TSI report for the period 2005-2009 - Département Traitement du ...

12.2. Main Results 12. Statistics and Applications (STA)
requires adaptive approximation of the optimal ROC (Receiver Operating Characteristic) curve.
The computation of confidence bands through resampling for the ROC curve and associated
performance criteria has been investigated in [2519, 2539]. Reference [2401] presents the main
ranking algorithm, termed tree-rank, and provides a thorough theoretical analysis of its performance.
In the context of the ANR project BEMOL, the team also started some preliminary works
on related tasks such as collaborative filtering.
More recently, with the arrival of A. Garivier, the team started working on themes related to
resource allocation and reinforcement learning, in particular in the context of the PhD thesis of
S. Filippi (funded by France Telecom R&D).
12.2.2 Statistical Methods for Astronomy
Contributors O. Cappé, J-F. Cardoso, G. Fort.
Projects ANR projects COSMOSTAT (Statistical methods for reconstruction and analysis of the
cosmic microwave background) and ECOSTAT (Exploration of the cosmic model by statistical
methods).
There is a growing interest in statistically and numerically efficient methods for the processing
of the complex massive data sets delivered by modern astronomical observatories and surveys.
Our team contribute to this domain along several axis, with a strong focus on the Planck space
mission of the European Spatial Agency. This mission, which will deliver measurements of the
Cosmic Microwave Background (CMB) of unprecedented resolution and sensitivity, requires data
processing of outstanding quality. The team has been contributing several challenges in this area.
In the context of the Planck mission, which will deliver multi-frequency sky maps, the first task
is to develop component separation methods for extracting the best possible CMB map from
these measurements. We contribute a powerful blind separation method which performed very
well in the Planck separation challenge [2432] and a fast and robust non-blind method [2404]
based on spherical needlets.
CMB maps are spherical maps. Usual space-frequency methods such as wavelet analysis
cannot be applied in this context. The ANR project COSMOSTAT has been dedicated to develop
multi-scale methods on the sphere. We proposed and studied a promising new tool for this
purpose, the needlets, a spherical frame for optimal filtering [2404] and spectral estimation on
the sphere [2426, 2415].
Ultimately, CMB data are exploited in a Bayesian framework for the inference of the cosmological
parameters (age of the Universe, Hubble constant, etc). The complexity of the models
requires a specific approach based on Monte Carlo methods (ANR project ECOSTAT) on which
the team enjoys a high level of expertise. In [2456], we have developed an adaptive importance
sampling scheme targeted to the specificities of cosmological data.
CMB data enter in cosmological inference via the likelihood of their angular spectrum, which
raises several issues in terms of the dependence structure. Again this specificity calls for new
methods in statistical analysis on the sphere. We developed exact and approximate likelihoods
function for the observation of the CMB sky with missing data [2379] via interpolations methods
on the sphere.
The formation of the large scale structures of the Universe by gravitational collapse can be
analyzed via the skeleton of the matter density field. Analytical skeleton models require knowing
the joint distribution of the field and of all its derivative tensors. This problem is related to the
theoretical description of spherical invariants of isotropic fields. We obtained closed form
expressions of it via a theory of spherical invariants for isotropic fields [2446].
12.2.3 Statistical Methods for Signal Processing
Contributors K. Abed-Meraim, P. Bianchi, M. Charbit, J. Jakubowicz, E. Moulines, J. Najim.
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