A theorem that is prior-free in its formal statement can still require prior-laden choices to generate the likelihoods it operates on, as Deborah Mayo's error-statistical critique of Bayesianism implies.
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Prior-free(as used in statistics and Bayesian reasoning)
A formal statement or process that doesn't depend on any pre-existing assumptions or beliefs built into it from the start.
Prior-laden(as used in statistics and epistemology)
Choices or decisions that are influenced by or depend on pre-existing assumptions, beliefs, or preferences that you bring to them.
Theorem
A theorem is a statement that has been proven to be true through logical reasoning and evidence. It's a fact that mathematicians or scientists have carefully verified using step-by-step arguments, starting from things already known to be true. Once proven, theorems become reliable building blocks that others can use to prove even more complex ideas.
likelihoods(Bayesian confirmation theory)
The probability of the evidence given a particular hypothesis, used in conjunction with prior probabilities to determine expectedness