/ 
Statistics-Sampler-Multinomial-1.02
River stage one • 1 direct dependent • 2 total dependents
/ Statistics::Sampler::Multinomial::AliasMethod

NAME

Statistics::Sampler::Multinomial - Generate multinomial samples using Vose's alias method

SYNOPSIS

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,
);

DESCRIPTION

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.

METHODS

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.

$object->draw

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).

$object->get_class_count

Returns the number of classes in the sample, or zero if initialise has not yet been run.

BUGS AND LIMITATIONS

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.

SEE ALSO

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...

AUTHOR

Shawn Laffan <shawnlaffan@gmail.com>

LICENCE AND COPYRIGHT

Copyright (c) 2016, Shawn Laffan <shawnlaffan@gmail.com>. All rights reserved.

This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

DISCLAIMER OF WARRANTY

BECAUSE THIS SOFTWARE IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE SOFTWARE, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE SOFTWARE "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR, OR CORRECTION.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE SOFTWARE AS PERMITTED BY THE ABOVE LICENCE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE SOFTWARE TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.