Monte_Carlo_ppt

# Monte_Carlo_ppt - are relatively simple Step 1: Create a...

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Monte Carlo Simulations A Monte Carlo method is a computational algorithm that relies on repeated random sampling to compute its results. The term Monte Carlo was coined in the 1940s by physicists working on nuclear weapon projects in the Los Alamos National Laboratory .

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Monte Carlo methods are often used when simulating physical and mathematical systems. Because of their reliance on repeated computation and random or pseudo-random numbers, Monte Carlo methods are most suited to calculation by a computer . Monte Carlo methods tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm .
A parametric deterministic model maps a set of input variables to a set of output variables.

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Schematic showing the principal of stochastic uncertainty propagation. (The basic principle behind Monte Carlo simulation.)
The steps in Monte Carlo simulation corresponding to the uncertainty propagation

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Unformatted text preview: are relatively simple Step 1: Create a parametric model , y = f (x1, x2, . .., x q ). Step 2: Generate a set of random inputs , x i 1, x i 2, . .., x iq . Step 3: Evaluate the model and store the results as y i . Step 4: Repeat steps 2 and 3 for i = 1 to n . Step 5: Analyze the results using histograms, summary statistics, confidence intervals, etc. Monte Carlo techniques can be used in Battleship The first figure is simply a unit circle circumscribed by a square. We could examine this problem in terms of the full circle and square, but it's easier to examine just one quadrant of the circle. Calculation of using Monte Carlo Techniques Poor dart players simulate Monte Carlo techniques MC makes it easy as pi! # darts hitting shaded area / # darts hitting square = r 2 / r 2 = 4 [# darts hitting shaded area / # darts hitting square]...
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## This note was uploaded on 06/10/2011 for the course EMA 7414 taught by Professor Mecholsky during the Spring '11 term at University of Florida.

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Monte_Carlo_ppt - are relatively simple Step 1: Create a...

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