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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
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.