Méthodologies
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<h1>Methodes Stats</h1><hr>
We have developed in the group different statistical tools relevant
for our research. Besides numerical simulations on cosmological
scales, we investigate statistical techniques in order to perform
cosmological parameter estimations, galaxy cluster caracterization or
non gaussianity tests on CMB maps.<p>
<b> Cosmological parameter estimations</b><p>
Over the years the use of CMB anisotropy data has become standard
procedure to perform cosmological parameter estimations. In order to
do so, one has to compare theoretical models (varying the cosmological
parameters) to the data (the CMB angular power spectrum estimates of
every experiment) through a likelihood function. As the number of
parameters investigated increases, the number of likelihood values to
be computed increases as well. And so the computational
time. Different ways are possible in order to test a family (different
sets of parameters) of models against data. First, in a kind of
frequentist way, one can sample the range of possible values of each
free parameter and compute the likelihood value for each step. This
gives a grid of likelihood (models) of dimension the number of
parameters and of size in each dimension the number of steps. The
maximum (likelihood) of the grid gives the best model and further work
gives the confidence level on each parameter. The second way, more of
the bayesian kind, is based on Monte Carlo Markov Chains. The
principle is to restrict the number of models/likelihoods to be
computed to the one near the best model. In order to do so, the Markov
Chain is generating a path in the N-parameter space which takes into
account the shape of the likelihood function (close to a N-dimensional
minimization process). In that case the number of likelihood
evaluation grows linearly with the number of parameters (as opposed to
exponentially in the case of grid computations). Both methods have
advantages and disadvantages; that why we have both techniques applied
to CMB data analysis.<p>
However, CMB alone can not constrain several parameters
(degeneracies), and the addition of other cosmological probes is
necessary. The procedure remains similar in the case of combinations
analyses. One has to compute the likelihood of the new dataset which
will be multiplied to the CMB one.<p>
<b> Non Gaussianity tests</b><p>
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<address><a href="mailto:douspis@localhost.localdomain">Douspis Marian</a></address>
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