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Introduction to Likelihood Statistics

Introduction to Likelihood Statistics 1. The Likelihood function. 2. Use of the Likelihood function to model data. 3. Comparison to standard frequentist and Bayesean Statistics . Edward L. Robinson* Department of Astronomy and McDonald Observatory University of Texas at Austin *Look for: Data Analysis for Scientists and Engineers Princeton University Press, Sept 2016. The Likelihood Function Let a probability distribution function for have m+1parameters ajf( ,a0,a1, ,am)=f( ,~a),The joint probability distribution for n samples of isf( 1, 2, , n,a0,a1, ,am)=f(~ ,~a).

noise. The noise is described by the width of the Gaussians, a di↵erent width for each measurement. The joint probability distribution for the data points is f(⇠~,~,a)= Yn i=1 1 p 2⇡ i exp 1 2 (⇠ i a)2 2, The joint likelihood function for all the measurements is L(~x,~,a)= Yn i=1 1 p 2⇡ i exp 1 2 (x i a)2 2.

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