WALKER_SAMPLE
Efficient Probability Vector Sampling

WALKER_SAMPLE is a C++ library which efficiently samples a discrete probability vector.

For outcomes labeled 1, 2, 3, ..., N, a discrete probability vector X is an array of N non-negative values which sum to 1, such that X[i] is the probability of outcome i.

To sample the probability vector is to produce a sequence of outcomes i1, i2, i3, ..., which are each drawn with probability corresponding to X. For a general discrete probability vector X, a single sample operation might be expected to take a time that is proportional to O(N), the number of outcomes. Walker showed that, by constructing a new data structure, it was possible to carry out a sample in time of order O(1), that is, independent of the number of possible outcomes.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

WALKER_SAMPLE is available in a C version and a C++ version and a FORTRAN90 version and a Matlab version and a Python version.

Related Data and Programs:

HISTOGRAM_DATA_2D_SAMPLE, a C++ program 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.

PDFLIB, a C++ library which evaluates Probability Density Functions (PDF's) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.

PROB, a C++ library which evaluates, samples, inverts, and characterizes a number of Probability Density Functions (PDF's) and Cumulative Density Functions (CDF's), including anglit, arcsin, benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford, burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged, dipole, dirichlet mixture, discrete, empirical, english sentence and word length, error, exponential, extreme values, f, fisk, folded normal, frechet, gamma, generalized logistic, geometric, gompertz, gumbel, half normal, hypergeometric, inverse gaussian, laplace, levy, logistic, log normal, log series, log uniform, lorentz, maxwell, multinomial, nakagami, negative binomial, normal, pareto, planck, poisson, power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular, student t, triangle, uniform, von mises, weibull, zipf.

RANLIB, a C++ library which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.

Reference:

1. Donald Knuth,
   Seminumerical algorithms,
   Addison-Wesley-Longman, 1999.
2. Warren Smith,
   How to sample from a probability distribution,
   April 18, 2002.
3. Alastair Walker,
   An efficient method for generating discrete random variables with general distributions,
   ACM Transactions on Mathematical Software,
   Volume 3, Number 3, September 1977, pages 253-256.

Source Code:

• walker_sample.cpp, the source code;
• walker_sample.hpp, the include file;

Examples and Tests:

• walker_sample_test.cpp, the calling program;
• walker_sample_test.txt, the output file.

List of Routines:

• NORMALIZE scales a vector X so its entries sum to 1.
• RANDOM_PERMUTATION applies a random permutation to an array.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WALKER_BUILD sets up the data for a Walker sampler.
• WALKER_SAMPLE returns a random sample i=1..N with prob X[i].
• WALKER_TEST01 tests the Walker sampler with a Zipf-type probability vector.
• WALKER_VERIFY verifies a Walker Sampler structure.
• ZIPF_PROBABILITY sets up a Zipf probability vector.

You can go up one level to the C++ source codes.