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Computational Methods for Physicists pp 207–275Cite as

Statistical Analysis and Modeling of Data

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Part of the book series: Graduate Texts in Physics ((GTP))

Abstract

Outcomes of physical measurements are most frequently recorded as signals that need to be processed statistically in order to infer their overall properties and features, and later compared to theoretical or phenomenological models. This chapter starts with an introduction to the basic statistical techniques of computing the averages and moments of distributions and their uncertainties. Particular emphasis is given on ways of identifying outliers and robust estimates of location (averages) and scale (dispersion). We introduce commonly used methods of computing confidence intervals for the sample means and variances, of comparing the means of samples with equal or different variances, of comparing two distributions, and computing correlations. Simple linear and multiple linear, as well as non-linear regression techniques are explained, again with attention to robust measures. Powerful multi-variate methods of principal component analysis, cluster analysis, linear discriminant analysis, and factor analysis are discussed in a separate section each. The illustrations in the Problems include the study of Raman spectra in fabric yarns, the analysis of geyser eruptions, radar reflections in the ionosphere, and the correlation analysis of astrophysical objects.

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  1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Simon Širca & Martin Horvat

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  1. Simon Širca
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  2. Martin Horvat
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Širca, S., Horvat, M. (2012). Statistical Analysis and Modeling of Data. In: Computational Methods for Physicists. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32478-9_5

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