Relabelling in Bayesian mixture models by pivotal units

Label switching is a well-known and fundamental problem in Bayesian estimation of finite mixture models. It arises when exploring complex posterior distributions by Markov Chain Monte Carlo (MCMC) algorithms, because the likelihood of the model is invariant to the relabelling of mixture components. If the MCMC sampler randomly switches labels, then it is unsuitable for exploring the posterior distributions for component-related parameters. In this paper, a new procedure based on the post-MCMC relabelling of the chains is proposed. The main idea of the method is to perform a clustering technique on the similarity matrix, obtained through the MCMC sample, whose elements are the probabilities that any two units in the observed sample are drawn from the same component. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and very low computational burden.     

Analysis of heat wave effects on health by using generalized additive model and bootstrap-based model selection

Summary.  It is known that high summer temperature may lead to worsening health conditions among fragile individuals within exposed populations. It is also argued that multiday patterns of high temperature—heat waves—may have relevant effects on health. We discuss the possible measures of intensities of heat waves to be included in a generalized additive model explaining the number of hospital admissions that occurred during summer months in Milan. The issue of variable selection is central to the analysis: a computational method is discussed which may help in assessing the robustness of the model selection method. Eventually, we obtain evidence supporting the relevance of heat waves in driving adverse health episodes.