Maximum Likelihood
What, exactly, do we mean when we say that the parameter values should afford the ‘best fit of the model to the data’? The convention we adopt is that our techniques should lead to unbiased, variance-minimizing estimators. We define ‘best’ in terms of maximum likelihood. This notion may be unfamiliar, so it is worth investing some time to get a feel for it. This is how it works:
- given the data,
- and given our choice of model,
- what values of the parameters of that model make the observed data most likely?
We judge the model on the basis how likely the data would be if the model were correct.
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