A geometric approach to non-linear correlations with intrinsic scatter

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http://hdl.handle.net/10138/228246

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Pihajoki , P 2017 , ' A geometric approach to non-linear correlations with intrinsic scatter ' , Monthly Notices of the Royal Astronomical Society , vol. 472 , no. 3 , pp. 3407-3424 . https://doi.org/10.1093/mnras/stx2179

Title: A geometric approach to non-linear correlations with intrinsic scatter
Author: Pihajoki, Pauli
Contributor: University of Helsinki, Department of Physics
Date: 2017-12
Language: eng
Number of pages: 18
Belongs to series: Monthly Notices of the Royal Astronomical Society
ISSN: 0035-8711
URI: http://hdl.handle.net/10138/228246
Abstract: We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-s correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is similar to 6 for the data sets used, rather than the values in the range of similar to 4-5 typically quoted in the literature for these data.
Subject: methods: data analysis
methods: statistical
galaxies: fundamental parameters
BLACK-HOLE MASS
ORTHOGONAL DISTANCE REGRESSION
LINEAR-REGRESSION
COSMOLOGICAL SIMULATIONS
HOST GALAXIES
VELOCITY DISPERSION
ELLIPTIC GALAXIES
ASTRONOMICAL DATA
LEAST-SQUARES
FEEDBACK
114 Physical sciences
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