105,960 research outputs found
Max-stable models for multivariate extremes
Multivariate extreme-value analysis is concerned with the extremes in a
multivariate random sample, that is, points of which at least some components
have exceptionally large values. Mathematical theory suggests the use of
max-stable models for univariate and multivariate extremes. A comprehensive
account is given of the various ways in which max-stable models are described.
Furthermore, a construction device is proposed for generating parametric
families of max-stable distributions. Although the device is not new, its role
as a model generator seems not yet to have been fully exploited.Comment: Invited paper for RevStat Statistical Journal. 22 pages, 3 figure
Infinite factorization of multiple non-parametric views
Combined analysis of multiple data sources has increasing application interest, in particular for distinguishing shared and source-specific aspects. We extend this rationale of classical canonical correlation analysis into a flexible, generative and non-parametric clustering
setting, by introducing a novel non-parametric hierarchical
mixture model. The lower level of the model describes each source with a flexible non-parametric mixture, and the top level combines these to describe commonalities of the sources. The lower-level clusters arise from hierarchical Dirichlet Processes, inducing an infinite-dimensional contingency table between the views. The commonalities between the sources are modeled by an infinite block
model of the contingency table, interpretable as non-negative factorization of infinite matrices, or as a prior for infinite contingency tables. With Gaussian mixture components plugged in for continuous measurements, the model is applied to two views of genes, mRNA expression and abundance of the produced proteins, to expose groups of genes that are co-regulated in either or both of the views.
Cluster analysis of co-expression is a standard simple way of screening for co-regulation, and the two-view analysis extends the approach to distinguishing between pre- and post-translational regulation
Extreme Dependence Models
Extreme values of real phenomena are events that occur with low frequency,
but can have a large impact on real life. These are, in many practical
problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991).
To study these events is of fundamental importance. For this purpose,
probabilistic models and statistical methods are in high demand. There are
several approaches to modelling multivariate extremes as described in Falk et
al. (2011), linked to some extent. We describe an approach for deriving
multivariate extreme value models and we illustrate the main features of some
flexible extremal dependence models. We compare them by showing their utility
with a real data application, in particular analyzing the extremal dependence
among several pollutants recorded in the city of Leeds, UK.Comment: To appear in Extreme Value Modelling and Risk Analysis: Methods and
Applications. Eds. D. Dey and J. Yan. Chapman & Hall/CRC Pres
Likelihood estimators for multivariate extremes
The main approach to inference for multivariate extremes consists in
approximating the joint upper tail of the observations by a parametric family
arising in the limit for extreme events. The latter may be expressed in terms
of componentwise maxima, high threshold exceedances or point processes,
yielding different but related asymptotic characterizations and estimators. The
present paper clarifies the connections between the main likelihood estimators,
and assesses their practical performance. We investigate their ability to
estimate the extremal dependence structure and to predict future extremes,
using exact calculations and simulation, in the case of the logistic model
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