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    On left-truncating and mixing poisson distributions  Open access

     Valero Baya, Jordi; Perez Casany, Marta; Ginebra Molins, Josep
    Communications in statistics. Theory and methods
    Date of publication: 2014-02-01
    Journal article

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    The distributions obtained by left-truncating at k a mixed Poisson distribution, kT-MP, and those obtained by mixing previously left-truncated Poisson distributions, M-kTP, are characterized by means of their probability generating function. The main consequence is that every kT-MP distribution is a M-kTP distribution, but not the other way around.

    The distributions obtained by left-truncating at k a mixed Poisson distribution, kT-MP, and those obtained by mixing previously left-truncated Poisson distributions, M-kTP, are characterized by means of their probability generating function. The main consequence is that every kT-MP distribution is a M-kTP distribution, but not the other way around.

  • A Bayesian cluster analysis of election results

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Journal of Applied Statistics
    Date of publication: 2014
    Journal article

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    A Bayesian cluster analysis for the results of an election based on multinomial mixture models is proposed. The number of clusters is chosen based on the careful comparison of the results with predictive simulations from the models, and by checking whether models capture most of the spatial dependence in the results. By implementing the analysis on five recent elections in Barcelona, the reader is walked through the choice of the best statistics and graphical displays to help chose a model and present the results. Even though the models do not use any information about the location of the areas in which the results are broken into, in the example they uncover a four-cluster structure with a strong spatial dependence, that is very stable over time and relates to the demographic composition.

  • A Cluster analysis of vote transitions

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Computational statistics and data analysis
    Date of publication: 2014
    Journal article

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    To help settle the debate triggered the day after any election around the origin and destination of the vote of winners and losers, a Bayesian analysis of the results in a pair of consecutive elections is proposed. It is based on a model that simultaneously carries out a cluster analysis of the areas in which the results are broken into and links the results in the two elections of areas in a given cluster through a vote switch matrix. The number of clusters is chosen both through predictive checks as well as by testing whether the residuals are spatially correlated or not. The analysis is tried on the results in Barcelona of a pair of consecutive elections held just four months apart, in 2003 for the Catalan parliament and in 2004 for the Spanish parliament. The proposed approach, which reconstructs individual behavior from aggregated data, can be exported to be a solution for any ecological inference problem where one cannot assume that all the areas are exchangeable the way typically assumed by other ecological inference methods.

    To help settle the debate triggered the day after any election around the origin and destination of the vote of winners and losers, a Bayesian analysis of the results in a pair of consecutive elections is proposed. It is based on a model that simultaneously carries out a cluster analysis of the areas in which the results are broken into and links the results in the two elections of areas in a given cluster through a vote switch matrix. The number of clusters is chosen both through predictive checks as well as by testing whether the residuals are spatially correlated or not. The analysis is tried on the results in Barcelona of a pair of consecutive elections held just four months apart, in 2003 for the Catalan parliament and in 2004 for the Spanish parliament. The proposed approach, which reconstructs individual behavior from aggregated data, can be exported to be a solution for any ecological inference problem where one cannot assume that all the areas are exchangeable the way typically assumed by other ecological inference methods.

    Bayesian model checking; Bayesian hierarchical model; Ecological inference; Election data; Spatial data

  • Bayesian analysis of frequency count data

     Font Valverde, Marti; Puig Oriol, Xavier; Ginebra Molins, Josep
    Journal of statistical computation and simulation
    Date of publication: 2013-02
    Journal article

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    The zero truncated inverse Gaussian–Poisson model, obtained by first mixing the Poisson model assuming its expected value has an inverse Gaussian distribution and then truncating the model at zero, is very useful when modelling frequency count data. A Bayesian analysis based on this statistical model is implemented on the word frequency counts of various texts, and its validity is checked by exploring the posterior distribution of the Pearson errors and by implementing posterior predictive consistency checks. The analysis based on this model is useful because it allows one to use the posterior distribution of the model mixing density as an approximation of the posterior distribution of the density of the word frequencies of the vocabulary of the author, which is useful to characterize the style of that author. The posterior distribution of the expectation and of measures of the variability of that mixing distribution can be used to assess the size and diversity of his vocabulary. An alternative analysis is proposed based on the inverse Gaussian-zero truncated Poisson mixture model, which is obtained by switching the order of the mixing and the truncation stages. Even though this second model fits some of the word frequency data sets more accurately than the first model, in practice the analysis based on it is not as useful because it does not allow one to estimate the word frequency distribution of the vocabulary.

  • A bayesian cluster analysis of election results

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Date: 2013
    Report

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  • On poisson-stopped-sums that are mixed poisson

     Valero Baya, Jordi; Perez Casany, Marta; Ginebra Molins, Josep
    Statistics and probability letters
    Date of publication: 2013
    Journal article

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    Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it.

    Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it.

  • Extended truncated Tweedie-Poisson model

     Valero Baya, Jordi; Ginebra Molins, Josep; Perez Casany, Marta
    Methodology and computing in applied probability
    Date of publication: 2012-03-05
    Journal article

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  • A bayesian analysis of the way in which voters switch their vote

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Date: 2012-07-10
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  • On vote switching, location and national divide in Catalonia

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Date: 2012-11-27
    Report

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  • A Cluster Analysis of vote transitions

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Date: 2012-12-17
    Report

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  • Estadística y probabilidad orientada al análisis de datos discreto

     Puig Oriol, Xavier; Fontdecaba Rigat, Sara; Valero Baya, Jordi; Perez Casany, Marta; Ginebra Molins, Josep; Delicado Useros, Pedro Francisco
    Participation in a competitive project

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  • On the measure and the estimation of evenness and diversity

     Ginebra Molins, Josep; Puig Oriol, Xavier
    Computational statistics and data analysis
    Date of publication: 2010
    Journal article

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    Modelling word or species frequency count data through zero truncated Poisson mixture models allows one to interpret the model mixing distribution as the distribution of the word or species frequencies of the vocabulary or population. As a consequence, estimates of their mixing density can be used as a fingerprint of the style of the author in his texts or of the ecosystem in its samples. Definitions of measure of the evenness and of measure of the diversity within a vocabulary or population are given, and the novelty of these definitions is explained. It is then proposed that the measures of the evenness and of the diversity of a vocabulary or population be approximated through the expectation of these measures under the word or species frequency distribution. That leads to the assessment of the lack of diversity through measures of the variability of the mixing frequency distribution estimates described above.

    Postprint (author’s final draft)

  • The Sichel Model and the mixing and truncation order

     Puig Oriol, Xavier; Ginebra Molins, Josep; Font Valverde, Marti
    Journal of Applied Statistics
    Date of publication: 2010
    Journal article

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    The analysis of word frequency count data can be very useful in authorship attribution problems. Zerotruncated generalized inverse Gaussian–Poisson mixture models are very helpful in the analysis of these kinds of data because their model-mixing density estimates can be used as estimates of the density of the word frequencies of the vocabulary. It is found that this model provides excellent fits for theword frequency counts of very long texts, where the truncated inverse Gaussian–Poisson special case fails because it does not allow for the large degree of over-dispersion in the data. The role played by the three parameters of this truncated GIG-Poisson model is also explored. Our second goal is to compare the fit of the truncated GIG-Poisson mixture model with the fit of the model that results from switching the order of the mixing and truncation stages. A heuristic interpretation of the mixing distribution estimates obtained under this alternative GIG-truncated Poisson mixture model is also provided.

  • On the measure and the estimation of the evenness and diversity of vocabulary

     Ginebra Molins, Josep; Puig Oriol, Xavier
    Computational statistics and data analysis
    Date of publication: 2010
    Journal article

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    Modelling word or species frequency count data through zero truncated Poisson mixture models allows one to interpret the model mixing distribution as the distribution of the word or species frequencies of the vocabulary or population. As a consequence, estimates of their mixing density can be used as a fingerprint of the style of the author in his texts or of the ecosystem in its samples. Definitions of measure of the evenness and of measure of the diversity within a vocabulary or population are given, and the novelty of these definitions is explained. It is then proposed that the measures of the evenness and of the diversity of a vocabulary or population be approximated through the expectation of these measures under the word or species frequency distribution. That leads to the assessment of the lack of diversity through measures of the variability of the mixing frequency distribution estimates described above.

  • On zero-truncating and mixing Poisson distributions

     Valero Baya, Jordi; Perez Casany, Marta; Ginebra Molins, Josep
    Advances in applied probability
    Date of publication: 2010
    Journal article

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  • Medida de la información en un experimento de la familia exponencial

     Rodero De Lamo, Lourdes
    Defense's date: 2010-06-25
    Department of Statistics and Operations Research, Universitat Politècnica de Catalunya
    Theses

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  • Multinomial cluster analysis of electoral Data

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Ninth Valencia International Meeting on Bayesian Satistics
    Presentation's date: 2010-06-06
    Presentation of work at congresses

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  • ANALISIS DE DATOS COMPLEJOS

     Fontdecaba Rigat, Sara; Valero Baya, Jordi; Puig Oriol, Xavier; Ginebra Molins, Josep; Riba Civil, Alexandre; Font Valverde, Marti; Rodero De Lamo, Lourdes; Delicado Useros, Pedro Francisco
    Participation in a competitive project

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  • Any count distribution is a weighted poisson distribution

     Perez Casany, Marta; Valero Baya, Jordi; Ginebra Molins, Josep
    Date: 2010-07-01
    Report

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  • Extended truncated Tweedie-Poisson model

     Valero Baya, Jordi; Ginebra Molins, Josep; Perez Casany, Marta
    Date: 2010-10-01
    Report

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  • On left-truncating and mixing poisson distributions

     Valero Baya, Jordi; Perez Casany, Marta; Ginebra Molins, Josep
    Date: 2010-10-01
    Report

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  • Extended truncated inverse Gaussian-Poisson model

     Puig Oriol, Xavier; Ginebra Molins, Josep; Perez Casany, Marta
    Statistical modeling
    Date of publication: 2009
    Journal article

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  • Anàlisi de dades discretes: freqüència de freqüències i dades multinomials

     Puig Oriol, Xavier
    Defense's date: 2009-12-18
    Department of Statistics and Operations Research, Universitat Politècnica de Catalunya
    Theses

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  • Sample size determination for 2k-r experiments with a binomial response

     González Dávila, Enrique; Ginebra Molins, Josep; Dorta Guerra, Roberto
    Journal of Applied Statistics
    Date of publication: 2008-01
    Journal article

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  • Access to the full text
    Anàlisi de la mortalitat per tumors malignes de mama i d'estómac a Catalunya  Open access

     Puig Oriol, Xavier; Ginebra Molins, Josep
    Date of publication: 2008
    Book chapter

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    Les diferències en la distribució geogràfica de les causes de mortalitat són una informació de gran interès per lluitar contra elles. Les primeres hipòtesis sobre les causes de moltes malalties han estat establertes a partir de la identificació d’una major freqüència d’aparició en àmbits geogràfics on hi ha presència o absència de certs factors, siguin tipus d’hàbits, alimentació, exposicions ambientals o d’altres. A més, conèixer el patró de distribució geogràfica de qualsevol causa de mort ja té valor per ell mateix, ja que pot servir de base per a la presa de decisions en l’àmbit de la gestió sanitària i salut pública, mostrant les àrees on és més prioritari intervenir, així com avaluar l’efectivitat d’algunes intervencions o programes sanitaris implantats en les diferents àrees. Per altra banda, conèixer l’evolució al llarg del temps de les causes de mortalitat aporta també una informació valuosa per identificar tendències, planificar recursos i, també, per avaluar els resultats de les accions que es van desenvolupant.

  • The Extension of the Parameter Space of the Zero-Truncated Poisson-Gaussian Inverse Distribution

     Ginebra Molins, Josep
    2nd International Conference on mathematics & statistics
    Presentation's date: 2008-06-16
    Presentation of work at congresses

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  • Distribución geográfica de la mortalidad por infarto agudo de miocardio en España

     Puig Oriol, Xavier; Gispert, Rosa; Tresserras, Ricard; Ginebra Molins, Josep
    IV Jornadas Científicas de las Sociedades Españolas de Epidemiología y Biometría.
    Presentation's date: 2008-06-19
    Presentation of work at congresses

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  • The Extension of the Parameter Space of the Zero-Truncated Poisson-Gaussian Inverse Distribution

     Perez Casany, Marta; Puig Oriol, Xavier; Ginebra Molins, Josep
    2nd International Conference on mathematics & statistics
    Presentation's date: 2008
    Presentation of work at congresses

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  • Bayesian Smoothing of Micro Array's Copy Number Data

     Puig Oriol, Xavier; Ginebra Molins, Josep; Beà, Sílvia
    XXIVth International Biometric Conference
    Presentation's date: 2008-07-13
    Presentation of work at congresses

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  • On the information in two-level experiments

     González-Dávila, Enrique; Ginebra Molins, Josep; Dorta Guerra, Roberto
    Model assisted statistics and applications
    Date of publication: 2007-09
    Journal article

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  • Simulation-Based Designs for Multiperiod Control

     González Dávila, Enrique; Dorta Guerra, Roberto; Ginebra Molins, Josep
    Computational statistics and data analysis
    Date of publication: 2007-05
    Journal article

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  • On the measure of the information in a statistical experiment

     Ginebra Molins, Josep
    The journal - Bayesian analysis (Online)
    Date of publication: 2007-01
    Journal article

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  • An integrated analysis of individual and aggregated health data using estimating equations

     Martínez Martínez, José Miguel; Benach de Rovira, Joan; Ginebra Molins, Josep; Benavides, Fernando G.; Yasui, Yutaka
    The international journal of biostatistics
    Date of publication: 2007-02
    Journal article

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  • One-half fractions of a 2^3 experiment for the logistic model

     Ginebra Molins, Josep
    Date of publication: 2007-07-31
    Book chapter

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  • One-half fractions of a 2^3 experiment for the logistic model

     Ginebra Molins, Josep
    8th International Workshop in Model-Oriented Design and Analysis
    Presentation's date: 2007-06-04
    Presentation of work at congresses

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  • Diseños factoriales D-óptimos en modelos de Poisson aplicados a problemas de toxicidad.

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2007-09-25
    Presentation of work at congresses

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  • Proceedings of the 8th International Workshop in Model-Oriented Design and Analysis (MODA 8)

     Ginebra Molins, Josep
    8th International Workshop in Model-Oriented Design and Analysis
    Presentation of work at congresses

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  • Bayesian Modeling of Vocabulary Distributions

     Font, Martí; Ginebra Molins, Josep; Puig Oriol, Xavier
    Case Studies in Bayesian Statistics Workshop 9
    Presentation's date: 2007-10-19
    Presentation of work at congresses

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  • Bayesian modelling of the vocabulary distribution

     Ginebra Molins, Josep
    Case Studies in Bayesian Statistics Workshop 9
    Presentation's date: 2007-10-19
    Presentation of work at congresses

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  • Diseños factoriales D-óptimos en modelos de Poisson aplicados a problemas de toxicidad

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation of work at congresses

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  • Diversity of Vocabulary and Homogeneity of Literary Style

     Riba Civil, Alexandre; Ginebra Molins, Josep
    Journal of Applied Statistics
    Date of publication: 2006-08
    Journal article

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  • Mortalidad por cáncer de estómago en Cataluña: distribución geográfica y evolución temporal entre 1986 y 2000

     Puig Oriol, Xavier; Gispert, Rosa; Ginebra Molins, Josep
    Medicina clínica
    Date of publication: 2006-04
    Journal article

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  • Principios de metodología de superficie de respuesta para modelos logísticos  Open access

     TARSICIO DE ZAN, ARTURO
    Defense's date: 2006-05-12
    Department of Statistics and Operations Research, Universitat Politècnica de Catalunya
    Theses

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    En esta tesis doctoral abordamos algunos principios para estudiar la Metodología de Superficie de Respuesta (que abreviaremos en adelante como MSR) para datos que siguen distribuciones binarias (Bernoulli y binomial), y que se ajustan mediante Modelos Lineales Generalizados (que abreviaremos como MLG). El punto de partida elegido ha sido el enfoque clásico de la MSR, es decir, en el contexto de modelos lineales y normales y, en particular, a partir del trabajo seminal de Box y Wilson (1951).Nuestra pregunta de investigación alrededor de la cual hemos elaborado este trabajo gira alrededor del siguiente planteamiento: "¿cómo podría proceder el experimentador cuando la naturaleza de su proceso no sigue los supuestos clásicos de normalidad y linealidad?". Enlazando esta cuestión con el estado actual del arte en materia de la MSR, una segunda pregunta fue: "¿Cómo podría ser un proceso secuencial de aprendizaje del funcionamiento de un sistema en los que intervengan respuestas de naturaleza binaria en el que se persiga un objetivo determinado?". Para poder investigar con mayor profundidad esta pregunta, y mediante un sustento metodológico lo suficientemente sólido, nos apoyamos en los MLG. Estos modelos -a partir de su primera presentación y formulación en el trabajo de Nelder y Wedderburn (1972)- son la herramienta que elegimos para encontrar una metodología de aplicación sistemática, que nos permita buscar modelos adecuados que puedan ajustar respuestas de naturaleza binaria. Consideramos como estrategia particular aquella en la que se encontraría el experimentador cuando dispone de un número fijo de observaciones a realizar de las variables de un sistema, que traducimos con el nombre de "estrategia de presupuesto fijo". Así, el objetivo será poder cuantificar de alguna forma la ganancia de información que alcanzamos a conocer del proceso luego de haber utilizado todo el presupuesto disponible. En todos los casos nuestro plan es el de utilizar familias de estrategias de diseños factoriales a dos niveles, secuencialmente encadenados. Nuestro estudio comienza definiendo una familia de estrategias de exploración de un proceso representado por una superficie de respuesta teórica binaria, en la que hemos identificado tres variables: un valor llamado w, acotado entre 0 y 1, el cual es utilizado para definir el primer centro de experimentación. Luego, se considera una segunda variable, que será el valor que tenga el rango de variación de los factores, L, y finalmente, cuando se ensayen nuevas alternativas de puntos de diseño, habrá un valor S, que llamaremos "salto", que representará la longitud que separa un centro de diseño del siguiente. De esta manera, diremos que una estrategia de diseño queda caracterizada por los valores L, S y w. Partiendo así de una superficie de respuesta que sea la que mejor se considera que se aproxima a un proceso real, el objetivo será el de encontrar a través de simulaciones los niveles de w, L y S que alcancen los mejores valores posibles bajo dos criterios de selección de diseños: (a) una basada en el determinante de la Matriz de Información de Fisher (que hemos llamado "criterio de la cantidad de información"), y (b) el otro, basado en el valor de la superficie teórica evaluado en las mejores condiciones que se obtengan del modelo ajustado (que hemos llamado "criterio de proximidad al máximo"). A tal efecto, hemos utilizado programas escritos en el lenguaje R (www.r-project.orq), un entorno de programación potente y flexible,La completa revisión bibliográfica de ambos temas (MSR y MLG), junto con el diseño de herramientas informáticas "ad-hoc", ofrecen un enfoque novedoso y origina! que puede servir como punto de partida para continuar buscando el enlace entre estas dos metodologías y su aplicación en problemas prácticos sobre la base de criterios objetivos que puedan soportar la toma de decisiones.

    In this PhD thesis we approached some principles that relate to the study the Response Surface Methodology (abbreviated as RSM) for binary responses (Bernoulli and binomial distributions), modellable through the scope of Generalized Linear Models (abbreviated as GLM}. Our starting point is the classic approach of the RSM, in the context of linear normal models and, particularly, from the seminal work on the subject, by the article of Box and Wilson (1951). Our first research question from which we started ellaborating this work was around of the following statement: "How could experimenters deal with this problem when the nature of the process does not follow the classical assumptions of normality and linearity?". Connecting this question with the present state-of-the-art in RSM, the second question that we address is: "How could one design a sequential strategy to learn about the operation of a system with binary response, when certain objectives are persecuted?". In order to explore these questions deeper by means of a methodological support, we leaned towards the GLM approach. These models -presented and formulated primarily in the work of Nelder and Wedderburn (1972)- are the tool that we have chosen in order to find a systematic applied methodology, that aims for suitable models that can be fitted to binary response.We consider as a particular strategy, the one in which the experimenter has a fixed number of observations to be made, in what we labeled as "strategy of fixed budget". Thus, the objective will be to quantify the information gain once we have used all the budget available. In both cases, our plan is to carry out 2-level factorial and sequential designs. Our approach starts with a definition of a family of design strategies for exploration of a process that is being represented by a certain response surface. These strategies are characterized though three variables: w, bounded between 0 and 1, used to define the first experimentation center point. Once that is determined, a second variable is considered: L, or the range of variation of the factors. Finally, when several experimental conditions were considered, the variable S, identifies the jump length that connects one center point of experimentation with the following one, Having defined the scope this way, we can say that a design strategy may be characterized by means of a three-variable picture: L, S and w. Once the experimenter defined what kind of response surface is the best one to approach the real process, the goal will be to find the levels of L, S and w that maximizes the value of two alternative criteria: the first one is based on the determinant of the Fisher's Information Matrix, and it captures (he amount of information gathered by the design, and the second one is the value taken by the theoretical surface on the maximum of the fitted surface. In order to this scope, we have written some programs in R language (www.r-proiect.org), a powerful and flexible environment of programming and doing statistics.A complete bibliographical review of both topics (RSM and GLM), as well as the design of "ad-hoc" specific software, try to offer a new and an original point of view to study this problem, which maybe useful as a starting point for continuing the research in these areas and the link between these two methodologies. It is of special interest the exploration of new practical applications to real problems based on some objective criteria that can support the process of decision making.

  • Distribución geográfica y temporal de la mortalidad por cáncer de estómago en Cataluña, 1986-2000

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2006-05-15
    Presentation of work at congresses

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  • Determinante de la matriz de información de Fisher y su aditividad

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2006-05-15
    Presentation of work at congresses

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  • Determinación del tamaño muestral mediante técnicas Bayesianas

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2006-05-15
    Presentation of work at congresses

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  • Diseños factoriales D-optimos a dos niveles para modelos de Poisson

     Ginebra Molins, Josep
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2006-05-15
    Presentation of work at congresses

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