Lecture 13: Systematics, Calibration, and Error Budgets

ASTR 476: Observational Cosmology · 2026-09-27

Driving question: How do we know what is limiting the measurement?

Learning objectives

  1. Build a categorized error budget with statistical and shared systematic terms.
  2. Explain calibration propagation through a multi-stage distance measurement.
  3. Audit provenance, version, units, and transformations for a derived result.
Terms · 8 min

Terms for This Lecture

Statistical uncertainty

Definition: Variation expected from finite noisy data under the adopted sampling model.

Why it matters here: It is required to answer How do we know what is limiting the measurement? and to distinguish direct observation from cosmological inference.

Relationships: Read it with Calibration uncertainty, the model \(C_total = C_stat + C_cal + C_model + ...\), and the evidence statement The package makes distinct records for live-verified Pantheon+ source data, published summary values not re-fetched from the paper, and theoretical or synthetic illustrations.

Boundary or common confusion: A checksum proves file identity, not scientific validity; provenance, versioning, units, and independent checks are also required.

Slide 1 · 8 min

Precision is a chain

Trace detector calibration, photometry, standardization, redshift, and cosmological model.

Slide 2 · 10 min

Random versus shared

Distinguish independent noise from common calibration offsets and model discrepancy.

Slide 3 · 12 min

Covariance is operational

Use the subset source's row order, checksums, and rounding tolerance as a concrete reproducibility case.

Slide 4 · 12 min

Nuisance parameters and priors

Show how uncertainty budgets become parameters or covariance terms in inference.

Slide 5 · 10 min

Validation stack

Use injection/recovery, cross-calibration, null tests, alternate pipelines, and posterior predictive checks.

Slide 6 · 8 min

Audit trail

Record source URL, retrieval date, source digest, transform, code version, and caveat for every data product.

Systematics, Calibration, and Error BudgetsThe package makes distinct records for live-verified Pantheon+ source data, published summary values not re-fetched from the paper, and theoretical or synthetic illustrations.A credible error budget tracks origin and correlationphotometry0.68 (schematic weight)calibration0.52 (schematic weight)population0.39 (schematic weight)selection0.30 (schematic weight)model0.24 (schematic weight)relative contribution (illustrative only)Schematic categories, not measured error fractions
The package makes distinct records for live-verified Pantheon+ source data, published summary values not re-fetched from the paper, and theoretical or synthetic illustrations.

Quantitative anchor

The selected covariance block preserves source order; file hashes verify identity but do not validate a scientific interpretation.

\[C_total = C_stat + C_cal + C_model + ...\]

Interpretation and limits

Precision cosmology depends on calibration chains and nuisance models as much as sample size. An error budget names sources, correlations, mitigation, and residual validation rather than collapsing every uncertainty into one bar.

Boundary: A checksum proves file identity, not scientific validity; provenance, versioning, units, and independent checks are also required.

Evidence: The package makes distinct records for live-verified Pantheon+ source data, published summary values not re-fetched from the paper, and theoretical or synthetic illustrations.

Active check: Record source URL, retrieval date, source digest, transform, code version, and caveat for every data product.

ASTR 476 · Lecture 13 · 60-minute module · Systematics, Calibration, and Error Budgets