A known property of conditional expectation is extended to the framework Markov kernels. Its meaning in terms densities provided. Some examples located field clinical diagnosis are presented delimit main result paper.

In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan product valuation, but the method is applicable in full generality. The method relies on three simple properties: 1. a forward or backward (automatic) diffe...