Abstract
In this chapter we introduce regression models, i.e., how to fit (regress) one, or more quantities, against each other through a functional relationship and estimate any unknown parameters that dictate this relationship. Questions of interest include: how to deal with samples affected by selection effects? How does a rich data structure influence the fitted parameters? And what about non-linear multiple-predictor fits, upper/lower limits, measurement errors of different amplitudes and an intrinsic variety in the studied populations, or an extra source of variability? A number of examples illustrate how to answer these questions and how to predict the value of an unavailable quantity by exploiting the existence of a trend with another, available, quantity.
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Notes
- 1.
Part of the material of this section has been drawn from Andreon and Hurn (2013).
- 2.
This example draws material from (the end-course assessment relation of) Andrea Benaglia.
- 3.
The table is given in electronic format at the link http://www.brera.mi.astro.it/~andreon/BayesianMethodsForThePhysicalSciences/Raichoor_Andreon12.dat.
- 4.
This section draws material from Andreon and Bergé (2012).
- 5.
There is only a 10 % probability that in a 5-parameter fit, all fitted values are found within 1 σ from the input values and 50 % that they are all within 1.5 σ.
- 6.
Part of the material of this section has been drawn from Andreon and Hurn (2010).
- 7.
This section has been drawn from Andreon (2012b).
- 8.
The table is given in electronic format at the link http://www.brera.mi.astro.it/~andreon/BayesianMethodsForThePhysicalSciences/SNdata.dat.
- 9.
The material of this section has been drawn from Andreon (2012a).
- 10.
The table in electronic format is available at the link http://www.brera.mi.astro.it/~andreon/BayesianMethodsForThePhysicalSciences/Andreon12_abundance.dat.
- 11.
The table is given in electronic format at the link http://www.brera.mi.astro.it/~andreon/BayesianMethodsForThePhysicalSciences/fstar.dat.
- 12.
The table is given in electronic format at the link http://www.brera.mi.astro.it/~andreon/BayesianMethodsForThePhysicalSciences/Coma_earlytype.dat.R.
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Andreon, S., Weaver, B. (2015). Fitting Regression Models. In: Bayesian Methods for the Physical Sciences. Springer Series in Astrostatistics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-15287-5_8
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DOI: https://doi.org/10.1007/978-3-319-15287-5_8
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