Block-bootstrapping for noisy data.
BACKGROUND
Statistical inference of signals is key to understand fundamental processes in the neurosciences. It is essential to distinguish true from random effects. To this end, statistical concepts of confidence intervals, significance levels and hypothesis tests are employed. Bootstrap-based approaches complement the analytical approaches, replacing the latter whenever these are not possible.


METHODS
Block-bootstrap was introduced as an adaption of the ordinary bootstrap for serially correlated data. For block-bootstrap, the signals are cut into independent blocks, yielding independent samples. The key parameter for block-bootstrapping is the block length. In the presence of noise, naïve approaches to block-bootstrapping fail. Here, we present an approach based on block-bootstrapping which can cope even with high noise levels. This method naturally leads to an algorithm of block-bootstrapping that is immediately applicable to observed signals.


RESULTS
While naïve block-bootstrapping easily results in a misestimation of the block length, and therefore in an over-estimation of the confidence bounds by 50%, our new approach provides an optimal determination of these, still keeping the coverage correct.


METHODS
In several applications bootstrapping replaces analytical statistics. Block-bootstrapping is applied to serially correlated signals. Noise, ubiquitous in the neurosciences, is typically neglected. Our new approach not only explicitly includes the presence of (observational) noise in the statistics but also outperforms conventional methods and reduces the number of false-positive conclusions.


CONCLUSIONS
The presence of noise has impacts on statistical inference. Our ready-to-apply method enables a rigorous statistical assessment based on block-bootstrapping for noisy serially correlated data.
Department of Neuropediatrics and Muscular Disease, University Medical Center of Freiburg, Mathildenstrasse 1, 79106 Freiburg, Germany; Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany; Institute for Physics, University of Freiburg, Hermann-Herder-Strasse 3a, 79104 Freiburg, Germany. Electronic address: Malenka.Mader@fdm.uni-freiburg.de.
Malenka
M
Mader
Wolfgang
W
Mader
Linda
L
Sommerlade
Jens
J
Timmer
Björn
B
Schelter
D000465:Algorithms; D016477:Artifacts; D004576:Electromyography; D006801:Humans; D015233:Models, Statistical
Autocorrelation; Dependent data; Distribution estimation; Measurement noise; Statistics; Tremor