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Statistics::Sampler::Multinomial - Generate multinomial samples using Vose's alias method
use Statistics::Sampler::Multinomial::AliasMethod; my $object = Statistics::Sampler::Multinomial::AliasMethod->new( data => [0.1, 0.3, 0.2, 0.4], ); $object->draw; # returns a number between 0..3 my $samples = $object->draw_n_samples(5) # returns an array ref that might look something like # [3,3,0,2,0] # to specify your own PRNG object, in this case the Mersenne Twister my $mrma = Math::Random::MT::Auto->new; my $object = Statistics::Sampler::Multinomial::AliasMethod->new( data => [1,2,4,6,200], prng => $mrma, );
Implements multinomial sampling using Vose's version of the alias method.
The setup time for the alias method is longer than for other methods, and the memory requirements are larger since it maintains two lists in memory, but this is amortised when when generating repeated samples because only two random numbers are needed for each draw, as compared to up to O(log n) for other methods. This should have a pay off when, for example calculating bootstrap confidence intervals for a set of classes, but benchmarking shows this implementation to not be faster than the GSL approach. Profiling suggests the method calls to rand() are the main bottleneck.
For more details and background, see http://www.keithschwarz.com/darts-dice-coins.
- my $object = Statistics::Sampler::Multinomial->new(data => [1,2,3,4,100])
- my $object = Statistics::Sampler::Multinomial->new(data => [0.1, 0.4, 0.5], data_sum_to_one => 1)
- my $object = Statistics::Sampler::Multinomial->new (data => [1,2,3,4,5,100], prng => $prng)
Creates a new object, optionally passing a PRNG object to be used. If no PRNG object is passed then it defaults to an internal object that uses the perl PRNG stream.
Passing your own PRNG mean you have control over the random number stream used, and can use it as part of a separate analysis. The only requirement of such an object is that it has a rand() method that returns a value in the interval [0,1) (the same as Perl's rand() builtin).
By default it will standardise the data to sum to one but callers can skip this step by promising that the data already sum to one (thus speeding up the code). No checks of the validity of such promises are made, so expect failures for lying.
Draw one sample from the distribution. Returns the chosen class number.
- $object->draw_n_samples ($n)
Returns an array ref of $n samples across the K classes, where K is the length of the data array passed in to the call to new. e.g. for $n=3 and the K=5 example from above, one could get (0,1,2,0,0).
Returns the number of classes in the sample, or zero if initialise has not yet been run.
Note that the results will differ between standard double and long double builds of Perl.
Math::Random::MT::Auto (a useful PRNG package) also gives different results between x32 and x64 architectures.
Please report any bugs or feature requests to https://github.com/shawnlaffan/perl-statistics-sampler-multinomial/issues.
Much of the code has been adapted from a python implementation at https://hips.seas.harvard.edu/blog/2013/03/03/the-alias-method-efficient-sampling-with-many-discrete-outcomes.
Statistics::Sampler::Multinomial is the parent class of this one, and uses the algorithm implemented in the GSL.
The Math::Random and Math::GSL::Randist packages also have multinomial samplers but do not use the alias method, and you cannot supply your own PRNG. They are also substantially faster so if you care not about the method or PRNG stream then perhaps you should use them...
Copyright (c) 2016, Shawn Laffan
<firstname.lastname@example.org>. All rights reserved.
This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
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