Likelihood probability of observing the data given a model with certain parameters Maximum Likelihood Estimation (MLE) –find the parameter combination.

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Presentation transcript:

Likelihood probability of observing the data given a model with certain parameters Maximum Likelihood Estimation (MLE) –find the parameter combination that maximizes the likelihood requires some basic knowledge of probability

A Poisson Example Pr(Observation=x) = e - x / x! – is the parameter of the model if Observation=4, –likelihood = e - 4 / 4! = e - 4 / 24

Multiple Observations if two independent observations (4 & 2) –likelihood = Pr(Obs 1 =4) x Pr(Obs 2 =2) to find the maximum –construct the likelihood equations –take the derivative(s) –solve for derivatives equal to zero

log-likelihood and deviance log-likelihood (lnL) is more tractable –L = Pr 1 x Pr 2 x Pr 3 x... –lnL = lnPr 1 + lnPr 2 + lnPr deviance = -2*lnL