Residual vector
Definition: The ordered differences between observed supernova magnitudes and model predictions.
Why it matters here: It is required to answer Why is a list of error bars not a likelihood? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Covariance matrix, the model \(chi^2 = r^T C^{-1} r\), and the evidence statement The public Pantheon+ release documents a 1701 by 1701 statistical-plus-systematic covariance; the included 18 by 18 block is aligned to the selected source rows.
Boundary or common confusion: Subsetting covariance preserves selected-row correlations but does not preserve the full survey's parameter constraints or selection function.
Covariance matrix
Definition: The variances and pairwise correlated uncertainties of the ordered data vector.
Why it matters here: It is required to answer Why is a list of error bars not a likelihood? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Cholesky factorization, the model \(chi^2 = r^T C^{-1} r\), and the evidence statement The public Pantheon+ release documents a 1701 by 1701 statistical-plus-systematic covariance; the included 18 by 18 block is aligned to the selected source rows.
Boundary or common confusion: Subsetting covariance preserves selected-row correlations but does not preserve the full survey's parameter constraints or selection function.
Cholesky factorization
Definition: A stable triangular decomposition of a positive-definite covariance used to whiten residuals.
Why it matters here: It is required to answer Why is a list of error bars not a likelihood? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Generalized least squares, the model \(chi^2 = r^T C^{-1} r\), and the evidence statement The public Pantheon+ release documents a 1701 by 1701 statistical-plus-systematic covariance; the included 18 by 18 block is aligned to the selected source rows.
Boundary or common confusion: Subsetting covariance preserves selected-row correlations but does not preserve the full survey's parameter constraints or selection function.
Generalized least squares
Definition: Least-squares estimation using the full inverse-covariance weighting implied by correlated errors.
Why it matters here: It is required to answer Why is a list of error bars not a likelihood? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Calibration mode, the model \(chi^2 = r^T C^{-1} r\), and the evidence statement The public Pantheon+ release documents a 1701 by 1701 statistical-plus-systematic covariance; the included 18 by 18 block is aligned to the selected source rows.
Boundary or common confusion: Subsetting covariance preserves selected-row correlations but does not preserve the full survey's parameter constraints or selection function.
Calibration mode
Definition: A shared systematic shift that moves multiple supernova measurements coherently.
Why it matters here: It is required to answer Why is a list of error bars not a likelihood? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Residual vector, the model \(chi^2 = r^T C^{-1} r\), and the evidence statement The public Pantheon+ release documents a 1701 by 1701 statistical-plus-systematic covariance; the included 18 by 18 block is aligned to the selected source rows.
Boundary or common confusion: Subsetting covariance preserves selected-row correlations but does not preserve the full survey's parameter constraints or selection function.