If you choose a single model to work with, you are effectively putting zero probability on all other models (that are not contained in your chosen model as sub-models).
I follow this reasoning and it applies in many cases. The reason I do not consider it applicable to the example given is due to the explicit mentioning of “We can make Z’s pre-evidence probability arbitrarily small, to make this seem reasonable at the time.” That changes the meaning of the example significantly in my understanding.
I claim that if Z is given enough consideration that ‘arbitrarily small’ is plugged in rather than mere exclusion from a model then it is just an error not an approximation. There are valid examples of bayes-in-practice that support the position John takes but I just don’t consider this example a fair representation. Partly because the mistake is a bad way to handle urns and partly because explicitly plugging in bad priors for Z should make you explicitly expect bad posteriors for Z. Exclusion from the model itself is a different problem.
Good answer. I got a bit confused because Z has two meanings: “ball labelled Z was observed” (data), and “ball came from urn Z” (hypothesis). John’s model can assign zero probability to data than could possibly be observed, and that’s the big no-no.
I follow this reasoning and it applies in many cases. The reason I do not consider it applicable to the example given is due to the explicit mentioning of “We can make Z’s pre-evidence probability arbitrarily small, to make this seem reasonable at the time.” That changes the meaning of the example significantly in my understanding.
I claim that if Z is given enough consideration that ‘arbitrarily small’ is plugged in rather than mere exclusion from a model then it is just an error not an approximation. There are valid examples of bayes-in-practice that support the position John takes but I just don’t consider this example a fair representation. Partly because the mistake is a bad way to handle urns and partly because explicitly plugging in bad priors for Z should make you explicitly expect bad posteriors for Z. Exclusion from the model itself is a different problem.
Good answer. I neglected to read up-thread with enough thoroughness.
Good answer. I got a bit confused because Z has two meanings: “ball labelled Z was observed” (data), and “ball came from urn Z” (hypothesis). John’s model can assign zero probability to data than could possibly be observed, and that’s the big no-no.