40 lines
2.0 KiB
Mathematica
40 lines
2.0 KiB
Mathematica
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function [LoadingRate, StandardError, ConfidenceInterval] = bootstrapErrorEstimation(this, NumberOfLoadedAtoms)
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n = this.NumberOfAtoms;
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NumberOfTimeSteps = int64(this.SimulationTime/this.TimeStep);
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Autocorrelation = autocorr(NumberOfLoadedAtoms,'NumLags', double(NumberOfTimeSteps - 1));
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if Autocorrelation(1)~=0
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CorrelationFactor = table(Helper.findAllZeroCrossings(linspace(1, double(NumberOfTimeSteps), double(NumberOfTimeSteps)), Autocorrelation)).Var1(1);
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if ~isnan(CorrelationFactor)
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SampleLength = floor(CorrelationFactor);
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NumberOfBootsrapSamples = 1000;
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MeanLoadingRatioInEachSample = zeros(1,NumberOfBootsrapSamples);
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for SampleNumber = 1:NumberOfBootsrapSamples
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BoostrapSample = datasample(NumberOfLoadedAtoms, SampleLength); % Sample with replacement
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MeanLoadingRatioInEachSample(SampleNumber) = mean(BoostrapSample) / n; % Empirical bootstrap distribution of sample means
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end
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LoadingRate = mean(MeanLoadingRatioInEachSample) * this.ReducedFlux;
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Variance = 0; % Bootstrap Estimate of Variance
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for SampleNumber = 1:NumberOfBootsrapSamples
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Variance = Variance + (MeanLoadingRatioInEachSample(SampleNumber) - mean(MeanLoadingRatioInEachSample))^2;
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end
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StandardError = sqrt((1 / (NumberOfBootsrapSamples-1)) * Variance) * this.ReducedFlux;
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ts = tinv([0.025 0.975],NumberOfBootsrapSamples-1); % T-Score
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ConfidenceInterval = LoadingRate + ts*StandardError; % 95% Confidence Intervals
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else
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LoadingRate = nan;
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StandardError = nan;
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ConfidenceInterval = [nan nan];
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end
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else
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LoadingRate = nan;
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StandardError = nan;
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ConfidenceInterval = [nan nan];
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end
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end
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