Let us know briefly discuss whether the conditions of Proposition 2 are fulfilled in realistic realistic scenarios. The factorization in (6b) is equivalent to the requirement that X and T are marginally independent, whichis a severe restriction. For example, the common setting in which T contains an indicator of time (such as Julian day) and in which X contains variables such as temperature, precipitation, etc., is ruled out by this assumption, as temperature shows a seasonable dependence on Julian day. Instead of the factorization in (6b), Proposition 2 can also be shown to hold if X and Y are conditionally independent