Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models. © 2016 Tayeb Mohammadi et al

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zeroinflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models

Estimación de resultados deportivos mediante modelos lineales generalizados

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Josep Fortiana Gregori[es] En este trabajo se explica el contexto histórico sobre diversos estudios que se han hecho tratando de encontrar una forma óptima para predecir el resultado de un partido de futbol. Explicaremos, definiremos y detallaremos también como calcular los modelos lineales generalizados. Finalmente trataremos de aplicar lo aprendido de cara a definir un modelo de regresión lineal de Poisson para predecir los resultados de una temporada de fútbol entera

Zero-inflated, hurdle and bivariate parameter-driven count models

A time series is a collection of observations made sequentially through time. Examples occur in a variety of fields, ranging from medicine to engineering. The analysis of time series of counts is one of the rapidly developing areas in time series modeling. In time series, it is unlikely that neighbouring observations are independent. To accommodate potential correlation for count data, two main classes of models are frequent in the literature: parameter-driven and observation-driven models. Central to both classes are the generalized linear models (GLMs). Parameter-driven models result when temporal random effects are used in the GLM to accommodate the autocorrelations. In this dissertation we propose zero-inflated and hurdle specifications for both Poisson and negative binomial parameter-driven models. We employ the data cloning approach as the numerical tool for performing inferences about the models. We carry out intensive simulations to examine the performance of the proposed methodologies. An application of the methods to a data set on the daily counts of emergency department visits for asthma cases in Ontario, Canada, is also provided. The second focus of this dissertation is to model dependence in bivariate time series of counts. In this direction, we propose two parameter-driven models based on a commonly used bivariate Poisson specification. The first model employs one latent process through the cross-correlation parameter of the bivariate Poisson distribution, thus leading to common temporal autocorrelations between the components of the bivariate Poisson, while the second model uses two latent processes to introduce separate autocorrelations in the two marginal processes. An intensive simulation study and real data applications are also provided in these scenarios

Exact Bayesian modeling for bivariate Poisson data and extensions

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics just to name a few) and the bivariate Poisson distribution being a generalization of the Poisson distribution plays an important role in modelling such data. In the present paper we present a Bayesian estimation approach for the parameters of the bivariate Poisson model and provide the posterior distributions in closed forms. It is shown that the joint posterior distributions are finite mixtures of conditionally independent gamma distributions for which their full form can be easily deduced by a recursively updating scheme. Thus, the need of applying computationally demanding MCMC schemes for Bayesian inference in such models will be removed, since direct sampling from the posterior will become available, even in cases where the posterior distribution of functions of the parameters is not available in closed form. In addition, we define a class of prior distributions that possess an interesting conjugacy property which extends the typical notion of conjugacy, in the sense that both prior and posteriors belong to the same family of finite mixture models but with different number of components. Extension to certain other models including multivariate models or models with other marginal distributions are discussed

Model-based clustering for multivariate time series of counts

This dissertation develops a modeling framework for univariate and multivariate zero-inflated time series of counts and applies the models in a clustering scheme to identify groups of count series with similar behavior. The basic modeling framework used is observation-driven Poisson regression with generalized linear model (GLM) structure. The zero-inflated Poisson (ZIP) model is employed to characterize the possibility of extra observed zeros relative to the Poisson, a common feature of count data. These two methods are combined to characterize time series of counts where the counts and the probability of extra zeros may depend on past data observations and on exogenous covariates. A key contribution of this work is a novel modeling paradigm for multivariate zero-inflated counts. The three related models considered are the jointly-inflated, the marginally-inflated, and the doubly-inflated multivariate Poisson. The doubly-inflated model encompasses both marginal-inflation, which allows for additional zeros at each time epoch for each individual count series, and joint-inflation, which allows for zero-inflation across all multivariate series. These models improve upon previously proposed models, which are either too rigid or too simplistic to be applicable in a wide variety of applications. To estimate the model parameters, a new Monte Carlo Estimation Maximization (MCEM) algorithm is developed. The Monte Carlo sampling eliminates complex recursion formulas needed for calculating the probability function of the multivariate Poisson. The algorithm is easily adapted for different multivariate zero-inflation schemes. The new models, new estimation methods, and applications in clustering are demonstrated on simulated and real datasets. For an application in finance, the number of trades and the number of price changes for bonds are modeled as a bivariate doubly zero-inflated Poisson time series, where observations of zero trades or zero price changes represent the liquidity risk for that bond. In an environmental science application, the new models are used in a model-based clustering scheme to study counts of high pollution events at air quality monitoring stations around Houston, Texas. Clustering reveals regions of the air monitoring network which behave similarly in terms of time dependence and response to covariates representing atmospheric conditions and physical sources of air pollution

Exploring Practical Methodologies for the Characterization and Control of Small Quantum Systems

We explore methodologies for characterizing and controlling small quantum systems. We are interested in starting with a description of a quantum system, designing estimators for parameters of the system, developing robust and high-fidelity gates for the system using knowledge of these parameters, and experimentally verifying the performance of these gates. A strong emphasis is placed on using rigorous statistical methods, especially Bayesian ones, to analyze quantum system data. Throughout this thesis, the Nitrogen Vacancy system is used as an experimental testbed. Characterization of system parameters is done using quantum Hamiltonian learning, where we explore the use of adaptive experiment design to speed up learning rates. Gates for the full three-level system are designed with numerical optimal control methods that take into account imperfections of the control hardware. Gate quality is assessed using randomized benchmarking protocols, including standard randomized benchmarking, unitarity benchmarking, and leakage/loss benchmarking