McGill Statistics Seminar

Date: 2011-09-23

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, we give a basic introduction to Sumio Watanabe’s Singular Learning Theory, as outlined in his book “Algebraic Geometry and Statistical Learning Theory”. Watanabe’s key insight to studying singular models was to use a deep result in algebraic geometry known as Hironaka’s Resolution of Singularities. This result allows him to reparametrize the model in a normal form so that central limit theorems can be applied. In the second half of the talk, we discuss new algebraic methods where we define fiber ideals for discrete/Gaussian models. We show that the key to understanding the singular model lies in monomializing its fiber ideal.

Date: 2011-09-16

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Pair-copula constructions (PCCs) provide an elegant way to construct highly flexible multivariate distributions. However, for convenience of inference, pair-copulas are often assumed to depend on the conditioning variables only indirectly. In this talk, I will show how nonparametric smoothing techniques can be used to avoid this assumption. Model selection for PCCs will also be addressed within the proposed method.

Speaker

Elif F. Acar is a Postdoctoral Fellow in the Department of Mathematics and Statistics at McGill University. She holds a Ph.D. in Statistics from the University of Toronto.

Date: 2011-08-31

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Volume estimators based on Cavalieri’s principle are widely used in the bio- sciences. For example in neuroscience, where volumetric measurements of brain structures are of interest, systematic samples of serial sections are obtained by magnetic resonance imaging or by a physical cutting procedure. The volume v is then estimated by ˆv, which is the sum over the areas of the structure of interest in the section planes multiplied by the width of the sections, t > 0. Assessing the precision of such volume estimates is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. In this talk, an overview of classical and new approaches to this problem will be presented. A special focus will be given to some recent advances on distribution estimators and confidence intervals for ˆv; see Hall and Ziegel (2011).