Placeholder.
Yuling Yao, The likelihood principle in model check and model evaluation
We are (only) interested in estimating an unknown parameter \(\theta\), and there are two data generating experiments both involving \(\theta\) with observable outcomes \(y_1\) and \(y_2\) and likelihoods \(p_1\left(y_1 \mid \theta\right)\) and \(p_2\left(y_2 \mid \theta\right)\). If the outcome-experiment pair satisfies \(p_1\left(y_1 \mid \theta\right) \propto p_2\left(y_2 \mid \theta\right)\), (viewed as a function of \(\theta\) ) then these two experiments and two observations will provide the same amount of information about \(\theta\).”
This idea seems to be useful in thinking about M-open, M-complete, M-closed problems.
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