Physics307L F07:Schedule/Week 9 agenda/Likelihood

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Last week:Media:307L 2007 Week 8 Millikan data.xlsx

For a given collection of data points, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle x_1, x_2, ... x_i} , can calculate relative probability of various parent gaussian distributions:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle prob \propto \frac {1}{\sigma^N} e^{-\sum(x_i-X)^2 / 2 \sigma^2} }

The best fit Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \sigma} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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