1 / 6

TS CONTOUR MAP

TS CONTOUR MAP. 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.

evangeline-phelps
Download Presentation

TS CONTOUR MAP

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TS CONTOUR MAP 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

  2. Boundaries for the parameters a) 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

  3. 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

  4. 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

  5. Example 1: Simulation of 3C279 - PowerLaw2 - src only, no bkg TS CONTOUR MAP (cont) 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

  6. 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

More Related