Physics307L:Schedule/Week 14 agenda/Likelihood

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Previously:Demonstrated max likelihood with normal distribution

For a given collection of data points, [math]\displaystyle{ x_1, x_2, ... x_i }[/math], can calculate relative probability of various parent gaussian distributions:

[math]\displaystyle{ prob \propto \frac {1}{\sigma^N} e^{-\sum(x_i-X)^2 / 2 \sigma^2} }[/math]

The best fit [math]\displaystyle{ \sigma }[/math] and [math]\displaystyle{ X }[/math] maximize this likelihood

This is a good introduction to the very common problem of optimizing (minimizing or maximizing) a function

Nelder-Mead method

Biophysics example

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