how do i use the bootstrap method with a custom fit function?

i am trying to globally fit 17 double Gaussian derivative functions and then use the bootstrap method to analyze the error in the parameter fits. looking at the examples for [bootstat,bootsam] = bootstrp(...), i can't figure out how to implement my function for the @corr that works for the example given online.

the function i'm using is somewhat complicated: y0+A*((f/g)-B)*(exp(-((B-f/g)^2)/(2*(Bhyp^2+(S^2)*(f/g)^2))))/(Bhyp^2+(S^2)*(f/g)^2)+A*((f/g)-B)*(exp(-((B-f/g)^2)/(2*(Bhyp1^2+(S1^2)*(f/g)^2))))/(Bhyp1^2+(S1^2)*(f/g)^2)

but i should be able to label it as something and use it in the bootstrap function correct?

Answer 1

[Aditya]

Hi Chad,

Yes, you can use your custom function within the bootstrp function by defining it as a function handle. The bootstrp function allows you to resample your data and apply a specified function to each bootstrap sample. Here's a step-by-step guide on how you can implement this for your double Gaussian derivative function:

• Define your custom data
• Prepare your data
• Set up your bootstrapping

Here is a sample code for the same:

% Example data (replace with your actual data)
data = randn(100, 17); % 100 samples of 17 functions

% Define your double Gaussian derivative function
doubleGaussDeriv = @(params, f, g) params(1) + ...
    params(2) * ((f ./ g) - params(3)) .* ...
    (exp(-(((params(3) - (f ./ g)).^2) ./ ...
    (2 * (params(4)^2 + (params(5)^2) * (f ./ g).^2)))) ./ ...
    (params(4)^2 + (params(5)^2) * (f ./ g).^2)) + ...
    params(6) * ((f ./ g) - params(7)) .* ...
    (exp(-(((params(7) - (f ./ g)).^2) ./ ...
    (2 * (params(8)^2 + (params(9)^2) * (f ./ g).^2)))) ./ ...
    (params(8)^2 + (params(9)^2) * (f ./ g).^2));

% Define a function to fit the model to data
fitModel = @(data) ...
    % Here you would include the fitting routine, such as using lsqcurvefit
    % or another fitting function to optimize the parameters for your model
    % For example:
    % params = [initial guesses for parameters];
    % options = optimset('Display','off');
    % fittedParams = lsqcurvefit(@(p, f) doubleGaussDeriv(p, f, g), params, f, data, [], [], options);
    % Return the fitted parameters
    % fittedParams;

% Number of bootstrap samples
nBootstraps = 1000;

% Apply bootstrap
[bootstat, bootsam] = bootstrp(nBootstraps, fitModel, data);

% Analyze the bootstrap results
% For example, compute the mean and standard deviation of the bootstrap estimates
meanParams = mean(bootstat);
stdParams = std(bootstat);

fprintf('Bootstrap mean of parameters:\n');
disp(meanParams);
fprintf('Bootstrap standard deviation of parameters:\n');
disp(stdParams);