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As a paradigm in statistics the 'Bayesian choice' goes back to Thomas Bayes in the 18th century, but is often contrasted with ‘classical’ statistics as developed in the 20th century. In the last decades its popularity has risen, partly due to increasing computational power and the invention of new algorithms, but also due to the needs of modelling high-dimensional data sets.
‘Nonparametrics’ refers to the use of functions as parameters, rather than Euclidean vectors. Bayesian nonparametrics was long thought to be problematic, because inference requires a prior probability distribution on the parameter set, which in nonparametric situations is a subset of an infinite-dimensional space. Not only was it difficult to come up with computationally tractable proposals for such priors, also by their nature prior probability measures support on small (sigma-compact) sets and hence were thought to add too much `prior information’ (prior to any observed data) to lead to useful statistical inference.
Mathematical and practical insights of the last decade have shown that these difficulties can be overcome. Developing new computational methods and theoretical (mathematical) investigation of properties of Bayesian methods go hand in hand with application of nonparametric Bayesian methodology in many areas of science.
The 25 participants investigated current challenges and solutions in a very interactive environment, about 60% of the time in plenary discussion and the remaining in smaller, specialised groups. For the plenary discussions, a topic was presented by a specialist in an informal manner, always also involving the ‘blackboard’. This invariably lead to many comments and questions from the audience, to the benefit of audience and presenter alike.
New insights were obtained regarding Bayesian uncertainty quantification, either through global measures or through functionals, or by the use of a different topology. There was special interest in species sampling priors, Bayesian sparse modelling, and applications in biostatistical modelling and causality. The work in smaller groups consisted of collaborations on ongoing research work as well as new projects, which eventually will lead to tangible output in the form of research papers.