Consiglio Nazionale delle Ricerche

Tipo di prodottoPresentazione
TitoloBayesian inference on mixtures of stable densities
Anno di pubblicazione2006
FormatoElettronico
Autore/iKuruoglu E.E., Salas D., Ruiz D. P.
Affiliazioni autoriCNR-ISTI, Pisa, Italy; Department of Applied Physics. Campus Fuente Nueva, University of Granada (Spain); Department of Applied Physics. Campus Fuente Nueva, University of Granada (Spain)
Autori CNR e affiliazioni
  • ERCAN ENGIN KURUOGLU
Lingua/e
  • inglese
AbstractStable distributions have attracted significant interest over the last decade in applications ranging from telecommunications to finance and from radar signal processing to biomedicine. This popularity is due to the fact that stable distributions provide a very flexible framework for modelling signals which exhibit impulsive behaviour that cannot be accommodated by the Gaussian distribution. In addition to being capable of modelling varying degrees of impulsiveness they can also model skewed behaviour which have been largely ignored. In addition to their empirical success, the stable distributions have important theoretical motivation: they are the outcome of a generalised version of the central limit theorem and moreover are generalisations of the Gaussian distribution and share attractive properties with it such as the stability property. Despite this flexibility, stable distributions fall short of describing multimodal data, while many real life data sets possess multimodal property indicating contributions from different contributing phenomena. Gaussian mixtures have been employed widely for modelling multimodal data and have obtained significant success, however for impulsive data there is still need for an alternative model. Moreover, although skewed data can be described with Gaussian mixtures, this is at the expense of large number of components. In this work we suggest stable mixture densities as an alternative which can model multimodal, impulsive and skewed data with a small number of components. We employ Bayesian inference, in particular Markov chain Monte Carlo techniques for this task. The mixture weights are estimated using Gibbs sampling and the distribution parameters are estimated using Metropolis sampling. In addition to estimating stable distribution parameters and mixing coefficients, the suggested technique is also capable of estimating the number of components for which the reversible jump MCMC algorithm has been employed. Simulation studies demonstrate the success of the estimation technique and we can conclude that a very flexible modelling framework has been proposed in this work.
Lingua abstractinglese
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Pagine totali1
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Verificato da referee-
Stato della pubblicazionePublished version
Indicizzazione (in banche dati controllate)-
Parole chiaveAlpha-stable distribution; Mixture distributions
Link (URL, URI)-
Titolo convegno/congressoValencia International Meeting on Bayesian Statistics
Luogo convegno/congressoValencia, Spain
Data/e convegno/congresso1-6/06/2006
RilevanzaInternazionale
RelazioneContributo
Titolo parallelo-
Note/Altre informazioniCodice Puma: cnr.isti/2006-A3-16
Strutture CNR
  • ISTI — Istituto di scienza e tecnologie dell'informazione "Alessandro Faedo"
Moduli/Attività/Sottoprogetti CNR
  • ICT.P10.012.001 : Elaborazione di segnali e immagini per impieghi diagnostici e interpretazione di immagini multisorgente
Progetti Europei-
Allegati

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Area disciplinareComputer Science & Engineering
NoteValencia International Meeting on Bayesian Statistics (Valencia, Spain, June 1-6 2006).
Descrizione sintetica del prodottoStable distributions have attracted significant interest over the last decade in applications ranging from telecommunications to finance and from radar signal processing to biomedicine. This popularity is due to the fact that stable distributions provide a very flexible framework for modelling signals which exhibit impulsive behaviour that cannot be accommodated by the Gaussian distribution. In addition to being capable of modelling varying degrees of impulsiveness they can also model skewed behaviour which have been largely ignored. In addition to their empirical success, the stable distributions have important theoretical motivation: they are the outcome of a generalised version of the central limit theorem and moreover are generalisations of the Gaussian distribution and share attractive properties with it such as the stability property. Despite this flexibility, stable distributions fall short of describing multimodal data, while many real life data sets possess multimodal property indicating contributions from different contributing phenomena. Gaussian mixtures have been employed widely for modelling multimodal data and have obtained significant success, however for impulsive data there is still need for an alternative model. Moreover, although skewed data can be described with Gaussian mixtures, this is at the expense of large number of components. In this work we suggest stable mixture densities as an alternative which can model multimodal, impulsive and skewed data with a small number of components. We employ Bayesian inference, in particular Markov chain Monte Carlo techniques for this task. The mixture weights are estimated using Gibbs sampling and the distribution parameters are estimated using Metropolis sampling. In addition to estimating stable distribution parameters and mixing coefficients, the suggested technique is also capable of estimating the number of components for which the reversible jump MCMC algorithm has been employed. Simulation studies demonstrate the success of the estimation technique and we can conclude that a very flexible modelling framework has been proposed in this work.