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## Shape Constrained Inference: Open Problems and New Directions |

In
parametric statistical inference, data are viewed as generated from an unknown
distribution that belongs to a ‘small’ class of possible distributions, usually
parameterized by a low dimensional Euclidean parameter vector. The class of
normal distributions is an example. In nonparametric inference, the class of
possible distributions (the model) is much larger. The class of all
distributions on the real line is an example of this Parametric
models are rigid and often too simple to model data realistically. On the other
hand, fully non-parametric models suffer from other drawbacks, in particular
the well-known curse of dimensionality. An alternative, intermediate approach
is to consider constrained nonparametric modeling that directly incorporates
prior knowledge about certain aspects of the shape of the underlying
distribution into the statistical procedure. Such approaches are practically
relevant, as there are many problems, e.g. from stereology and survival
analysis, where such knowledge on the shape of the underlying distribution
arises from the design of the study. While
statistical methods resulting from this approach often are quite intuitive from
a practical point of view, the theoretical analysis and the computations
involved tend to be challenging and tackling such problems requires novel
ideas. This workshop brings together researchers in statistics, working in the
area of shape and geometry, providing a forum to advance both the methodological
and the algorithmic aspects of shape constrained inference and other
statistical methodologies driven by geometric considerations. [Back] |