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Recipes for a Good Statistical Analysis Read chapter Read first chapter

2015 | OriginalPaper | Chapter

2. A Bit of Theory

Authors : Stefano Andreon, Brian Weaver

Published in: Bayesian Methods for the Physical Sciences

Publisher: Springer International Publishing

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Abstract

This short chapter introduces the basics of probability theory in an intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods.

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previous chapter Recipes for a Good Statistical Analysis
next chapter A Bit of Numerical Computation
Footnotes
1
The notation p(y | x) reads “probability of y given x.” See Appendix B.2 for the mathematical definition of conditional probability.
 
2
Some of the material of this section has been drawn from Andreon and Hurn (2010).
 
3
While the example is real, we have idealized it in several aspects.
 
4
This is one of the very few analytic computation of this book. Later on, a computer will be charged with the burden of performing the computations. Why else call it computer?
 
5
This section can be skipped the first time through.
 
Literature
S. Andreon and M.A. Hurn. The scaling relation between richness and mass of galaxy clusters: a Bayesian approach. Monthly Notices of the Royal Astronomical Society, 404(4):1922–1937, 2010.
S. Andreon, B. Maughan, G. Trinchieri, and J. Kurk. JKCS 041: a colour-detected galaxy cluster at z phot  ∼ 1. 9 with deep potential well as confirmed by X-ray data. Astronomy & Astrophysics, 507:147–157, 2009.
K.B. Athreya and S.N. Lahiri. Measure theory and probability theory. Springer-Verlag New York Inc, 2006.
Y. Avni. Energy spectra of X-ray clusters of galaxies. The Astrophysical Journal, 210:642–646, 1976.CrossRef
G. Casella and R.L. Berger. Statistical Inference. Duxbury Press, 2001.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. Numerical Recipes. Cambridge University Press, Cambridge, third edition, 2007.MATH
Metadata
Title
A Bit of Theory
Authors
Stefano Andreon
Brian Weaver
Copyright Year
2015
Book
Bayesian Methods for the Physical Sciences

Print ISBN: 978-3-319-15286-8

Electronic ISBN: 978-3-319-15287-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-15287-5_2

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