The first treacherous model works by replacing the bad simplicity prior with a better prior, and then using the better prior to more quickly infer the true model. No reason for the same thing to happen a second time.
(Well, I guess the argument works if you push out to longer and longer sequence lengths—a treacherous model will beat the true model on sequence lengths a billion, and then for sequence lengths a trillion a different treacherous model will win, and for sequence lengths a quadrillion a still different treacherous model will win. Before even thinking about the fact that each particular treacherous model will in fact defect at some point and at that point drop out of the posterior.)
Does it make sense to talk about ˇμ1, which is like μ1 in being treacherous, but is uses the true model μ0 instead of the honest model ^μ0? I guess you would expect ˇμ1 to have a lower posterior than μ0?
The first treacherous model works by replacing the bad simplicity prior with a better prior, and then using the better prior to more quickly infer the true model. No reason for the same thing to happen a second time.
(Well, I guess the argument works if you push out to longer and longer sequence lengths—a treacherous model will beat the true model on sequence lengths a billion, and then for sequence lengths a trillion a different treacherous model will win, and for sequence lengths a quadrillion a still different treacherous model will win. Before even thinking about the fact that each particular treacherous model will in fact defect at some point and at that point drop out of the posterior.)
Does it make sense to talk about ˇμ1, which is like μ1 in being treacherous, but is uses the true model μ0 instead of the honest model ^μ0? I guess you would expect ˇμ1 to have a lower posterior than μ0?