An anti-Laplacian prior is defined in the obvious way; if you’ve observed R red balls and W white balls, assign probability (W + 1) / (R + W + 2) of seeing a red ball on the next round.
An anti-Occamian prior is more difficult, for essentially the reasons Unknown states; but let’s not forget that, in real life, Occam priors are technically uncomputable because you can’t consider all possible simple computations. So if you only consider a finite number of possibilities, you can have an improper prior that assigns greater probability to more complex explanations, and then normalize with whatever explanations you’re actually considering.
This is coherent if you require that the probability of different permutations of the same sequence be the same. An Anti-Laplacian urn must necessarily be finite.
On the other hand, Laplace assigns both a probability of 1⁄12.
An anti-Laplacian prior is defined in the obvious way; if you’ve observed R red balls and W white balls, assign probability (W + 1) / (R + W + 2) of seeing a red ball on the next round.
An anti-Occamian prior is more difficult, for essentially the reasons Unknown states; but let’s not forget that, in real life, Occam priors are technically uncomputable because you can’t consider all possible simple computations. So if you only consider a finite number of possibilities, you can have an improper prior that assigns greater probability to more complex explanations, and then normalize with whatever explanations you’re actually considering.
WRW has probability 1⁄2 2⁄3 1⁄2 = 1⁄6
WWR has probability 1⁄2 1⁄3 3⁄4 = 1⁄8
This is coherent if you require that the probability of different permutations of the same sequence be the same. An Anti-Laplacian urn must necessarily be finite.
On the other hand, Laplace assigns both a probability of 1⁄12.