Introduction To Monte Carlo Simulation

Abstract

This paper reviews the history and principles of Monte Carlo simulation, emphasizing techniques commonly used in the simulation of medical imaging.

FIGURE 1

Buffon's Needle: after N tosses, the estimate for pi is (2N/X), where X is the number of times the needle intersects a line [2].

FIGURE 2

PDF For The Exponential Distribution [10].

FIGURE 3

CDF For The Exponential Distribution [10].

FIGURE 4

Sampling The Exponential Distribution. Given u from the uniform distribution, find x such that F(x)=u.

FIGURE 5

Acceptance-Rejection Method. Sample v from g(x) using method from the previous section, sample u from the uniform distribution, accept v if c*u ≤ f(v)/g(v) [11].

FIGURE 6

PDF For The Normal Distribution [12].

FIGURE 7

PMF For The Poisson Distribution [14]. The lines between the points are for clarity only; the PMF is a function of the non-negative integers only.