C. J. Pérez

Bayesian analysis of a generalized lognormal distribution

Many data arising in reliability engineering can be modeled by a lognormal distribution. Empirical evidences from many sources support this argument. However, sometimes the lognormal distribution does not completely satisfy the fitting expectations in real situations. This fact motivates the use of a more flexible family of distributions with both heavier and lighter tails compared to the lognormal one, which is always an advantage for robustness. A generalized form of the lognormal distribution is presented and analyzed from a Bayesian viewpoint. By using a mixture representation, inferences are performed via Gibbs sampling. Although the interest is focused on the analysis of lifetime data coming from engineering studies, the developed methodology is potentially applicable to many other contexts. A simulated and a real data set are presented to illustrate the applicability of the proposed approach.

Computer-aided diagnosis system

A novel method to classify multi-class biomedical objects is presented. The method is based on a hybrid approach which combines pairwise comparison, Bayesian regression and the k-nearest neighbor technique. It can be applied in a fully automatic way or in a relevance feedback framework. In the latter case, the information obtained from both an expert and the automatic classification is iteratively used to improve the results until a certain accuracy level is achieved, then, the learning process is finished and new classifications can be automatically performed. The method has been applied in two biomedical contexts by following the same cross-validation schemes as in the original studies. The first one refers to cancer diagnosis, leading to an accuracy of 77.35% versus 66.37%, originally obtained. The second one considers the diagnosis of pathologies of the vertebral column. The original method achieves accuracies ranging from 76.5% to 96.7%, and from 82.3% to 97.1% in two different cross-validation schemes. Even with no supervision, the proposed method reaches 96.71% and 97.32% in these two cases. By using a supervised framework the achieved accuracy is 97.74%. Furthermore, all abnormal cases were correctly classified.

Sensitivity estimations for Bayesian inference models solved by MCMC methods

The advent of Markov Chain Monte Carlo (MCMC) methods to simulate posterior distributions has virtually revolutionized the practice of Bayesian statistics. Unfortunately, sensitivity analysis in MCMC methods is a difficult task. In this paper, a computationally low-cost method to estimate local parametric sensitivities in Bayesian models is proposed. The sensitivity measure considered here is the gradient vector of a posterior quantity with respect to the parameter. The gradient vector components are estimated by using a result based on the integral/derivative interchange. The MCMC simulations used to estimate the posterior quantity can be re-used to estimate the sensitivity measures and their errors, avoiding the need for further sampling. The proposed method is easy to apply in practice as it is shown with an illustrative example.

Addressing voice recording replications for Parkinson's disease detection

A general subject-based Bayesian approach has been proposed.Special treatment is provided for the probit model.Latent variables are used to provide a predictive model that can handle replications.A Gibbs sampling-based method is derived to compute the model parameters.The approach is used to discriminate healthy people from people suffering PD. A clinical expert system has been developed for detection of Parkinsons Disease (PD). The system extracts features from voice recordings and considers an advanced statistical approach for pattern recognition. The significance of the work lies on the development and use of a novel subject-based Bayesian approach to account for the dependent nature of the data in a replicated measure-based design. The ideas under this approach are conceptually simple and easy-to-implement by using Gibbs sampling. Available information could be included in the model through the prior distribution. In order to assess the performance of the proposed system, a voice recording replication-based experiment has been specifically conducted to discriminate healthy people from people suffering PD. The experiment involved 80 subjects, half of them affected by PD. The proposed system is able to discriminate acceptably well healthy people from people with PD in spite that the experiment has a reduced number of subjects.

MCMC-based local parametric sensitivity estimations

Bayesian inferences for complex models need to be made by approximation techniques, mainly by Markov chain Monte Carlo (MCMC) methods. For these models, sensitivity analysis is a difficult task. A novel computationally low-cost approach to estimate local parametric sensitivities in Bayesian models is proposed. This method allows to estimate the sensitivity measures and their errors with the same random sample that has been generated to estimate the quantity of interest. Conditions to allow a derivative-integral interchange in the operator of interest are required. Two illustrative examples have been considered to show how sensitivity computations with respect to the prior distribution and the loss function are easily obtained in practice.

Bayesian analysis of some models that use the asymmetric exponential power distribution

The asymmetric exponential power (AEP) family includes the symmetric exponential power distribution as a particular case. It provides flexible distributions with lighter and heavier tails compared to the normal one. The distributions of this family can successfully handle both symmetry/asymmetry and light/heavy tails simultaneously. Even more, the distributions can fit each tail separately. This provides a great flexibility when fitting experimental data. The idea of using a scale mixture of uniform representation of the AEP distribution is exploited to derive efficient Gibbs sampling algorithms in three different Bayesian contexts. Firstly, a posterior exploration is performed, where the AEP distribution is considered for the likelihood model. Secondly, a linear regression model, that uses the AEP distribution for the error variable, is developed. And finally, a binary regression model is analyzed, by using the inverse of the AEP cumulative distribution function as the link function. These three models have been built in such a way that they share some full conditional distributions to sample from their respective posterior distributions. The theoretical results are illustrated by comparing with other competing models using some previously published datasets.

New approaches to compute Bayes factor in finite mixture models

Two new approaches to estimate Bayes factors in a finite mixture model context are proposed. Specifically, two algorithms to estimate them and their errors are derived by decomposing the resulting marginal densities. Then, through Bayes factor comparisons, the appropriate number of components for the mixture model is obtained. The approaches are based on simple theory (Monte Carlo methods and cluster sampling), what makes them appealing tools in this context. The performance of both algorithms is studied for different situations and the procedures are illustrated with some previously published data sets.

Local parametric sensitivity for mixture models of lifetime distributions

Mixture models are receiving considerable significance in the last years. Practical situations in reliability and survival analysis may be addressed by using mixture models. When making inferences on them, besides the estimates of the parameters, a sensitivity analysis is necessary. In this paper, a general technique to estimate local prior sensitivities in finite mixtures of distributions from natural exponential families having quadratic variance function (NEF-QVF) is proposed. Those families include some distributions of wide use in reliability theory. An advantage of this method is that it allows a direct implementation of the sensitivity measure estimates and their errors. In addition, the samples that are drawn to estimate the parameters in the mixture model are re-used to estimate the sensitivity measures and their errors. An illustrative application based on insulating fluid failure data is shown.

A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.

Bayesian analysis of finite mixtures of multinomial and negative-multinomial distributions

The Bayesian implementation of finite mixtures of distributions has been an area of considerable interest within the literature. Computational advances on approximation techniques such as Markov chain Monte Carlo (MCMC) methods have been a keystone to Bayesian analysis of mixture models. This paper deals with the Bayesian analysis of finite mixtures of two particular types of multidimensional distributions: the multinomial and the negative-multinomial ones. A unified framework addressing the main topics in a Bayesian analysis is developed for the case with a known number of component distributions. In particular, theoretical results and algorithms to solve the label-switching problem are provided. An illustrative example is presented to show that the proposed techniques are easily applied in practice.