rejection_sample, a MATLAB code which demonstrates acceptance/rejection sampling.
We suppose that for A <= X <= B, we are given a probability density function PDF(X), and wish to randomly sample X. If it is not feasible to compute the cumulative density function CDF(X) and invert it to X(CDF), then acceptance/rejection sampling can provide an alternate way of carrying out the sampling.
Briefly, a comparison curve Z(X) must be determined, such that PDF(X) <= Z(X) for all A <= X <= B, and with the property that data can be uniformly sampled under the Z curve.
If that is the case, then we uniformly sample an X value under the Z curve. Then we pick an R value uniformly between 0 and Z(X). We accept X if R <= PDF(X); otherwise, we reject this X and prepare to generate and test another value.
rejection_sample is available in a Matlab version.
histogram_data_2d_sample, a MATLAB code which demonstrates how to construct a Probability Density Function (PDF) from a frequency table over a 2D domain, and then to use that PDF to create new samples.
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