Major change how the loading rate is calculated from the raw output of the simulator - Zero crossing of the autocorrelation of the time series - which is the number of loaded atoms at each time step - is used to determine the length of each of a 1000 bootstrap samples obtained by sampling with replacement. Mean in each sample is calculated and a sampling distribution of means obtained. The capture ratio is the mean of this distribution which when multiplied by the "reduced" flux gives the loading rate. Standard Error and 95% confidence interval are also calculated from the sampling distribution.

MOT Capture Process Simulation/@MOTSimulator/bootstrapErrorEstimation.m

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