Physics307L:Schedule/Week 14 agenda/Likelihood

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Previously:Demonstrated max likelihood with normal distribution

For a given collection of data points, x1,x2,...xi, can calculate relative probability of various parent gaussian distributions:

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

The best fit σ and X 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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