In a generic sense, *Monte Carlo simulation*^{1} is an invaluable experimental tool for tackling difficult problems that are mathematically intractable; but the tool is imprecise in that it provides statistical estimates. Nevertheless, provided that the Monte Carlo simulation is conducted properly, valuable insight into a problem of interest is obtained, which would be difficult otherwise.

In this appendix, we focus on *Monte Carlo integration*, which is a special form of Monte Carlo simulation. Specifically, we address the difficult integration problem encountered in Chapter 5 dealing with computation of the differential entropy *h*(*Y*), based on the mathematically intractable conditional probability density function of (5.102) in Chapter 5.

To elaborate, we may say:

Monte Carlo integration is a computational tool, which is used to integrate a given function defined over a prescribed area of interest that is not easy to sample in a random and uniform manner.

Let *W* denote the difficult area over which random sampling of the differential entropy *h*(*Y*) is to be performed. To get around this difficulty, let *V* denote an area so configured that it incudes the area *W* and is easy to randomly sample. Desirably, the selected area *V* enclosed *W* as closely as possible for the simple reason that samples picked outside of *W* are of no practical interest.

Suppose now we pick a total of *N* samples in the area *V*, randomly and uniformly. Then according to Press, *et al*. (1998), ...

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