Likelihood ratio vs. Bayes factor

The Likelihood ratio uses the Maximum Likelihood Estimator (MLE) and subs it in for to find the max probabilities of each model. So it uses a point estimate and doesn’t take into account possible unknowns about the parameter

The Bayes Factor integrates across the entire space so it takes the (weighted) average of different probabilities of ‘s.

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References

Criticisms of MLE - similar idea here. The likelihood ratio doesn’t mean that the data is specifically the most likely realization @lancaster2004 - Chapter 2