J. Martín

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.

Non-parametric Bayesian estimation for multitype branching processes through simulation-based methods

The problem of statistical inference from a Bayesian outlook is studied for the multitype Galton-Watson branching process, considering a non-parametric framework. The only data assumed to be available are each generations population size vectors. The Gibbs sampler is used in estimating the posterior distributions of the main parameters of the model, and the predictive distributions for as yet unobserved generations. The algorithm provided is independent of whether the process becomes extinct or not. The method is illustrated with simulated examples.

Logistic regression for simulating damage occurrence on a fruit grading line

Abstract Many factors influence the incidence of mechanical damage in fruit handled on a grading line. This makes it difficult to address damage estimation from an analytical point of view. During fruit transfer from one element of a grading line to another, damage occurs as a combined effect of machinery roughness and the intrinsic susceptibility of fruit. This paper describes a method to estimate bruise probability by means of logistic regression, using data yielded by specific laboratory tests. Model accuracy was measured via the statistical significance of its parameters and its classification ability. The prediction model was then linked to a simulation model through which impacts and load levels, similar to those of real grading lines, could be generated. The simulation output sample size was determined to yield reliable estimations. The process makes it possible to derive a suitable line design and the type of fruit that should be handled to maintain bruise levels within European Union (EU) Standards. A real example with peaches was carried out with the aid of the software implementation simlin® , developed by the authors and registered by Madrid Technical University. This kind of tool has been demanded by inter-professional associations and grading lines designers in recent years.

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.

A perceptual similarity method by pairwise comparison in a medical image case

The evolution of image techniques in medicine has improved decision making based on physicians’ experience by means of computer-aided diagnosis (CAD). This paper focuses on the development of content-based image retrieval (CBIR) and CAD techniques applied to bronchoscopies and according to different pathologies. A novel pairwise comparison method based on binary logistic regression is developed to determine those images must alike to a new image from incomplete property information, after accounting for the physicians’ appreciation of the image similarity. This method is particularly useful when problems with both a large number of features and few images are involved.

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.

Joint Sensitivity in Bayesian Decision Theory

Research in Bayesian robustnes has mainly concentrated on sensitivity to the prior, although it is well-known that joint changes in both the prior and the utility (and likelihood, as well) may be very influential. We provide some tools to detect changes in the ranking of decisions under perturbations of the prior and the utility, as well as relevant changes in expected utility. The methods allow us to detect also the most critical judgements in determining choices and they may guide additional modeling efforts.