By Michael Small
Nonlinear time sequence equipment have built quickly over 1 / 4 of a century and feature reached a complicated country of adulthood over the last decade. Implementations of those equipment for experimental information at the moment are commonly accredited and reasonably regimen; despite the fact that, surely necessary functions stay infrequent. This booklet specializes in the perform of making use of those the right way to clear up actual difficulties. to demonstrate the usefulness of those tools, a large choice of actual and physiological structures are thought of. The technical instruments used in this ebook fall into 3 distinctive, yet interconnected parts: quantitative measures of nonlinear dynamics, Monte-Carlo statistical speculation trying out, and nonlinear modeling. Ten hugely designated functions function case reviews of fruitful purposes and illustrate the mathematical ideas defined within the textual content.
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Extra resources for Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance
Notation To emphasize the dependence of a MTP on parameters deﬁning the Type I error rate mapping Θ, we may adopt a longer notation, whereby sets of null hypotheses and their cardinality are indexed by these parameters as well as by the nominal Type I error level α. For instance, for a gFWER-controlling MTP with k allowed false positives, we may use Rn (k; α) and Rn (k; α) = |Rn (k; α)|, for the set of rejected hypotheses and its cardinality, respectively, and Vn (k; α) = |Rn (k; α) ∩ H0 |, for the number of Type I errors.
8 Errors in multiple hypothesis testing: Type I, Type II, and Type III errors In any testing problem, two types of errors can be committed. A Type I error, or false positive, is committed by rejecting a true null hypothesis (Rn ∩ H0 ). A Type II error, or false negative, is committed by failing to reject a false null hypothesis (Rcn ∩ H1 ). 16) m∈H1 = Rn − Vn = h1 − Un . Note that Sn , Un , Vn , and Wn each depend on the unknown data generating distribution P through the unknown set of true null hypotheses H0 = H0 (P ).
6 Apo AI dataset: FWER-controlling permutation-based MTPs. 7 Apo AI dataset: FWER-controlling non-parametric bootstrap-based vs. permutation-based step-down maxT MTPs. 8 Apo AI dataset: Unadjusted and step-down maxT adjusted p-values for three test statistics null distributions. . . . . . . 9 Apo AI dataset: Gene descriptions from Entrez Gene database. 10 Cancer miRNA dataset, diﬀerential expression: Tests for logistic regression coeﬃcients. . . . .