Modelling ethnic differences in the distribution of insulin resistance via Bayesian nonparametric processes: an application to the SABRE cohort study

We analyse data from the Southall And Brent REvisited (SABRE) tri-ethnic study, where measurements of metabolic and anthropometric variables have been recorded. In particular, we focus on modelling the distribution of insulin resistance which is strongly associated with the development of type 2 diabetes. We propose the use of a Bayesian nonparametric prior to model the distribution of Homeostasis Model Assessment insulin resistance, as it allows for data-driven clustering of the observations. Anthropometric variables and metabolites concentrations are included as covariates in a regression framework. This strategy highlights the presence of sub-populations in the data, characterised by different levels of risk of developing type 2 diabetes across ethnicities. Posterior inference is performed through Markov Chains Monte Carlo (MCMC) methods.

Bayesian Nonparametric Monotone Regression of Dynamic Latent Traits in Item Response Theory Models

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain monotone and smooth conditions. To incorporate such conditions and to alleviate the strong parametric assumption on regressing latent trajectories, a flexible nonparametric prior has been introduced to model the dynamic changes of latent traits for item response theory models over the study period. Suitable Bayesian computation schemes are developed for such analysis of the longitudinal and dichotomous item responses. Simulation studies and a real data example from educational testing have been used to illustrate our proposed methods.

Bayesian local extremum splines

SummaryWe consider shape-restricted nonparametric regression on a closed set $\mathcal{X} \subset \mathbb{R},$ where it is reasonable to assume that the function has no more than $H$ local extrema interior to $\mathcal{X}$. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use itto develop methods for testing hypotheses on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.

Shared Parts Latent Topic Model for Image Classification

This paper addresses the problem of accurately classifying image categories without any human interaction. A shared parts latent topic model is presented to share mixture components between categories. Different categories share the similar parts which make the model more accurate. As the number of components is unknown and is to be inferred from the train set, the Dirichlet process is introduced into the model to provide a nonparametric prior for the number of mixture components within each category. Gaussian mixture model is adopted to present the object color feature and the Wishart distribution is applied to estimate the parameters of object shape feature. A number of classification experiments are used to verify the success of our model.