Skip to content
QFT .org

Statistical Inference and Error Budgets

Lattice measurements begin as correlated histories and often pass through several fits before producing a continuum result. This chapter follows uncertainty through that chain, distinguishing autocorrelation, covariance estimation, model choices, equilibration, and shared systematic effects.

Enter this chapter

Section titled “Enter this chapter”

Begin with Autocorrelation Times and Effective Sample Size to measure how correlations change the uncertainty of a sample mean.

Topics

Section titled “Topics”
  1. Autocorrelation Times and Effective Sample Size — Relates observable-dependent autocorrelation to effective information.
  2. Estimators, Covariance, and Resampling — Propagates correlated data through nonlinear estimators.
  3. Correlated Fits, Model Selection, and Stability Tests — Tests covariance conditioning and fit-model stability.
  4. Equilibration, Stationarity, and Chain Diagnostics — Separates finite-chain equilibration from transition correctness.
  5. Blinding, Analysis Choices, and Independent Reproduction — Controls discretionary analysis choices and checks reproducibility.
  6. Multi-Stage Analyses and Correlated Uncertainty Propagation — Carries common inputs through successive inference stages.
  7. Complete Lattice Error Budgets — Assembles statistical and systematic errors without double counting.

How the ideas fit together

Section titled “How the ideas fit together”

A long chain can contain much less information than its configuration count suggests, and different observables can have different slow modes. Resampling must preserve the relevant dependence before nonlinear quantities or fits are formed. Later stages introduce further correlations: the same configurations can determine both an observable and its scale conversion. Treating those outputs as independent can either overstate or understate the final error. An uncertainty estimate is therefore a property of the complete estimator and its data history. Wolff 2004, §§ 2–3.

Where to go next

Section titled “Where to go next”

Continue to Finite-Volume Spectra and Amplitudes to identify the infrared deformation and the physical limits it requires.

References

Section titled “References”
  • Wolff, U. (2004). Monte Carlo errors with less errors. Computer Physics Communications, 156, 143–153. DOI.