bootan

Bootstrap analysis for uncertainty estimation

Syntax

[bootci,stats] = bootan(fcn,V,Vfit)
[bootci,stats] = bootan(fcn,V,Vfit,Nsamples)
[bootci,stats] = bootan(___,'Property',Value)
Parameters
  • fcn - Function to analyze (function handle)
  • V - Experimental signal (N-element array)
  • Vfit - Fitted signal (N-element array)
  • Nsamples - Number of bootstrap samples (scalar)
Returns

  • bootci - Bootstrapped confidence intervals (struct)

    • .ci50 - 50%-confidence intervals of the output variables
    • .ci95 - 95%-confidence intervals of the output variables
    • .ci99 - 99%-confidence intervals of the output variables

  • stats - Summary statistics (struct)

    • .median - Median of output the variables
    • .mean - Mean of the output variables
    • .std - Standard deviation of the output variables
    • .p1 - 1st percentile of the output variables
    • .p25 - 25th percentile of the output variables
    • .p75 - 75th percentile of the output variables
    • .p99 - 99th percentile of the output variables
    • .boothist - Bootstrap histogram of the output variables
      • .edges - Histogram edges
      • .bins - Histogram bins
    • .bootdist - Bootstrap KDE distribution of the output variables
      • .values - Evaluated values
      • .pdf - Estimated probability density function

Description

[bootci,stats] = bootan(fcn,V,Vfit)

Performs a uncertainty analysis of the output variables of the function fcn from 1000 bootstrap samples. The output argument of fcn is evaluated for all level-combinations of the factors. The function to be analyzed must be a function handle accepting the V experimental signal as input. Example:

[bootci,stats] = bootan(@(V)myfcn(p,varargin),V,Vfit)

function [Pfit1,Pfit2] = myfcn(V,varargin)
   Pfit1 = fitparamodel(V,@dd_gauss,r,K)
   Pfit2 = fitparamodel(V,@dd_randcoil,r,K)
end

From the evaluation of all level-combinations an ensemble of outputs is obtained on which statistical estimators are used. The 99%, 95% and 50% confidence intervals of all output variables are returned in a structure bootci. The summary of these statistics is returned in the stats structure. This summary contains the mean, median, standard deviation, 99t, 75th, 25th and 1st percentile values for all outputs.

For non-vectorial variables (e.g. non-parametric distributions, background functions,etc.) the stats structure will contain an histogram of the distribution of values for the different outputs as well as a corresponding probability density function obtained from a kernel densitiy estimation of the histogram data.

stats = bootan(fcn,V,Vfit,Nsamples)

The number of bootstrap samples can be specified in Nsamples. The quality of bootstrapping results improve with the number of boostrap samples evaluated.

stats = bootan(fcn,{V1,V2,___},{Vfit1,Vfit2,___},Nsamples)

If the evaluated function fcn requries multiple signals {V1,V2,___} as input, these can be specified aloong the same number of fitted signals {Vfit1,Vfit2,___}.

Additional Settings

Additional settings can be specified via name-value pairs. All property names are case insensitive and the property-value pairs can be passed in any order after the required input arguments have been passed.

stats = bootan(___,'Property1',Value1,'Property2',Value2,___)
  • 'Verbose' - Display progress information

    Specifies whether to print the progress of the bootstrap analysis on the command window.

    Default: false

    Example:

    stats = bootan(___,'Verbose',true)
  • 'Resampling' - Re-sampling method

    Specifies the method employed for re-sampling new bootstrap samples.

    • 'gaussian' - Sample noise from a Gaussian distribution
    • 'residual' - Sample noise from the fit residuals

    Default: gaussian

    Example:

    stats = bootan(___,'Resampling',residual)