María Teresa Rodríguez-Bernal

Using Weibull Mixture Distributions to Model Heterogeneous Survival Data

In this article we use Bayesian methods to fit a Weibull mixture model with an unknown number of components to possibly right censored survival data. This is done using the recently developed, birth-death MCMC algorithm. We also show how to estimate the survivor function and the expected hazard rate from the MCMA output.

Posterior predictive p-values: what they are and what they are not

Schervish (1996) carried out an interesting study about some properties of the classicalp-value. In this paper, a similar study is carried out for posterior predictivep-values, in a general setting, showing that: a) the posterior predictivep-value is a continuous function of the null hypothesis, for fixed data, b) the posterior predictivep-value cannot be interpreted (in general) as a measure of support for the null hypothesis.

Asymptotic behaviour of the posterior predictive p-value

The posterior predictive p-value is a Bayesian-motivated alternative to the classical concept of p-value. This paper is devoted to study its asymptotic behaviour. Under mild assumptions, it is proved that: a)When θ*, the true value of the parameter, belongs to the null hypothesis, the distribution of the posterior predictive p-value converges to the uniform distribution over the interval (0,1). b)When θ* does not belong to the null hypothesis, the posterior predictive p-value converges almost surely to zero

The posterior predictive p-value for the problem of goodness of fit

The aim of this paper is to explore some features and possible uses of the posterior predictivep-value for the problem of goodness of fit. First, the behaviour of the posterior predictivep-value is compared with the behaviour of the classicalp-value through some interesting examples. Then, we consider a decision problem for simultaneously deciding to accept/reject a modelM and to accept/reject a null hypothesis (if we have accepted the modelM); the posterior predictivep-value is used for estimating the posterior probability of the model.

Bayesian Robustness of the Posterior Predictive p-Value

Abstract In this paper, the Bayesian robustness of the posterior predictive p-value is studied. First of all, it is proved that Lavines linearization technique can be extended for analyzing this problem. Then, the result is applied to the ϵ-contamination class of prior distributions.Abstract In this paper, the Bayesian robustness of the posterior predictive p-value is studied. First of all, it is proved that Lavines linearization technique can be extended for analyzing this problem. Then, the result is applied to the ϵ-contamination class of prior distributions.

Optimality of the posterior predictive p-value based on the posterior. Odds

Thompson (1997) considered a wide definition of p-value and found the Baves p-value for testing a ooint null hypothesis H0: θ= θ0 versus H1: θ ≠ θ0. In this paper, the general case of testing H0: θ ∈ ⊝0 versus H1: θ ∈ ⊝c 0 is studied. A generalization of the concept of p-value is given, and it is proved that the posterior predictive p-value based on the posterior odds is (asymptotically) a Bayes p-value. Finally, it is suggested that this posterior predictive p-value could be used as a reference p-value

Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments

Recently, the field of multiple hypothesis testing has experienced a great expansion, basically because of the new methods developed in the field of genomics. These new methods allow scientists to simultaneously process thousands of hypothesis tests. The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. Alternatively, in this article, a Bayesian hierarchical model based on mixture distributions and an empirical Bayes approach are proposed in order to produce a list of rejected hypotheses that will be declared significant and interesting for a more detailed posterior analysis. In particular, we develop a straightforward implementation of a Gibbs sampling scheme where all the conditional posterior distributions are explicit. The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show that our model improves the FDR procedure in the sense that it diminishes the percentage of false negatives keeping an acceptable percentage of false positives.

Prior Density Selection as a Particular Case of Bayesian Model Selection: A Predictive Approach

A Bayesian model consists of two elements: a sampling model and a prior density. The problem of selecting a prior density is nothing but the problem of selecting a Bayesian model where the sampling model is fixed. A predictive approach is used through a decision problem where the loss function is the squared L 2 distance between the sampling density and the posterior predictive density, because the aim of the method is to choose the prior that provides a posterior predictive density as good as possible. An algorithm is developed for solving the problem; this algorithm is based on Lavines linearization technique.

Multiple hypothesis testing and clustering with mixtures of non-central t-distributions applied in microarray data analysis

Multiple testing analysis and clustering methodologies are usually applied in microarray data analysis. A combination of both methods to deal with multiple comparisons among groups obtained from microarray expressions of genes is proposed. Assuming normal data, a statistic which depends on sample means and sample variances, distributed as a non-central t-distribution is defined. As multiple comparisons among groups are considered, a mixture of non-central t-distributions is derived. The estimation of the components of mixtures is obtained via a Bayesian approach, and the model is applied in a multiple comparison problem from a microarray experiment obtained from gorilla, bonobo and human cultured fibroblasts.

Bayesian inference and data cloning in the calibration of population projection matrices

ABSTRACT Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models. Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978–2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values.