In Bayesian inference, terms like "observation" and "event" are just conveniences; there is no fundamental importance to them, so don't get hung up on them.

In particular, there is no physical causality or time's arrow -- no "events". Whether you can carry out some calculations in more than one order depends solely on the form of the model. If, algebraically, the results are the same assuming different orders of assignments to some variables (i.e., "observations"), then, terrific, you can do whatever is convenient. If not, well, so what?

About the representation of p > 1/2, you could represent that as a likelihood function which is just a step at 1/2. That is, it is zero to the left of 1/2, and any positive constant to the right. Note that ordinary "observations" yield likelihood functions which are vary smoothly, but the smoothness is not a requirement.

In Bayesian inference, terms like "observation" and "event" are just conveniences; there is no fundamental importance to them, so don't get hung up on them.

In particular, there is no physical causality or time's arrow -- no "events". Whether you can carry out some calculations in more than one order depends solely on the form of the model. If, algebraically, the results are the same assuming different orders of assignments to some variables (i.e., "observations"), then, terrific, you can do whatever is convenient. If not, well, so what?

About the representation of p > 1/2, you could represent that as a likelihood function which is just a step at 1/2. That is, it is zero to the left of 1/2, and any positive constant to the right. Note that ordinary "observations" yield likelihood functions which vary smoothly, but the smoothness is not a requirement.