Note that for M2, conceptually we don’t need to modify it, we just need to use the original M2 but apply it only to the subcomponents of the new X-variable which correspond to the original X-variable. Alternatively, we can take the approach you do: construct M′2 which has a distribution over the new X, but “doesn’t say anything” about the new components, i.e. the it’s just maxentropic over the new components. This is equivalent to ignoring the new components altogether.
Ah yes, that’s right. Yeah, I just wanted to make this part fully explicit to confirm my understanding. But I agree it’s equivalent to just let M′2 ignore the extra X′0 (or whatever) component.
The construction is correct.
Note that for M2, conceptually we don’t need to modify it, we just need to use the original M2 but apply it only to the subcomponents of the new X-variable which correspond to the original X-variable. Alternatively, we can take the approach you do: construct M′2 which has a distribution over the new X, but “doesn’t say anything” about the new components, i.e. the it’s just maxentropic over the new components. This is equivalent to ignoring the new components altogether.
Ah yes, that’s right. Yeah, I just wanted to make this part fully explicit to confirm my understanding. But I agree it’s equivalent to just let M′2 ignore the extra X′0 (or whatever) component.
Thanks very much!