Littérature scientifique sur le sujet « Discrete multivariate model »

Modeling and discovering knowledge from multi-relational and multivariate discrete data is a crucial task that arises in many research and application domains, e.g. text mining, intelligence analysis, epidemiology, social science, etc. In this dissertation, we study and address three problems involving the modeling of multi-relational discrete data and multivariate multi-response count data, viz. (1) discovering surprising patterns from multi-relational data, (2) constructing a generative model for multivariate categorical data, and (3) simultaneously modeling multivariate multi-response count data and estimating covariance structures between multiple responses. To discover surprising multi-relational patterns, we first study the ``where do I start?'' problem originating from intelligence analysis. By studying nine methods with origins in association analysis, graph metrics, and probabilistic modeling, we identify several classes of algorithmic strategies that can supply starting points to analysts, and thus help to discover interesting multi-relational patterns from datasets. To actually mine for interesting multi-relational patterns, we represent the multi-relational patterns as dense and well-connected chains of biclusters over multiple relations, and model the discrete data by the maximum entropy principle, such that in a statistically well-founded way we can gauge the surprisingness of a discovered bicluster chain with respect to what we already know. We design an algorithm for approximating the most informative multi-relational patterns, and provide strategies to incrementally organize discovered patterns into the background model. We illustrate how our method is adept at discovering the hidden plot in multiple synthetic and real-world intelligence analysis datasets. Our approach naturally generalizes traditional attribute-based maximum entropy models for single relations, and further supports iterative, human-in-the-loop, knowledge discovery. To build a generative model for multivariate categorical data, we apply the maximum entropy principle to propose a categorical maximum entropy model such that in a statistically well-founded way we can optimally use given prior information about the data, and are unbiased otherwise. Generally, inferring the maximum entropy model could be infeasible in practice. Here, we leverage the structure of the categorical data space to design an efficient model inference algorithm to estimate the categorical maximum entropy model, and we demonstrate how the proposed model is adept at estimating underlying data distributions. We evaluate this approach against both simulated data and US census datasets, and demonstrate its feasibility using an epidemic simulation application. Modeling data with multivariate count responses is a challenging problem due to the discrete nature of the responses. Existing methods for univariate count responses cannot be easily extended to the multivariate case since the dependency among multiple responses needs to be properly accounted for. To model multivariate data with multiple count responses, we propose a novel multivariate Poisson log-normal model (MVPLN). By simultaneously estimating the regression coefficients and inverse covariance matrix over the latent variables with an efficient Monte Carlo EM algorithm, the proposed model takes advantages of association among multiple count responses to improve the model prediction accuracy. Simulation studies and applications to real world data are conducted to systematically evaluate the performance of the proposed method in comparison with conventional methods.<br>Ph. D.

Abstract In a two-level hierarchical linear model(HLM2), the outcome as well as covariates may have missing values at any of the levels. One way to analyze all available data in the model is to estimate a multivariate normal joint distribution of variables, including the outcome, subject to missingness conditional on covariates completely observed by maximum likelihood(ML); draw multiple imputation (MI) of missing values given the estimated joint model; and analyze the hierarchical model given the MI [1,2]. The assumption is data missing at random (MAR). While this method yields efficient estimation of the hierarchical model, it often estimates the model given discrete missing data that is handled under multivariate normality. In this thesis, we evaluate how robust it is to estimate a hierarchical linear model given discrete missing data by the method. We simulate incompletely observed data from a series of hierarchical linear models given discrete covariates MAR, estimate the models by the method, and assess the sensitivity of handling discrete missing data under the multivariate normal joint distribution by computing bias, root mean squared error, standard error, and coverage probability in the estimated hierarchical linear models via a series of simulation studies. We want to achieve the following aim: Evaluate the performance of the method handling binary covariates MAR. We let the missing patterns of level-1 and -2 binary covariates depend on completely observed variables and assess how the method handles binary missing data given different values of success probabilities and missing rates. Based on the simulation results, the missing data analysis is robust under certain parameter settings. Efficient analysis performs very well for estimation of level-1 fixed and random effects across varying success probabilities and missing rates. MAR estimation of level-2 binary covariate is not well estimated when the missing rate in level-2 binary covariate is greater than 10%. The rest of the thesis is organized as follows: Section 1 introduces the background information including conventional methods for hierarchical missing data analysis, different missing data mechanisms, and the innovation and significance of this study. Section 2 explains the efficient missing data method. Section 3 represents the sensitivity analysis of the missing data method and explain how we carry out the simulation study using SAS, software package HLM7, and R. Section 4 illustrates the results and useful recommendations for researchers who want to use the missing data method for binary covariates MAR in HLM2. Section 5 presents an illustrative analysis National Growth of Health Study (NGHS) by the missing data method. The thesis ends with a list of useful references that will guide the future study and simulation codes we used.

This work is an extension of the classical Cox-Ross-Rubinstein discrete time market model in which only one risky asset is considered. We introduce another risky asset into the model. Moreover, the random structure of the asset price sequence is generated by bivariate finite state Markov chain. Then, the interest rate varies over time as it is the function of generating sequences. We discuss how the model can be adapted to the real data. Finally, we illustrate sample implementations to give a better idea about the use of the model.

Cette thèse s’intéresse à certains aspects théoriques de la modélisation des données de comptage. Deux cadres distincts sont abordés : celui des valeurs extrêmes et celui de la modélisation multivariée. Notre première contribution explore, en termes des comportements extrêmes, les liens existants entre le mélange Poisson et sa loi de mélange. Ce travail permet de caractériser et séparer plusieurs familles de lois de mélanges Poisson selon leur comportement en queue. Bien que ce travail soit théorique, nous discutons de son utilité d’un point de vue pratique, notamment pour le choix de la loi de mélange. Notre deuxième contribution porte sur une nouvelle classe de modèles multivariés dénommée Tree Pólya Splitting. Celle-ci repose sur une modélisation hiérarchique et suppose qu’une quantité aléatoire est répartie successivement selon une loi de Pólya à travers une structure d’arbre de partition. Dans ce travail, nous caractérisons les lois marginales univariées et multivariées, les moments factoriels, ainsi que les structures de dépendance (covariance/corrélation) qui en découlent. Nous mettons en évidence, à l’aide d’un jeu de données correspondant à l’abondance de trichoptères, l’intérêt de cette classe de modèles en comparant nos résultats à ceux obtenus, par exemple, avec des modèles de type Poisson log-normale multivariée. Nous concluons cette thèse en présentant diverses perspectives de recherche<br>This thesis focuses on certain theoretical aspects of counting data modeling. Two distinct frameworks are addressed: extreme values and multivariate modeling. Our first contribution explores, in terms of extreme behaviors, the existing connections between the Poisson mixture and its mixing distribution. This work allows us to characterize and discriminate several families of Poisson mixture according to their tail behavior. Although this work is theoretical, we discuss its practical utility, particularly regarding the choice of the mixing distribution. Our second contribution focuses on a new class of multivariate models called Tree Pólya Splitting. This class is based on hierarchical modeling and assumes that a random quantity is successively divided according to a Pólya distribution through a partition tree structure. In this work, we characterize univariate and multivariate marginal distributions, factorial moments, as well as the resulting dependency structures (covariance/correlation). Using a dataset corresponding to the abundance of Trichoptera, we highlight the interest of this class of models by comparing our results to those obtained, for example, with multivariate Poisson-lognormal models. We conclude this thesis by presenting various perspectives

The present thesis is a compendium of three original works produced between 2014 and 2018. The papers have a common link: they are different contributions made by compositional data analysis to the study of the models based on mixtures of probability distributions. In brief, we could say that compositional data analysis is a methodology that consists of studying a sample of measures that are strictly positive from a relative point of view. Mixtures of distributions are a specific type of probability distribution defined to be the convex linear combination of other distributions<br>La present tesi representa un compendi de tres treballs originals realitzats durant els anys 2014-2018. Aquests treballs comparteixen un nexe comú: tots ells són diferents aportacions de l'anàlisi composicional a l'estudi dels models basats en mixtures de distribucions de probabilitat. D'una forma molt breu, podríem dir que l'anàlisi composicional és una metodologia consistent en estudiar una mostra de mesures estrictament positives des d'un punt de vista relatiu. Les mixtures de distribucions, també anomenades barreges de distribucions, són un tipus particular de distribucions de probabilitat definides com la combinació lineal convexa d'altres distribucions

Predicting terrain trafficability of deformable terrain is a difficult task with applications in e.g, forestry, agriculture, exploratory missions. The currently used techniques are neither practical, efficient, nor sufficiently accurate and inadequate for certain soil types. An online method which predicts terrain trafficability is of interest for any vehicle with purpose to reduce ground damage, improve steering and increase mobility. This thesis presents a novel approach for predicting the model parameters used in modelling a virtual terrain. The model parameters include particle stiffness, tangential friction, rolling resistance and two parameters related to particle plasticity and adhesion. Using multi-body dynamics, both vehicle and terrain can be simulated, which allows for an efficient exploration of a great variety of terrains. A vehicle with access to certain sensors can frequently gather sensor data providing information regarding vehicle-terrain interaction. The proposed method develops a statistical model which uses the sensor data in predicting the terrain model parameters. However, these parameters are specified at model particle level and do not directly explain bulk properties measurable on a real terrain. Simulations were carried out of a single tracked bogie constrained to move in one direction when traversing flat, homogeneous terrains. The statistical model with best prediction accuracy was ridge regression using polynomial features and interaction terms of second degree. The model proved capable of predicting particle stiffness, tangential friction and particle plasticity, with moderate accuracy. However, it was deduced that the current predictors and training scenarios were insufficient in estimating particle adhesion and rolling resistance. Nevertheless, this thesis indicates that it should be possible to develop a method which successfully predicts terrain model properties.

Thesis (Ph. D.)--Dept. of Mathematics and Statistics and Dept. of Economics. University of Missouri--Kansas City, 2006.<br>"A dissertation in mathematics and economics." Advisor: Yong Zeng. Typescript. Vita. Title from "catalog record" of the print edition Description based on contents viewed Jan. 29, 2007. Includes bibliographical references (leaves 121-124). Online version of the print edition.

It has previously been determined that using 3 or 4 points on a categorized response scale will fail to produce a continuous distribution of scores. However, there is no evidence, thus far, revealing the number of scale points that may indeed possess an approximate or sufficiently continuous distribution. This study provides the evidence to suggest the level of categorization in discrete scales that makes them directly comparable to continuous scales in terms of their measurement properties. To do this, we first introduced a novel procedure for simulating discretely scaled data that was both informed and validated through the principles of the Classical True Score Model. Second, we employed a measurement invariance (MI) approach to confirmatory factor analysis (CFA) in order to directly compare the measurement quality of continuously scaled factor models to that of discretely scaled models. The simulated design conditions of the study varied with respect to item-specific variance (low, moderate, high), random error variance (none, moderate, high), and discrete scale categorization (number of scale points ranged from 3 to 101). A population analogue approach was taken with respect to sample size (N = 10,000). We concluded that there are conditions under which response scales with 11 to 15 scale points can reproduce the measurement properties of a continuous scale. Using response scales with more than 15 points may be, for the most part, unnecessary. Scales having from 3 to 10 points introduce a significant level of measurement error, and caution should be taken when employing such scales. The implications of this research and future directions are discussed.