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Appendix A Background Information on Statistical Techniques
Pages 170-175

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From page 170...
... The following sections provide some background material on several statistical techniques that are frequently mentioned in the report. First, a table listing 11 commonly used statistical techniques is provided, listing some of the advantages and disadvantages in their application to model validation efforts and forecasting.
From page 171...
... Traditional multiple linear regression makes Regression Well understood in basic numerous assumptions that are rarely met in climate form. Many variations exist analyses.
From page 172...
... However, such a relationship assumes both fields are bivariate normally distributed, which is rarely the case, and that there is a linear mapping between the fields, as both correlation and covariance measure the linear portion of the relationship between fields. Relationships that are nonlinear cannot be measured by these metrics, nor does a value of zero indicate statistical independence, despite such a statement in numerous research papers.
From page 173...
... While that is not always possible, the low dimensional representation of a problem often leads to useful results. Assuming that the correlation or covariance matrix is positive semidefinite in the real domain, the eigenvalue of that matrix can be ordered in descending value to establish the relative importance of the associated eigenvectors.
From page 174...
... The kernel projects the data into three-space and a linear separation is possible. Kernel techniques have a high potential for mode identification where linear low level modes provide ambiguous separability (e.g., the Arctic Oscillation versus the North Atlantic Oscillation)
From page 175...
... Appendix A 175 FIGURE A.1 A kernel map, φ , converts a nonlinear problem into a linear problem in the feature space. "+" belongs to positive class and "o" belongs to negative class.

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