14 research outputs found
Dynamic Weights in Gaussian Mixture Models: A Bayesian Approach
This paper proposes a generalization of Gaussian mixture models, where the
mixture weight is allowed to behave as an unknown function of time. This model
is capable of successfully capturing the features of the data, as demonstrated
by simulated and real datasets. It can be useful in studies such as clustering,
change-point and process control. In order to estimate the mixture weight
function, we propose two new Bayesian nonlinear dynamic approaches for
polynomial models, that can be extended to other problems involving polynomial
nonlinear dynamic models. One of the methods, called here component-wise
Metropolis-Hastings, apply the Metropolis-Hastings algorithm to each local
level component of the state equation. It is more general and can be used in
any situation where the observation and state equations are nonlinearly
connected. The other method tends to be faster, but is applied specifically to
binary data (using the probit link function). The performance of these methods
of estimation, in the context of the proposed dynamic Gaussian mixture model,
is evaluated through simulated datasets. Also, an application to an array
Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer
illustrates our proposal, highlighting the ability of the method to detect
chromosome aberrations
Bayesian Analysis of a Health Insurance Model
We consider the problem of determining health insurance premiums based on past information on size of loss, number of losses, and size of population at risk. The size of loss and the number of losses are treated as mutually independent random variables. The number of losses is assumed to follow a Poisson process, and the loss sizes are independent and identically distributed non-negative random variables, and the population at risk is assumed to follow a non-linear growth model. An expression for the premium is obtained through maximization of the insurer\u27s expected utility under a Bayesian model. The parameter estimation process is based on Monte Carlo Markov chain (MCMC). Our methology is applied to two real data sets
Statistical inference : an integrated approach
This book presents an account of the Bayesian and frequentist approaches to statistical inference. In this second edition this book provides students with an integrated understanding of statistical inference from both classical and Bayesian perspectives, describes the strengths and weaknesses of the two viewpoints, emphasizing the importance of a comparative approach to inference, covers all the main topics of standard inference courses, including point and interval estimation, hypothesis testing, prediction, approximation, and linear models, includes real data examples and numerous exercises, some with solution
Bayesian binary regression model: an application to in-hospital death after AMI prediction
A Bayesian binary regression model is developed to predict death of patients after acute myocardial infarction (AMI). Markov Chain Monte Carlo (MCMC) methods are used to make inference and to evaluate Bayesian binary regression models. A model building strategy based on Bayes factor is proposed and aspects of model validation are extensively discussed in the paper, including the posterior distribution for the c-index and the analysis of residuals. Risk assessment, based on variables easily available within minutes of the patients' arrival at the hospital, is very important to decide the course of the treatment. The identified model reveals itself strongly reliable and accurate, with a rate of correct classification of 88% and a concordance index of 83%.<br>Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o Ãndice de concordância e análise de resÃduos. A determinação de fatores de risco, baseados em variáveis disponÃveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um Ãndice de concordância de 83%