Lorentz Center

International center for scientific workshops

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## Bayesian Nonparametrics |

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. Differences between Bayesian and non-Bayesian
statistics are also blurring, and intermediate forms as ``empirical Bayesian
methods'' are gaining importance. '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, and Bayesian nonparametrics has grown into a lively subbranch
of statistics. 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. This workshop is planned in the week
following the 9th BNP meeting in Amsterdam, and will focus on the full range of
Bayesian statistics: from computational methods to analytical and theoretical
analysis of priors and posterior distributions. In particular: A. Nonparametric Bayes models for constrained
shapes and surfaces. B. Bayesian nonparametrics
and machine learning. C. Bayesian adaptation (organizer: Judith
Rousseau) D. New Models and Simulation Methods in
Bayesian Nonparametrics. E. Dependent random partition and processes. F. Asymptotic behaviour
of posterior distributions. G. Hierarchical models. H. Bayesian testing in large parameter spaces. I. Extensions of Beta Processes and Dirichlet Processes. J. Applications in biostatistics and beyond. [Back] |