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cff-version: 1.2.0
message: "If you use SCOPE in published work, please cite both the software release and the associated paper below."
type: software
title: "SCOPE: Symmetric COvariance Population Estimator"
authors:
- family-names: Graham
given-names: Alister W.
affiliation: "Centre for Astrophysics and Supercomputing, Swinburne University of Technology"
orcid: "https://orcid.org/0000-0002-6496-9414"
version: "1.0.0"
date-released: 2026-06-04
license: MIT
repository-code: "https://github.com/A-Graham/SCOPE"
doi: "10.5281/zenodo.20536917"
identifiers:
- type: doi
value: "10.5281/zenodo.20536917"
description: "Zenodo archive"
abstract: >
SCOPE (Symmetric COvariance Population Estimator) is a hierarchical Bayesian
regression framework implemented in R and Stan. It fits a linear scaling
relation between two observed quantities while fully accounting for
measurement uncertainties in both variables, including asymmetric
uncertainties modelled via a skew-normal approximation. The regression slope
is derived from the intrinsic population covariance
(beta = rho * sigma_y / sigma_x), treating both variables symmetrically
during fitting. The method is designed for astrophysical scaling relations
but is applicable to any two-variable relation with measurement uncertainty
in both coordinates.
keywords:
- astronomy
- astrophysics
- Bayesian inference
- hierarchical modelling
- regression
- Stan
- scaling relations
- black holes
preferred-citation:
type: article
title: "Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations"
authors:
- family-names: Graham
given-names: Alister W.
affiliation: "Centre for Astrophysics and Supercomputing, Swinburne University of Technology"
orcid: "https://orcid.org/0000-0002-6496-9414"
journal: "Monthly Notices of the Royal Astronomical Society"
year: 2026
url: "https://arxiv.org/abs/2606.05808"
notes: "Submitted; arXiv:2606.05808 [astro-ph.GA]"