MONTE_CARLO_SAMPLING.TEX
Monte Carlo Sampling

MONTE_CARLO_SAMPLING.TEX is the LaTeX source for a classroom presentation on sampling via the Monte Carlo Method, given 02-04-06 November 2009.

A PDF version is available as ../../presentations/monte_carlo_sampling.pdf.

The following files constitute the LaTeX file:

• alpine.png, a PNG image of a function that is highly varying.
• cdf_root.png, a PNG image illustrating the task of finding an X value for which CDF(X) = P.
• circle_sample_nonuniform.png, a PNG image of a sampling of the circle that is nonuniform.
• circle_sample_rejection.png, a PNG image of a uniform sampling of the circle by the rejection method.
• day13.png, a PNG image illustrating day 13 of a disease epidemic model.
• error_decrease.png, a PNG image of the decrease in error for a Monte Carlo estimate.
• exp_icdf.png, a PNG image of the inverse CDF for the exponential distribution.
• exp_pdf.png, a PNG image of the PDF for the exponential distribution.
• exp_seq_100000.png, a PNG image of the distribution of 100,000 samples from the exponential distribution.
• f2d_plot.png, a PNG image of a function F(X,Y).
• fcircle_plot.png, a PNG image of a function F(X,Y).
• integral_rectangles.png, a PNG image illustrating the approximation of an integral.
• lcg_image.png, a PNG image of the mapping induced from [0,30] to [0,30] by a simple linear congruential random number generator.
• monte_carlo_sampling.tex, the main LaTeX file.
• myf.m, a MATLAB function that evaluates a function f(x) that is difficult to optimize.
• myf.png, a PNG image of the optimization function.
• myf_50_tries.png, a PNG image of the results of 50 randomized optimizations.
• myfmin.m, a MATLAB program which carries out 50 randomized optimizations.
• normal_approx_100000.png, a PNG image of a histogram of 100,000 points from an approximation to the normal PDF.
• normal_icdf.png, a PNG image of the inverse CDF for the normal distribution.
• normal_pdf.png, a PNG image of the PDF for the normal distribution.
• p21_plot.png, a PNG image of a function P21(X).
• p21_plot_error.png, a PNG image of the error for function P21.
• p77_plot.png, a PNG image of a function P77(X).
• p77_plot_error.png, a PNG image of the error for function P77.
• protein_minima.png, a PNG image of a minimization surface for protein folding.
• sphere_sample.png, a PNG image of a uniform sampling of the surface of the sphere.
• square_sample.png, a PNG image of a uniform sampling of the unit square.
• traffic.png, a PNG image of traffic.
• uniform_icdf.png, a PNG image of the inverse CDF for the uniform distribution.
• vt_logo.pdf, a PDF file of a logo.
• walks_1_steps_10000_plot.png, a PNG image of a single random walk in 2D using 10,000 steps.

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