Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time

Analysis of paediatric visual acuity using Bayesian copula models with sinh-arcsinh marginal densities

We analyse paediatric ophthalmic data from a large sample of children aged between 3 and 8 years. We modify the Bayesian additive conditional bivariate copula regression model of Klein and Kneib [1] by using sinh-arcsinh marginal densities with location, scale and shape parameters that depend smoothly on a covariate. We perform Bayesian inference about the unknown quantities of our model using a specially tailored Markov chain Monte Carlo algorithm. We gain new insights about the processes which determine transformations in visual acuity with respect to age, including the nature of joint changes in both eyes as modelled with the age-related copula dependence parameter. We analyse posterior predictive distributions to identify children with unusual sight characteristics, distinguishing those who are bivariate, but not univariate outliers. In this way we provide an innovative tool that enables clinicians to identify children with unusual sight who may otherwise be missed. We compare our simultaneous Bayesian method with the two-step frequentist generalized additive modelling approach of Vatter and Chavez-Demoulin [2]

Restricting exchangeable nonparametric distributions

Distributions over exchangeable matrices with infinitely many columns, such as the Indian buffet process, are useful in constructing nonparametric latent variable models. However, the distribution implied by such models over the number of features exhibited by each data point may be poorly- suited for many modeling tasks. In this paper, we propose a class of exchangeable nonparametric priors obtained by restricting the domain of existing models. Such models allow us to specify the distribution over the number of features per data point, and can achieve better performance on data sets where the number of features is not well-modeled by the original distribution