Learn Parameter Estimation Techniques at INFN School of Statistics 2022
Join the hands-on session on parameter estimation at INFN School of Statistics in Paestum led by Glen Cowan from Royal Holloway, University of London. Explore exercises and solutions, and gain insights into fitting methods using Python and ROOT/C++. Enhance your skills in data analysis and model fitting for scientific research.
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Parameter Estimation Hands-on Session INFN School of Statistics Paestum, 15-20 May 2022 https://agenda.infn.it/event/28039/ Glen Cowan Physics Department Royal Holloway, University of London g.cowan@rhul.ac.uk www.pp.rhul.ac.uk/~cowan G. Cowan / RHUL Physics INFN 2022, Paestum / Parameter Estimation, Hands-on Session 1
Introduction and materials The exercises for parameter estimation are at (linked also to indico) https://www.pp.rhul.ac.uk/~cowan/stat/paestum/exercises The exercise and are described in the file fitting_exercises.pdf. There are both python and ROOT/C++ versions. For python, you need python 3 and install iminuit from https://pypi.org/project/iminuit/ with pip install iminuit For ROOT you should have version 6 and C++ installed with a cern-like (e.g., lxplus) setup. G. Cowan / RHUL Physics INFN 2022, Paestum / Parameter Estimation, Hands-on Session 2
Comment on the lnL = lnLmax contour In the lectures, we saw that the standard deviations of fitted parameters are found from the tanget lines (planes) to the contour A similar procedure can be used to find a confidence region in the parameter space that will cover the true parameter with probability CL = 1 (the confidence level). This uses the contour , N = number of parameters If you want the contour lnL = lnLmax in iminuit, you need to choose CL (= 1 ) such that F 2 1(1 ,N) = 1, i.e., G. Cowan / RHUL Physics INFN 2022, Paestum / Parameter Estimation, Hands-on Session 3
Solutions 1a) Running the program mlFit.py produces the following plots: A fit of the pdf: G. Cowan / RHUL Physics INFN 2022, Paestum / Parameter Estimation, Hands-on Session 4
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1b) Assume i.i.d. data sample, so Assume inverse covariance from Fisher Information (large sample): Since we find But V 1V = Iso if V 1 n, then V 1/n, and so from the square roots of the diagonal elements G. Cowan / RHUL Physics INFN 2022, Paestum / Parameter Estimation, Hands-on Session 7
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