The purpose of model-based experimental design is to maximise the information gathered for quantitative model identification. Instead of the commonly used optimal experimental design, robust experimental design aims to address parametric uncertainties in the design process. In this paper, the Bayesian robust experimental design is investigated, where both a Monte Carlo sampling strategy and loc...

We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coeecients by establishing a relationship between the hyperparameters of the proposed model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relation may be seen as giving insig...

We consider Bayesian and information-theoretic approaches for determining non-informative prior distributions in a parametric model family. The information-theoretic approaches are based on the recently modiied deenition of stochastic complexity by Rissanen, and on the Minimum Message Length (MML) approach by Wallace. The Bayesian alternatives include the uniform prior, and the equivalent sampl...

How to include censored data in a statistical analysis is a recurrent issue in statistics. In multivariate extremes, the dependence structure of large observations can be characterized in terms of a non parametric angular measure, while marginal excesses above asymptotically large thresholds have a parametric distribution. In this work, a flexible semi-parametric Dirichlet mixture model for ang...

Small variance asymptotics is emerging as a useful technique for inference in large scale Bayesian non-parametric mixture models. This paper analyses the online learning of robot manipulation tasks with Bayesian non-parametric mixture models under small variance asymptotics. The analysis yields a scalable online sequence clustering (SOSC) algorithm that is non-parametric in the number of cluste...

We consider Bayesian and information-theoretic approaches for determining non-informative prior distributions in a parametric model family. The information-theoretic approaches are based on the recently modiied deenition of stochastic complexity by Rissanen, and on the Minimum Message Length (MML) approach by Wallace. The Bayesian alternatives include the uniform prior, and various equivalent s...

Non-parametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this non-parametric method naturally infers an appropriate dictionary size. The Dirichlet process and a probit stick-breaking process are als...

We consider inference for longitudinal data based on mixed-effects models with a non-parametric Bayesian prior on the treatment effect. The proposed non-parametric Bayesian prior is a random partition model with a regression on patient-specific covariates. The main feature and motivation for the proposed model is the use of covariates with a mix of different data formats and possibly high-order...

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists...

We develop a Bayesian nonparametric Poisson factorization model for recommendation systems. Poisson factorization implicitly models each user’s limited budget of attention (or money) that allows consumption of only a small subset of the available items. In our Bayesian nonparametric variant, the number of latent components is theoretically unbounded and effectively estimated when computing a po...