PHYS 257 Lecture Notes - Lecture 7: Maxima And Minima, Confidence Interval
21 Feb 2018
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Document Summary
Plot the 2 function itself as a function of a and b both give a downward parabolic curve. This makes it clear to see a minimum in the 2 surface. This minimum determines the best fit parameters (a,b) (ee: the least squares best fit lie) For simple functions (polynomials),, you can find the minimum by differentiating 2 with respect to each parameters, setting each to 0, then solving. For complicated functions: we cant do this analytically must find it numerically. This can be done on python using: Some algorithm to make changes to the starting values in order to search out the global minimum value of chi-square. Brute force: map out surface over grid of trail values that cpvers the important region of the parameter space. More sophisticated: apply a gradient search to search out minima. This is necessary when there are a lot of parameters. Determining the uncertainties in the best fit parameters: curvatures of the 2.
