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Summary Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non‐parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation. [ABSTRACT FROM AUTHOR]

Research has shown that high blood glucose levels are important predictors of incident diabetes. However, they are also strongly associated with other cardiometabolic risk factors such as high blood pressure, adiposity, and cholesterol, which are also highly correlated with one another. The aim of this analysis was to ascertain how these highly correlated cardiometabolic risk factors might be associated with high levels of blood glucose in older adults aged 50 or older from wave 2 of the English Longitudinal Study of Ageing (ELSA). Due to the high collinearity of predictor variables and our interest in extreme values of blood glucose we proposed a new method, called quantile profile regression, to answer this question. Profile regression, a Bayesian nonparametric model for clustering responses and covariates simultaneously, is a powerful tool to model the relationship between a response variable and covariates, but the standard approach of using a mixture of Gaussian distributions for the response model will not identify the underlying clusters correctly, particularly with outliers in the data or heavy tail distribution of the response. Therefore, we propose quantile profile regression to model the response variable with an asymmetric Laplace distribution, allowing us to model more accurately clusters that are asymmetric and predict more accurately for extreme values of the response variable and/or outliers. Our new method performs more accurately in simulations when compared to Normal profile regression approach as well as robustly when outliers are present in the data. We conclude with an analysis of the ELSA. [ABSTRACT FROM AUTHOR]

Research indicates that multiple outdoor air pollutants and adverse neighborhood conditions are spatially correlated. Yet health risks associated with concurrent exposure to air pollution mixtures and clustered neighborhood factors remain underexplored. Statistical models to assess the health effects from pollutant mixtures remain limited, due to problems of collinearity between pollutants and area-level covariates, and increases in covariate dimensionality. Here we identify pollutant exposure profiles and neighborhood contextual profiles within Los Angeles (LA) County. We then relate these profiles with term low birth weight (TLBW). We used land use regression to estimate NO 2 , NO, and PM 2.5 concentrations averaged over census block groups to generate pollutant exposure profile clusters and census block group-level contextual profile clusters, using a Bayesian profile regression method. Pollutant profile cluster risk estimation was implemented using a multilevel hierarchical model, adjusting for individual-level covariates, contextual profile cluster random effects, and modeling of spatially structured and unstructured residual error. Our analysis found 13 clusters of pollutant exposure profiles. Correlations between study pollutants varied widely across the 13 pollutant clusters. Pollutant clusters with elevated NO 2 , NO, and PM 2.5 concentrations exhibited increased log odds of TLBW, and those with low PM 2.5 , NO 2 , and NO concentrations showed lower log odds of TLBW. The spatial patterning of pollutant cluster effects on TLBW, combined with between-pollutant correlations within pollutant clusters, imply that traffic-related primary pollutants influence pollutant cluster TLBW risks. Furthermore, contextual clusters with the greatest log odds of TLBW had more adverse neighborhood socioeconomic, demographic, and housing conditions. Our data indicate that, while the spatial patterning of high-risk multiple pollutant clusters largely overlaps with adverse contextual neighborhood cluster, both contribute to TLBW while controlling for the other. [ABSTRACT FROM AUTHOR]