths, within a pathway, mostly involved in the biological problem. Here, we present a novel algorithm for pathway analysis clipper, that tries to fill in this gap. clipper im- plements a two-step empirical approach based on the exploitation of graph decomposition into a junction tree to reconstruct the most relevant signal path. In the first step clipper selects signifi- cant pathways according to statistical tests on the means and the concentration matrices of the graphs derived from pathway topologies. Then, it identifies within these pathways the signal paths having the greatest association with a specific phenotype. We test our approach on simulated and two real expres- sion datasets. Our results demonstrate the efficacy of clipper in the identification of signal transduc- tion paths totally coherent with the biological problem.

In this paper, we explore a range of concerns that arise in measuring short-term effects of ozone on health. In particular, we tackle the problem of mea- suring exposure using alternative daily measures of ozone derived from hourly con- centrations. We adopt the exposure paradigm of Chiogna and Bellini (Environmetrics 13:55–69, 2002) extending it to ozone concentrations, and we compare its perfor- mances with respect to traditional exposure measures by exploiting model selection. To investigate the stability of model selection, we then apply the idea of bootstrapping the modelling process.

BACKGROUND: Recently, a great effort in microarray data analysis is directed towards the study of the so-called gene sets. A gene set is defined by genes that are, somehow, functionally related. For example, genes appearing in a known biological pathway naturally define a gene set. The gene sets are usually identified from a priori biological knowledge. Nowadays, many bioinformatics resources store such kind of knowledge (see, for example, the Kyoto Encyclopedia of Genes and Genomes, among others). Although pathways maps carry important information about the structure of correlation among genes that should not be neglected, the currently available multivariate methods for gene set analysis do not fully exploit it. RESULTS: We propose a novel gene set analysis specifically designed for gene sets defined by pathways. Such analysis, based on graphical models, explicitly incorporates the dependence structure among genes highlighted by the topology of pathways. The analysis is designed to be used for overall surveillance of changes in a pathway in different experimental conditions. In fact, under different circumstances, not only the expression of the genes in a pathway, but also the strength of their relations may change. The methods resulting from the proposal allow both to test for variations in the strength of the links, and to properly account for heteroschedasticity in the usual tests for differential expression. CONCLUSIONS: The use of graphical models allows a deeper look at the components of the pathway that can be tested separately and compared marginally. In this way it is possible to test single components of the pathway and highlight only those involved in its deregulation.

We describe a model-based approach to analyse space–time count data. Such data can arise as a number of time series of counts, each representing a specific geographical area, i.e. as spatial time series, or as a number of spatial maps at different time points, i.e. as temporal spatial processes. We propose a Bayesian hierarchical formulation capable of embracing both cases, with principal kriging functions combined with latent parameters having prior distributions able to deal with spatial/temporal dependence. The methodology is applied to monitoring problems in environmental and epidemiological applications. Copyright © 2010 John Wiley & Sons, Ltd.

Recently, a great effort in microarray data analysis has been directed towards the study of the so-called gene sets. A gene set is defined by genes that are, somehow, functionally related. For example, genes appearing in a known biological pathway naturally define a gene set. Gene sets are usually identified from a priori biological knowledge. Nowadays, many bioinformatics resources store such kind of knowledge (see, for example, the Kyoto Encyclopedia of Genes and Genomes, among others). In this paper we exploit a multivariate approach, based on graphical models, to deal with gene sets defined by pathways. Given a sample of microarray data corresponding to two experimental conditions and a pathway linking some of the genes, we investigate whether the strength of the relations induced by the functional links change among the two experimental conditions.

This paper describes a framework for flexibly modeling zero-inflated data. Semiparametric regression based on penalized regression splines for zero-inflated Poisson models is introduced. Moreover, an EM-type algorithm is developed to perform maximum likelihood estimation. As an illustration, a study of animal abundance is tackled. In fact, abundance often shows excess of zeroes and is a complicated function of the explanatory variables. In particular, the relationships between avian abundance and environmental variables indicating land use are tackled. Copyright © 2007 John Wiley & Sons, Ltd.

We consider likelihood based inference for the parameter of a skew-normal distribution. One of the problems shown by this model is the singularity of the Fisher information matrix when skewness is absent. We derive the rate of convergence to the asymptotic distribution of the maximum likelihood estimator and study an alternative parameterization which overcomes problems related to the singularity of the information matrix.

In epidemiology, time-series regression models are specially suitable for evaluating short-term effects of time-varying exposures to pollution. To summarize findings from different studies on different cities, the techniques of designed meta-analyses have been employed. In this context, city-specific findings are summarized by an ‘effect size’ measured on a common scale. Such effects are then pooled together on a second hierarchy of analysis. The objective of this article is to exploit exploratory analysis of city-specific time series. In fact, when dealing with many sources of data, that is, many cities, an exploratory analysis becomes almost unaffordable. Our idea is to explore the time series by fitting complete dynamic regression models. These models are easier to fit than models usually employed and allow implementation of very fast automated model selection algorithms. The idea is to highlight the common features across cities through this analysis, which might then be used to design the meta-analysis. The proposal is illustrated by analysing data on the relationship between daily nonaccidental deaths and air pollution in the 20 US largest cities.

In this paper, we tackle the study of the relationship between daily non accidental deaths and air pollution in the city of Philadelphia in the years 1974 -1988. For modelling the data, we propose to make use of dynamic generalized linear models. These models allow to deal with the serial dependence and time-varying effects of the covariates. Inference is performed by using extended Kaiman filter and smoother.

How infectious diseases spread in space and time is an important question that has received considerable theoretical attention. There are, however, few empirical studies to support theoretical approaches, because data is scarce. In this paper we propose to model the epidemic spread of measles in the London boroughs between 1960 and 1970 by an extension of the Kriged Kalman filter (Mardia et al. , 1998) to count data. Results show the flexibility of our approach in describing complex spatio-temporal dynamics.

In this article, we introduce an automatic identification procedure for transfer function models. These models are commonplace in time-series analysis, but their identification can be complex. To tackle this problem, we propose to couple a nonlinear conditional least-squares algorithm with a genetic search over the model space. We illustrate the performances of our proposal by examples on simulated and real data.