M-open, M-complete, M-closed

May 30, 2016 — July 23, 2023

Bayes
how do science
statistics
Figure 1

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.

1 References

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