Title: Dynamic models for multiple quantiles
Prof. Alessandra Luati, University of Bologna, Italy.
Summary: Recent developments in models for dynamic multiple quantiles are discussed. The baseline semiparametric model introduced recently, based on quantile spacings and score-type updates, is reviewed and extended to account for: heterogeneous tail behaviour, cross-tail effects, and exogenous variables. The extensions result in a flexible class of models ensuring that quantiles do not cross in finite samples and that extreme quantiles are estimated based on information coming from all the regions of the underlying conditional distribution. M-estimation is carried out, and the asymptotic properties of the estimators are discussed. Open problems and illustrations conclude the tutorial.
Title: Bayesian variable selection for survival data: theory, methods, software and applications
Prof. Javier Rubio, UCL, UK.
Summary: Survival analysis is one of the main branches of Statistics, with applications in medicine, biology, and engineering, to name but a very few. Thanks to recent data linkage and data collection developments, survival data can be enriched with additional individual characteristics, such as sociodemographic, clinical, and genetic information. Thus, it is of interest to select the variables that explain the survival times (i.e. the variables that are associated with the survival times). Two of the most popular models for analysing survival data will be presented: the proportional hazards model and the accelerated failure time model. After that, we will present an overview of different methods for conducting variable selection using these models, including penalised likelihood methods, and Bayesian methods based on spike-and-slab, local, and non-local priors. Then, we will focus the attention on the analysis of the theoretical/asymptotic properties of the methodology based on local and non-local priors, including a discussion of these properties when the model is misspecified (the most common case in practice). Finally, we will illustrate the use of available R packages for conducting variable selection based on these methods and models using simulated and real data. R code will be provided.