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Alvarado Barrantes, Ricardo (2013) Statistical models in biogeography. [Ph.D. thesis]

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Abstract (english)

We concentrate on the statistical methods used in Biogeography for modelling the spatial distribution of bird species. Due to the difficulty of specifying a joint multivariate spatial covariance structure in environmental processes, we factor such a joint distribution into a series of conditional models linked together in a hierarchical framework. We have a process that corresponds to an unobservable map with the actual information about a bird species, and the data correspond to the observations that are connected to that process. Markov chain Monte Carlo (MCMC) simulation approaches are used for models involving multiple levels incorporating dependence structures. We use a Bayesian algorithm for drawing samples from the posterior distribution in order to obtain estimates of the parameters and reconstruct the true map based on data. We present different methods to overcome the problem of calculating the distribution of the Markov random field that is used in the MCMC algorithm. During the analysis it is desirable to delete some of the predictors from the model and only use a subset of covariates in the estimation procedure. We use the method by Kuo & Mallick (1998) (KM) for variable selection and combine it with multiple independent chains which successfully improves the mixing behaviour. In simulation studies we show the better performance of the pseudolikelihood over other likelihood approximation methods, and the good performance of the KM method with this type of data. We illustrate the application of the methods with the complete analysis of the spatial distribution of two bird species (Sturnella magna and Anas rubripes) based on a real data set. We show the advantages of using the hidden structure and the spatial interaction parameter in the spatial hidden Markov model over other simpler models, like the ordinary logistic model or the autologistic model without observation errors.

Abstract (italian)

Ci concentriamo sui metodi statistici utilizzati in Biogeografia per modellare la distribuzione spaziale delle specie di uccelli. A causa della difficoltà nello specificare una struttura multivariata congiunta della covarianza spaziale nei processi ambientali, fattorizziamo tale distribuzione congiunta in una serie di modelli condizionati connessi asieme in un modello gerarchico. Abbiamo un processo che corrisponde ad una mappa non osservabile con le informazioni effettive su una specie di uccelli, ed i dati corrispondono alle osservazioni che sono collegate a tale processo. Vengono utilizzati gli approcci di simulazione Markov chain Monte Carlo (MCMC) per i modelli a più livelli che incorporano strutture di dipendenza. Usiamo un algoritmo Bayesiano per estrarre campioni dalla distribuzione a posteriori al fine di ottenere stime dei parametri e ricostruire la vera immagine basata sui dati. Presentiamo diversi metodi per superare il problema del calcolo della distribuzione del campo aleatorio markoviano che viene utilizzato nell’ algoritmo MCMC. Durante l’analisi, è opportuno eliminare alcuni predittori dal modello e utilizzare solo un sottoinsieme di covariate nella procedura di stima. Usiamo il metodo di Kuo & Mallick (1998) (KM) per la selezione delle variabili che, combinato all’uso dei più catene independenti, incrementa con successo il mixing delle catene. Negli studi di simulazione, presentiamo le migliori prestazioni della pseudo-verosimiglianza rispetto agli altri metodi di approssimazione e le buone prestazioni del metodo KM per queso tipo di dati. Illustriamo l’applicazione dei metodi con l’analisi completa della distribuzione spaziale di due specie di uccelli (Sturnella magna e Anas rubripes), basandoci su di un insieme di dati reale. Dimostriamo i vantaggi nell’uso della struttura latente e del parametro di interazione spaziale nel modello spaziale markoviano latente rispetto agli altri modelli più semplici, come l’ordinario modello logistico o il modello autologistico senza errori di osservazione.

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EPrint type:Ph.D. thesis
Tutor:Gaetan, Carlo
Ph.D. course:Ciclo 25 > Scuole 25 > SCIENZE STATISTICHE
Data di deposito della tesi:30 January 2013
Anno di Pubblicazione:30 January 2013
Key Words:campo aleatorio markoviano latente selezione delle variabili MCMC distribuzione spaziale modello autologistico hidden Markov random field variable selection MCMC spatial distribution autologistic model
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:5784
Depositato il:15 Oct 2013 10:51
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