## The module "mbootstrap_idx" of the Mastrave modelling library

**Daniele de Rigo**

#### Copyright and license notice of the function mbootstrap_idx

Copyright © 2009,2010,2011,2012,2013,2014,2015 Daniele de Rigo

The file mbootstrap_idx.m is part of Mastrave.

Mastrave is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

Mastrave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Mastrave. If not, see http://www.gnu.org/licenses/.

#### Function declaration

[resampled_vals,resampled_pos,category_glossary] = mbootstrap_idx(values,n_runs,weights= [] ,categories= [] ,rand_func= [] )

#### Description

Module to compute a bootstrap statistical resampling over an array of
` values `. Pseudo-random sampling with replacement is applied to the
position of each element in

`. The statistical resampling generates`

**values**`vectors of bootstrapped positions, returned as the columns of the matrix`

**n_runs**`. Each column has the same number of lines as the ones of the original`

**resampled_pos**`. The corresponding matrix of bootstrapped values is returned in`

**values**`. Within each bootstrapped column, the sampling with replacement implies that a given element may be missing while another one may be resampled multiple times. For equally weighted elements, each bootstrapping run contains on average about 63.2 % of distinct elements sampled from`

**resampled_vals**`.`

**values**To each element of ` values `, an optional weight may be associated so as
to alter the frequency with which that particular element is resampled.
For this purpose, an array

`may be passed as optional input argument. Higher weights increase the frequency of resampling of the corresponding elements in`

**weights**`.`

**values**An optional array of ` categories ` may be passed to identify a partition
of

`in subsets. Each bootstrap run preserves the number of elements resampled from each category. The array`

**values**`is returned with the unique categories.`

**category_glossary**Finally, the handle to a custom function ` rand_func ` may be passed so
as for the pseudo-random sampling to be generated with it.

#### Input arguments

valuesArray of elements to be boostrapped.::numeric,col_vector::n_runsNumber of bootstrap runs.::scalar_index::weightsArray of custom weights associated to the elements of::nonnegative,col_vector::. Ifvaluesis an empty matrix [], the same weight is associated to each element ofweights. If omitted, the default value is an empty matrix: [].valuescategoriesArray of custom categories associated to the elements of::integer,col_vector::. Ifvaluesis an empty matrix [], the same category is associated to each element ofcategories. If omitted, the default value is an empty matrix: [].valuesrand_funcHandle to a custom function which generates the pseudo-random resampling. If::function_handle::is an empty matrix [], the function @rand is used. If omitted, the default value is an empty matrix: [].rand_func

#### Example of usage

```
n_vals = 8
categories = ceil( rand( n_vals, 1 )*3 )*10;
values = categories * 100 + [1:n_vals].';
weights = [1:n_vals].';
disp( 'values weights categories' )
disp( [values weights categories] )
[ res_vals, res_pos, category_glossary ] = ...
mbootstrap_idx( values, 5, weights, categories );
res_vals
values( res_pos )
assert( isequal( res_vals , values( res_pos ) ) )
```

See also: rand_idx Keywords: statistical_resamling Version: 0.3.8

#### Support

The Mastrave modelling library is committed to provide reusable and general - but also robust and scalable - modules for research modellers dealing with computational science. You can help the Mastrave project by providing feedbacks on unexpected behaviours of this module. Despite all efforts, all of us - either developers or users - (should) know that errors are unavoidable. However, the free software paradigm successfully highlights that scientific knowledge freedom also implies an impressive opportunity for collectively evolve the tools and ideas upon which our daily work is based. Reporting a problem that you found using Mastrave may help the developer team to find a possible bug. Please, be aware that Mastrave is entirely based on voluntary efforts: in order for your help to be as effective as possible, please read carefully the section on reporting problems. Thank you for your collaboration.