By H. John B. Birks, André F. Lotter, Steve Juggins, John P. Smol
Numerical and statistical equipment have quickly turn into a part of a palaeolimnologist’s tool-kit. they're used to discover and summarise complicated facts, reconstruct earlier environmental variables from fossil assemblages, and attempt competing hypotheses in regards to the factors of saw alterations in lake biota via historical past. This e-book brings jointly a big selection of numerical and statistical strategies at present on hand to be used in palaeolimnology and different branches of palaeoecology.
Visit http://extras.springer.com the Springer's Extras web site to view data-sets, figures, software program, and R scripts used or pointed out during this book.
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Extra resources for Tracking Environmental Change Using Lake Sediments: Data Handling and Numerical Techniques
14; Simpson 2012: Chap. 15) but is a categorical group variable (Næs et al. 2002). The overall aim is to assess whether or not a set of variables distinguish or discriminate between two (or more) a priori groups of objects. In the two-group case the most commonly used method is Fisher’s linear discriminant function (Davis 2002; Everitt 2005; Hammer and Harper 2006; Fielding 2007; Wehrens 2011) in which a linear combination or transformation (z) of the m variables (x) that gives the maximum separation between the two a priori groups is determined z D a1 x1 C a2 x2 C a3 x3 C C am xm The ratio of the between-group variance of z to the within-group variance is maximised.
Mixture discriminant analysis (Hastie and Tibshirani 1996) creates a classifier by fitting a Gaussian mixture model to each group. A penalised discriminant analysis (Hastie et al. 1995) attempts to overcome the problems of collinearity created when many variables are correlated by using a penalised regression. Robust quadratic discriminant analysis allows the boundaries between the groups to be curved quadratic surfaces in contrast to the flat boundaries in linear discriminant analysis (Fielding 2007).
The standard texts on EDA are Tukey (1977) and Velleman and Hoaglin (1981). There are several wide-ranging and thought-provoking reviews and texts on graphical data display in EDA, including Chambers et al. (1983), Tufte (1983, 1990), Cleveland (1993, 1994), Jacoby (1997, 1998), and Gelman et al. (2002). Zuur et al. (2010) provide a valuable protocol for data exploration that avoids many common statistical problems, in particular avoiding Type I (the null hypothesis is erroneously rejected, representing a false positive) and Type II (the null hypothesis is erroneously accepted, representing a false negative) errors, thereby reducing the chance of making wrong conclusions.
Tracking Environmental Change Using Lake Sediments: Data Handling and Numerical Techniques by H. John B. Birks, André F. Lotter, Steve Juggins, John P. Smol