The KOSMOSHOWS What is it ? The statistic inside What it can do ? Future development Demonstration A. Tilquin (CPPM)

What is it? Interactive graphic tools for cosmological parameters extractions Now only for SN experiments It is written in IDL and can be run on Linux or Windows It can be used as a physics analysis tools Fitting of parameters Errors and full correlation computation Ellipse construction It can be used as a cosmological simulator Standard cosmology User define cosmology

The statistic We have to minimized %  k According to a set of measurement and a given parametric model, what are the best parameter values ? The most probable. Use of the likelihood We have to maximized L %  k  If we take the log: 

Minimization At the first order we use an iterative equation to solve If the model is linear, minimum is found in one step

Error computation By construction the covariance matrix is the second derivative of the chi2 at the minimum This is usually called the Fisher analysis. It gives the correct answer if the model is linear. The error are independent of the measured points. In such an analysis errors are symmetric.

Correct error computation If the model is non linear the Fisher analysis is an approximation. To get the correct errors we have to solve the equation: Where s 2 =1 for a 1  error (68% probability). They are 2 solutions,  +,  -. Fisher analysis  2 =  min 2 +1 -- Second minimum ++ Asymmetric errors

Contour construction The Fisher approach: Quadratic form  Ellipse For non linear model the  2 is no more a quadratic from: 1.Integration over unwanted variables (average contour): 2.Minimization over unwanted variables (most probable contour): Unwanted variables should be marginalized :

Contours —Fisher —Rigorous 39% —Fisher —Rigorous M s,  m,  X fitM s,  m,  X,w 0 fit M s,  m,  X,w 0 w 1 fit

Monte Carlo verification Ellipse:(30.4  2)% Contour:(39.6  2)% 1  contour = 39.3%

Limitation of the method P(ellipse) = (49.5  1.6)% P(contour)=(54.7  1.6)% The wrong normalization is due to the unphysical red zone ->complex luminosity distance !!! Solved in the kosmoshows by taking the real part of of luminosity distance.

What it can do 1.Fit real data or simulated data with various cosmology 2.Estimate error and correlation 3.Use external constraint (prior) 4.Construct probability contour 5.Perform statistical analysis as pool or probability  2 6.Perform evolution of errors and central values with respect to parameters 7.Simulate user defined cosmology and experiment 8.Produce various plots and save them in postscript 9.Read external data, write ntuple to be read by a graphic tool (paw) 10.Call external procedure to perform specific user analysis 11.Etc…

Future development Make this tools more “professional” Make it public. New language (JAVA/ROOT) ? Perform combined fit by using directly the public software: SN1a/CMB/Weak lensing/Baryon oscillation/GRB….. Because of CMB complexity software (1000 hours of CPU to construct contour) new developments are necessary Parallelism on PC cluster Use of Neural Network to speed up processing. Parameterization of the  2 with a NN

Now the demonstration Usually the most difficult part of an online talk Sorry if program crashes But it is still under development lines of code !!!!