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.

New method: 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, naive 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 naive 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.

Comparison with existing 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.