ECE532 Biomedical Optics © 1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute

Monte Carlo simulations: Sampling from probability density function

The Monte Carlo method is essentially a technique for sampling a probability density function based on a computer generated random number.

Consider a particular random number, rnd₁. The following figure illustrates how rnd₁ selects a particular value x₁ from the probability density function p(x). If a large number of such x₁ values were selected using a series of random numbers rnd₁, the histogram of all the x₁ choices, normalized by the integral of the histogram (sum of all histogram bin values times the bin widths), will match the original p(x).

The next page illustrates how to use the above scheme with a specific example.