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The Monte Carlo Flow
Monte Carlo Analysis
The Monte Carlo Flow
To be more precise, the Monte Carlo is defined as a systematic sampling from the random
distribution f X (x)=PDF X (x) for the input variables X. A simple Monte Carlo estimate of the
distribution of Y=H(X) is obtained by generating X i for i = 1, 2, ..., n from the PDF X , and
simulating Y i =H(X i ). The observed values Y i are used as an estimate of the distribution of Y.
This is depicted in Figure 11-3.
Figure 11-3. Propagation of Distributions
In some sense, the Monte Carlo method provides an efficient way to propagate the input
distributions through the simulation engine, and to compute the distribution function:
Any property of the output distribution, such as the expectation (average value), variance and
coverage intervals can be obtained using CDF Y .
Basic Statistical Concepts
This short section formalizes some concepts in Probability Theory used in this chapter.
Some other materials can be found in Basic Concepts on Multivariate Distributions.
The basic ingredients of a statistical model are the following. First, a random variable Y, which
represents a quantity whose outcome is uncertain. The set of possible outcomes of Y, denoted Ω,
is the sample space. Second, a probability distribution, which assigns probabilities to events
associated with Y. The random variables we consider are continuous random variables: they
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