Méthodologies       Methodes Stats

Methodes Stats

We have developed in the group different statistical tools relevantfor our research. Besides numerical simulations on cosmologicalscales, we investigate statistical techniques in order to performcosmological parameter estimations, galaxy cluster caracterization ornon gaussianity tests on CMB maps.

Cosmological parameter estimations

Over the years the use of CMB anisotropy data has become standardprocedure to perform cosmological parameter estimations. In order todo so, one has to compare theoretical models (varying the cosmologicalparameters) to the data (the CMB angular power spectrum estimates ofevery experiment) through a likelihood function. As the number ofparameters investigated increases, the number of likelihood values tobe computed increases as well. And so the computationaltime. Different ways are possible in order to test a family (differentsets of parameters) of models against data. First, in a kind offrequentist way, one can sample the range of possible values of eachfree parameter and compute the likelihood value for each step. Thisgives a grid of likelihood (models) of dimension the number ofparameters and of size in each dimension the number of steps. Themaximum (likelihood) of the grid gives the best model and further workgives the confidence level on each parameter. The second way, more ofthe bayesian kind, is based on Monte Carlo Markov Chains. Theprinciple is to restrict the number of models/likelihoods to becomputed to the one near the best model. In order to do so, the MarkovChain is generating a path in the N-parameter space which takes intoaccount the shape of the likelihood function (close to a N-dimensionalminimization process). In that case the number of likelihoodevaluation grows linearly with the number of parameters (as opposed toexponentially in the case of grid computations). Both methods haveadvantages and disadvantages; that why we have both techniques appliedto CMB data analysis.

However, CMB alone can not constrain several parameters(degeneracies), and the addition of other cosmological probes isnecessary. The procedure remains similar in the case of combinationsanalyses. One has to compute the likelihood of the new dataset whichwill be multiplied to the CMB one.

Non Gaussianity tests

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