1,721,108 research outputs found
The wrapping approach for circular data Bayesian modeling
No full textSebbene i dati circolari sono piuttosto speciali, si presentano in molti contesti. Esempi sono trovati nelle scienze della terra, nella meteorologia, nella biologia, nella fisica, ecc. Le usuali tecniche statistiche non possono essere usate per analizzare i dati circolari a causa della geometria circolare del loro spazio campionario. Ci sono metodi diversi per trattare tali dati come l'approccio embedding e l'approccio intrinsic con la distribuzione di von Mises. Un'alternativa è data dal cosiddetto metodo wrapping, in cui le distribuzioni circolari sono ottenute "arrotolando" le distribuzioni definite sull'asse dei reali. In questa tesi, dopo avere fatto una descrizione generale dei dati circolari, si analizza dettagliatamente l'approccio wrapping. Inerentemente la distribuzione wrapped normal, ne forniamo un'approssimazione che risulta essere molto utile ai fini inferenziali. Questa approssimazione, infatti, è direttamente usata nella procedura di stima bayesana permettendo di superare il problema di identificabilità intrinseco a tale metodo, mostrandone la flessibilità e le facilità di applicazione anche a modelli strutturalmente complessi come i modelli a errore di misura e a modelli spaziali e spatiotemporali. Il contributo principale di questo lavoro è sostanzialmente quello di fornire un metodo per poter applicare ai dati circolari le usuali tecniche e procedure applicate ai dati in linea. Per apprezzare la flessibilità e la facilità di applicazione del metodo wrapping si presentano due applicazioni originali: la prima in contesto spaziale e la seconda in un contesto spazio-temporale. Alcune osservazioni e discussioni su possibili applicazioni e sviluppi futuri concludono la tesi.Although circular data are special, they arise in many different contexts. Examples
are found in earth sciences, meteorology, biology, physics, etc. Standard statistical
techniques cannot be used to analyze circular data because of circular geometry of
the sample space. There are different approaches to handle circular data. In the
embedding approach the directions are treated as angles, while in the most popular
intrinsic approach the directions are treated as unit complex number and modeled
by von Mises distribution. An alternative, and more general class of distribution
models can be obtained using the so called wrapping approach, in which the circular
distributions are obtained wrapping the distributions on the real line onto the unit
circle.
In this thesis, after giving a general overview about circular data, we deeply
analyze the wrapping approach showing the main drawback and advantages of this
method. Focusing on wrapped Normal distribution, we provide an approximation
for this circular distribution that turns out to be very useful to improve the inferential
results. This approximation, in fact, is directly used into the Bayesian inference
procedure allowing to overcome the main disadvantage, the identiability problem,
and to show the
flexibility and ease of applicability of this approach in model with
complex structure as measurement error model and high dimensional spatial and
spatiotemporal model. The main contribution of this work is substantially of overcoming
the identiability problem with the consequently possibility to apply the
standard in line inferential procedures and methods to circular data as well.
In order to appreciate the
flexibility and the ease of applicability and interpretability
of the wrapping approach two original applications of measurement error
model for circular data are presented: the first in a spatial context and the second
in a dynamic spatiotemporal context. Some remarks and discussions about future
developments conclude the thesis
Circular Data Bayesian Modeling: The Wrapping Approach
No full textThis book provides the tool to extend all the common statistical methods and models to circular data as well. In the first part of the book both the descriptive and probabilistic aspects of circular data are given. Then, the wrapping approach and the wrapped Normal distribution are deeply analyzed and an ad hoc inferential Bayesian procedure is provided. Finally, two applications of the measurement error model for circular data in a spatial and in a dynamic spatiotemporal context are presented
Multivariate geostatistical mapping of radioactive contamination in the Maddalena Archipelago (Sardinia, Italy)
No full textTo improve the quality of prediction of radioactive contamination, geostatistical methods, and in particular multivariate geostatistical models, are increasingly being used. These methods, however, are optimal only in the case in which the data may be assumed Gaussian and do not properly cope with data measurements that are discrete, nonnegative or show some degree of skewness. To deal with these situations, here we consider a hierarchical model in which non-Gaussian variables of different kind are handled simultaneously. We show that when observations are assumed to be conditionally distributed as Poisson and Gamma, variograms and cross-variograms have convenient simple forms, and estimation of the parameters of the model can be carried out by Monte Carlo EM. This work has been inspired by radioactive contamination data from the Maddalena Archipelago (Sardinia, Italy)
Multivariate geostatistical mapping of radioactive contamination in the Maddalena Archipelago (Sardinia, Italy)
No full textTo improve the quality of prediction of radioactive contamination, geostatistical methods, and in particular multivariate geostatistical models, are increasingly being used. These methods, however, are optimal only in the case in which the data may be assumed Gaussian and do not properly cope with data measurements that are discrete, nonnegative or show some degree of skewness. To deal with these situations, here we consider a hierarchical model in which non-Gaussian variables of different kind are handled simultaneously. We show that when observations are assumed to be conditionally distributed as Poisson and Gamma, variograms and cross-variograms have convenient simple forms, and estimation of the parameters of the model can be carried out by Monte Carlo EM. This work has been inspired by radioactive contamination data from the Maddalena Archipelago (Sardinia, Italy)
A Hierarchical Geostatistical Factor Model forMultivariate Poisson Count Data
No full textIn this work we deal with multivariate spatial non-Gaussian data, by analyzing, in particular, variables for count data. Building on generalized linear mixed models, we extend these frameworks to multivariate spatial data in a new flexible fashion involving a linear factor model structure for the latent part of the model. Statistical inference is likelihood based and the parameter estimates are obtained via a stochastic version of the EM algorithm. For the mapping of the latent spatial factors, Markov Chain Monte Carlo methods are used. A deep analysis of the performance of the inferential procedure as well as an empirical evaluation of the estimates properties are carried out by a simulation study. The application to the multivariate spatial plankton data of the lake Trasimeno (Italy) allows to appreciate the efficacy of the model to detect the latent spatial structure of the observed data
Binomial factor analysis with the MCEM algorithm
No full textSince its introduction, the classical linear factor model has been central in many fields of application, notably in psychology and sociology, and, assuming continuous and normally distributed observed variables, its likelihood analysis has typically been tackled with the use of the EM algorithm. For the case in which the observed variables are not Gaussian, extensions of this model have been proposed. Here, we present a hierarchical factor model for binomial data for which likelihood inference is carried out through a Monte Carlo EM algorithm. In particular, we discuss some implementations of the estimation procedure with the aim to improve its computational performances. The binomial factor model and the Monte Carlo EM estimation procedure are illustrated on a data set coming from a psychological study on the evaluation of the professional self-efficacy of social workers
Likelihood inference in binomial factor analysis with the Monte Carlo EM algorithm
No full textSince its introduction, the classical linear factor model has been central in many fields of application, notably in psychology and sociology, and, assuming continuous and normally distributed observed variables, its likelihood analysis has typically been tackled with the use of the EM algorithm. For the case in which the observed variables are not Gaussian, extensions of this model have been proposed. Here, we present a hierarchical factor model for binomial data for which likelihood inference is carried out through a Monte Carlo EM algorithm. In particular, we discuss some implementations of the estimation procedure with the aim to improve its computational performances. The binomial factor model and the Monte Carlo EM estimation procedure are illustrated on a data set coming from a psychological study on the evaluation of the professional self-efficacy of social workers
Monte Carlo likelihood inference in multivariate model-based geostatistics
No full textThough in the last decade many works have appeared in the literature dealing with model-based extensions of the classical (univariate) geostatistical mapping methodology based on linear Kriging, very few authors have concentrated, mainly for the inferential problems they pose, on model-based extensions of classical multivariate geostatistical techniques like the linear model of coregionalization, or the related ‘factorial kriging analysis’. Nevertheless, in presence of multivariate spatial non-Gaussian data, in particular count data, as in many environmental applications, the use of these classical techniques can lead to incorrect predictions about the underling factors. To overcome this problem, here we discuss a hierarchical geostatistical factor model that extends, following a model-based geostatistical approach, the classical geostatistical proportional covariance model. For this model we investigate a likelihood-based inferential procedure using the Monte Carlo EM algorithm. In particular, we discuss some of its theoretical properties and show, through some thorough simulation studies, its sampling performances
Likelihood inference in multivariate model-based geostatistics
No full textMultivariate model-based geostatistics refers to the extension of classical multivariate geostatistical techniques, in particular the classical linear model of coregionalization, to the case of non-Gaussian data. Extensions of this kind are still limited in the statistical literature, mainly for the inferential problems they pose, and almost invariably inference is carried out in a Bayesian context. In this work we present some new results on likelihood inference for the unknown parameters of a hierarchical geostatistical factor model. In particular, we show the implementation of some Monte Carlo EM algorithms and discuss their performances, in particular their sampling distributions, mainly through some simulation studies
Analisi dell’autoefficacia professionale con un modello fattoriale per dati binomiali
No full textL’autoefficacia professionale è, come richiamato anche nei precedenti capitoli, un costrutto teorico non direttamente misurabile e la sua valutazione può avvenire solo attraverso l’analisi dei diversi aspetti osservabili ad essa correlati. In altre parole, l’autoefficacia professionale può essere definita come quella variabile latente che costituisce la parte comune dei diversi aspetti direttamente osservabili ad essa correlati e responsabile della correlazione tra di essi. Da un punto di vista statistico, un tale costrutto ricade naturalmente nel contesto classico dell’analisi fattoriale il cui scopo principale è quello di identificare alcune (esigue) variabili latenti (fattori) incorrelate tra di loro in grado di spiegare i legami, le interrelazioni e le dipendenze tra le variabili statistiche osservate. Lo studio delle relazioni esistenti tra le variabili osservate tramite l’individuazione di fattori comuni a tutte le variabili e di fattori specifici a ciascuna variabile, si è sviluppato a partire dalle idee di Galton, e deve la coniazione del suo nome ed i primi sviluppi, soprattutto in ambito psicologico, a Spearman. Solo successivamente, grazie a Lawley, l'analisi fattoriale ebbe la sua completa formalizzazione, da un punto di vista inferenziale, con la derivazione delle stime di massima verosimiglianza. Negli ultimi anni, importanti sviluppi hanno riguardato l’estensione del modello fattoriale a diverse tipologie di variabili osservate, spaziando dall’estensione del modello fattoriale a dati non gaussiani, all’estensione a dati aventi distribuzioni probabilistiche diverse. Altri recenti studi hanno invece riguardato lo sviluppo di modelli fattoriali in cui anche per i fattori latenti, oltre che per le variabili osservate, si ipotizzano distribuzioni diverse dalla gaussiana
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