TS CONTOUR MAP GOAL Produce maps of confidence levels for any

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Presentation transcript:

TS CONTOUR MAP GOAL Produce maps of confidence levels for any Analia Nilda Cillis GOAL Produce maps of confidence levels for any pair of source model parameters. Procedure: 1_Predict boundaries for the map 2_Produce TS Contour MAP A. Cillis 11/01/06 1

Boundaries for the parameters 1_A first fit is generated using python likelihood, and the values of the model parameters are obtained along with the log likelihood value. 2_One parameter is stepped (to the right and left side of the value obtained with the first fit). 3_For each of these new values, which now are fixed, python likelihood is run again to produce a new fit until (eventually) a new maximum of log likelihood is found. 4_Python Likelihood runs again for the value obtained in step (a3) +/- two times the error in the parameter. A. Cillis 11/01/06 2

Boundaries for the parameters (cont) 4_With the point obtained in (a3) and the two points obtained in (a4) a parabola is fitted (x-axis: parameter, y-axis: delta loglikelihood). 5_From this new maximum and assuming that the likelihood statistic is distributed like Chi2 the value of this parameter is obtained until a confidence level of 68% 90% 95% 99%. 6_The same procedure is repeated for the second parameter. Simulation: 3C279 PowerLaw2 2 months Points to be fitted: (-1.968, 2.1239) (-1.996,0) (-2.024, 1.8807) Delta Loglikelihod Index First fit: Npred~2967 Integral=2.49 Index=-2.0 A. Cillis 11/01/06 3

TS CONTOUR MAP b) 1_After the boundaries in both parameters are obtained python likelihood runs several times in a nxn grid (with the boundaries obtained in the previous step) with the parameters fixed. 2_Finally the contour plot is produced with x-axis first parameter, y-axis second parameter, and z-axis confidence levels: 68%, 90%, 95%, 99%. 3_This procedure may be repeated for each pair of parameters. A. Cillis 11/01/06 4

TS CONTOUR MAP (cont) Example 1: Simulation of 3C279 - PowerLaw2 - src only, no bkg 7 days: Npred~293, Integral:2.65, index:-2.03; grid:61x61 1 month: Npred~1508 Integral:2.52, index:-2; grid:61x61 2 months: Npred~2967 Integral:2.49, index:-2; grid:61x61 Par 0: Integral Par 1: Index Confidence levels: 68%, 90%, 95%, 99% A. Cillis 11/01/06 5

TS CONTOUR MAP (cont) Example 2: Simulation 3C279, 3C273, Background 7 days: 3C279: PowerLaw2, Npred~390 Index=-2.1, Grid 61x61 A. Cillis 11/01/06 6