Software for Bayesian Statistics

In this summary we introduce the papers published in the special issue on Bayesian statistics. This special issue comprises 20 papers on Bayesian statistics and Bayesian inference on different topics such as general packages for hierarchical linear model fitting, survival models, clinical trials, missing values, time series, hypothesis testing, priors, approximate Bayesian computation, and others

Missing data analysis and imputation via latent Gaussian Markov random fields

Acknowledgements. V. Gomez-Rubio has been supported by grants MTM2016-77501-P and PID2019-106341GB-I00 from the Spanish Ministry of Economy and Competitiveness co-fnanced with FEDER funds, grant SBPLY/17/180501/000491 and SBPLY/21/180501/000241 funded by Consejería de Educacion, Cultura y Deportes (JCCM, Spain) and FEDER. Marta Blangiardo acknowledges partial support through the grant R01HD092580 funded by the National Institute of Health and from the MRC Centre for Environment and Health, which is currently funded by the Medical Research Council (MR/S019669/1).This paper recasts the problem of missing values in the covariates of a regression model as a latent Gaussian Markov random field (GMRF) model in a fully Bayesian framework. The proposed approach is based on the definition of the covariate imputation sub-model as a latent effect with a GMRF structure. This formulation works for continuous covariates but for categorical covariates a typical multiple imputation approach is employed. Both techniques can be easily combined for the case in which continuous and categorical variables have missing values. The resulting Bayesian hierarchical model naturally fts within the integrated nested Laplace approximation (INLA) framework, which is used for model fitting. Hence, this work fills an important gap in the INLA methodology as it allows to treat models with missing values in the covariates. As in any other fully Bayesian framework, by relying on INLA for model fitting it is possible to formulate a joint model for the data, the imputed covariates and their missingness mechanism. In this way, it is possible to tackle the more general problem of assessing the missingness mechanism by conducting a sensitivity analysis on the different alternatives to model the non-observed covariates. Finally, the proposed approach is illustrated in two examples on modeling health risk factors and disease mapping

Bayesian joint spatio-temporal analysis of multiple diseases

In this paper we propose a Bayesian hierarchical spatio-temporal model for the joint analysis of multiple diseases which includes specific and shared spatial and temporal effects. Dependence on shared terms is controlled by disease-specific weights so that their posterior distribution can be used to identify diseases with similar spatial and temporal patterns. The model proposed here has been used to study three different causes of death (oral cavity, esophagus and stomach cancer) in Spain at the province level. Shared and specific spatial and temporal effects have been estimated and mapped in order to study similarities and differences among these causes. Furthermore, estimates using Markov chain Monte Carlo and the integrated nested Laplace approximation are compared.Peer Reviewe

Bayesian analysis of population health data

The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with different types of fixed and random effects to account for risk factors, spatial and temporal variations, multilevel effects and other sources on uncertainty. To illustrate the potential of Bayesian hierarchical models, a dataset of about 500,000 inhabitants released by the Polish National Health Fund containing information about ischemic stroke incidence for a 2-year period is analyzed using different types of models. Spatial logistic regression and survival models are considered for analyzing the individual probabilities of stroke and the times to the occurrence of an ischemic stroke event. Demographic and socioeconomic variables as well as drug prescription information are available at an individual level. Spatial variation is considered by means of region-level random effects