arXiv subjects

Gonzalo García-Donato

Publications and source records attributed to Gonzalo García-Donato.

5 recordsLinked to original sources

arXiv2026

Objective Model Prior Probabilities in Variable Selection

For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the increasingly huge model spaces being considered in genomics and other fields. A popular replacement was to adopt a suggestion of Harold Jeffreys for the variable selection problem in which a total of $k$ possible variables are being considered for inclusion in the model: give the collection of all models containing $d$ variables ($d = 0, . . . , k$) prior probability $1/(k + 1)$ and then divide this prior probability equally among the models in the collection. Many other choices of model prior probabilities that impose severe parsimony have also been introduced. We begin by reviewing the problems with using equal model prior probabilities and then discuss some serious problems with the Jeffreys choice. Finally, we introduce and study a number of objective alternative choices of model prior probabilities, from both numerical and theoretical perspectives.

stat.ME↗

arXiv2026

Efficient model exploration with the integrated nested Laplace approximation

Model and variable selection are important topics in Bayesian inference. In particular, the selection of different fixed, random effects and hyperparameters in hierarchical models can be difficult because of their complex structure. In this paper, we introduce the use of approximate Bayesian inference for model and variable selection for hierarchical Bayesian models. The approach is based on the application of Markov chain Monte Carlo methods on the model space. In particular, the Metropolis-Hastings algorithm is used to sample from the set of model indices. In this way, the marginal likelihood is used to compute the acceptance probability so that it is not required to estimate the parameter models directly. For this, the integrated nested Laplace approximation (INLA) is used because it provides accurate estimates of the marginal likelihood and it can also provide estimates of the posterior marginal of the model parameters. This method can be applied not only to variable selection but to a wide range of problems subject to model uncertainty. To illustrate the potential of this approach, examples on variable selection, changepoint models and log-Gaussian Cox processes are developed.

stat.ME↗

arXiv2024

Model Uncertainty and Missing Data: An Objective Bayesian Perspective

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the probabilistic justification of Rubin's rules applied to the usual components of Bayesian variable selection, arguing that prior predictive marginals should be central to the pursued methodology. In the regression settings, we explore the conditions of prior distributions that make the missing data mechanism ignorable. Moreover, when comparing multiple linear models, we provide a complete methodology for dealing with special cases, such as variable selection or uncertainty regarding model errors. In numerous simulation experiments, we demonstrate that our method outperforms or equals others, in consistently producing results close to those obtained using the full dataset. In general, the difference increases with the percentage of missing data and the correlation between the variables used for imputation. Finally, we summarize possible directions for future research.

stat.ME↗

arXiv2020

Bayesian classification for dating archaeological sites via projectile points

Dating is a key element for archaeologists. We propose a Bayesian approach to provide chronology to sites that have neither radiocarbon dating nor clear stratigraphy and whose only information comes from lithic arrowheads. This classifier is based on the Dirichlet-multinomial inferential process and posterior predictive distributions. The procedure is applied to predict the period of a set of undated sites located in the east of the Iberian Peninsula during the IVth and IIIrd millennium cal. BC.

stat.AP↗

arXiv2011

A Bayesian Joinpoint regression model with an unknown number of break-points

Joinpoint regression is used to determine the number of segments needed to adequately explain the relationship between two variables. This methodology can be widely applied to real problems, but we focus on epidemiological data, the main goal being to uncover changes in the mortality time trend of a specific disease under study. Traditionally, Joinpoint regression problems have paid little or no attention to the quantification of uncertainty in the estimation of the number of change-points. In this context, we found a satisfactory way to handle the problem in the Bayesian methodology. Nevertheless, this novel approach involves significant difficulties (both theoretical and practical) since it implicitly entails a model selection (or testing) problem. In this study we face these challenges through (i) a novel reparameterization of the model, (ii) a conscientious definition of the prior distributions used and (iii) an encompassing approach which allows the use of MCMC simulation-based techniques to derive the results. The resulting methodology is flexible enough to make it possible to consider mortality counts (for epidemiological applications) as Poisson variables. The methodology is applied to the study of annual breast cancer mortality during the period 1980--2007 in Castellón, a province in Spain.

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