Multivariate data analysis: The French way

This paper presents exploratory techniques for multivariate data, many of them well known to French statisticians and ecologists, but few well understood in North American culture. We present the general framework of duality diagrams which encompasses discriminant analysis, correspondence analysis and principal components, and we show how this framework can be generalized to the regression of graphs on covariates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000455 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Sampling From A Manifold

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory

Threshold graph limits and random threshold graphs

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.Comment: 47 pages, 8 figure

The duality diagram in data analysis: Examples of modern applications

Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses circles as the Duality Diagram Approach, put to new uses through the use of a variety of metrics and ways of combining different diagrams together. This issue of the Annals of Applied Statistics contains contemporary examples of how this approach provides solutions to hard problems in data integration. We present here the genesis of the technique and how it can be seen as a precursor of the modern kernel based approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS408 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org