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.
J Neurosci Methods. 2013 Oct 15;219(2):285-91. doi: 10.1016/j.jneumeth.2013.07.022. Epub 2013 Aug 8.
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.
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.
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.
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.
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.
信号的统计推断是理解神经科学基本过程的关键。区分真实效应和随机效应至关重要。为此，采用了置信区间、显著性水平和假设检验等统计概念。基于引导的方法补充了分析方法，在无法使用后者时，取而代之。
块引导被引入作为对序列相关数据的普通引导的改编。对于块引导，信号被切成独立的块，产生独立的样本。块引导的关键参数是块长度。在存在噪声的情况下，对块引导的天真方法会失败。在这里，我们提出了一种基于块引导的方法，即使在高噪声水平下也能应对。这种方法自然会产生一种块引导的算法，该算法可以立即应用于观察到的信号。
虽然天真的块引导很容易导致块长度的错误估计，从而导致置信区间的高估 50%，但我们的新方法可以最佳地确定这些置信区间，同时仍然保持覆盖率的正确性。
在许多应用中，引导代替了分析统计。块引导应用于序列相关信号。噪声在神经科学中普遍存在，但通常被忽略。我们的新方法不仅在统计中明确包含（观测）噪声的存在，而且优于传统方法，减少了错误的阳性结论的数量。
噪声的存在对统计推断有影响。我们的即用型方法为噪声序列相关数据提供了基于块引导的严格统计评估。
