Study Weekend Program...

## Liking Likelihood

*
Airlie J. McCoy
*

Cambridge Institute for Medical Research, University of Cambridge, UK

Ever wondered what the D in 2mFo-DFc maps means? Even wondered what the
Refmac keywords “REFI RESI MLKF” do? Ever wondered what dice have to do
with crystallography? Well, this is your chance to find out!

There are five things you need to know about likelihood

- 1.
**Maximum Likelihood**
- The best model is the one that maximizes the probability of
observing the experimental data
- 2.
**Independence**
- Probabilities multiply when the experimental data points are
independent
- 3.
**Log-Likelihood**
- The log-likelihood is used instead of the likelihood as it has a
maximum at the same values as the likelihood but the numbers are not too
small for computers to use
- 4.
**Prior Probability and Bayes's Theorem**
- p(model;data) = p(model)x p(data; model)
- p(data;model) is called the likelihood
- p(model) is called the prior probability

- 5.
**Integrating Out Parameters**
- Nuisance variables in a joint probability distribution can be
eliminated by integration

We will explore these concepts with the help of some examples using dice
and see how maximum likelihood helps us produce and interpret electron
density maps during structure solution and refinement.