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Overlapping Processes Estimation in Noise-Free and Noisy Data Environments

This study explores the estimation of overlapping processes using Ordinary Least Squares (OLS) under various conditions, including scenarios with zero noise and increasing noise levels in data. The convergence of estimates is examined visually, revealing challenges in verifying convergence as trial numbers increase, especially under noisy conditions. The paper presents comparative analyses of estimates derived from 5 and 10 trials, highlighting performance in noise-free environments and under noise levels of 0.2, demonstrating how start times influence model accuracy.

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Overlapping Processes Estimation in Noise-Free and Noisy Data Environments

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  1. LS experiments—2 overlapping processes, 7/11/2004 • In noise-free case, perfect estimates for both processes. • Visually, it is hard to verify convergence when the number of trials increases in the presence of noise in the data.

  2. OLS learns 2 processes, overlapping in time, 1 voxel, zero noise, start times known, 5 trials Estimates: -0 0.25 0.5 0.75 1 0.75 0.5 0.25 4.9651e-17 9.3095e-17 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

  3. OLS learns 2 processes, overlapping in time, 1 voxel, zero noise, start times known, 10 trials Estimates: -0 0.25 0.5 0.75 1 0.75 0.5 0.25 3.5108e-17 -4.7535e-17 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

  4. OLS learns 2 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 5 trials Estimates: 0.094915 0.26407 0.42792 0.7071 1.0337 0.81342 0.59745 0.42883 -0.048884 -0.17886 0.73122 0.22735 0.56561 0.52506 0.53043 0.43789 0.59811 0.51577

  5. OLS learns 2 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 10 trials Estimates: 0.0054956 0.32446 0.48847 0.83317 0.99872 0.86555 0.55624 0.23633 -0.050592 -0.017376 0.36435 0.36134 0.4856 0.60143 0.46168 0.54137 0.47466 0.52419

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