43-EFT.WP.Data.DatasetCards v1.0 | Chapter 10 Uncertainty & Error Budget

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Chapter 10 Uncertainty & Error Budget

I. Chapter Purpose & Scope

II. Terminology & Dependencies

• Terminology source: General terms follow EFT.WP.Core.Terms v1.0; this chapter only adds uncertainty-related fields.
• Dependent volumes: Metrology/units & dimensional checks: Core.Metrology v1.0; error taxonomy & combination workflows: Core.Errors v1.0; path/arrival-time equations: Core.Equations v1.1; export & citation anchors: Core.DataSpec v1.0.

III. Fields & Structure (Normative)

uncertainty:

model: "GUM" # Reference posture: GUM-like / bayesian

components: # Error components (systematic/random)

- name: "thermal"

type: "random" # random | systematic

value: 2.1

unit: "K"

distribution: "normal" # normal | uniform | triangular | student-t | user

coverage: {k: 1.0} # k=1 for standard uncertainty

corr_group: null # correlation group; null = independent

method: "repeatability" # evaluation method

note: "receiver noise"

- name: "cal_gain"

type: "systematic"

value: 0.8

unit: "%"

distribution: "normal"

coverage: {k: 2.0}

corr_group: "instrument"

method: "cal-lab"

correlation:

posture: "groups" # groups | covariance

groups:

- name: "instrument"

pairwise: "rho=0.6" # shorthand; or specify covariance.Sigma

covariance:

Sigma: [] # optional full covariance matrix

propagation:

rule: "rss" # rss | linear | bayesian | montecarlo

linearization: "first-order" # when applicable

samples: 0 # >0 enables Monte Carlo

coverage_policy:

target_p: 0.95 # default 95% coverage

k: 2.0 # coverage factor (approx. or solved from distribution)

report:

significant_figures: 3

unit_consistency: true

see:

- "EFT.WP.Core.Metrology v1.0:check_dim"

- "EFT.WP.Core.DataSpec v1.0:EXPORT"

(uncertainty is conditionally required: present whenever measured or inferred quantities exist; export references appear in export_manifest.references[].)

IV. Component Taxonomy & Minimal Inventory

• Random (Type A): e.g., thermal, shot, background, labeler-variance.
• Systematic (Type B): e.g., cal_gain (calibration drift), quantization, timebase drift, path_corrections (ionosphere/troposphere/instrumental), model mismatch.
• Recording requirements: Each component must include name/type/value/unit/distribution/coverage/method and indicate corr_group or the covariance source.

V. Propagation & Combination Rules

• Root-sum-of-squares (rss) for independent standard uncertainties:
  u_c = ( sqrt( Σ u_i^2 ) ).
• Linearization (linear) (first-order Taylor, with correlation):
  u_c = ( sqrt( J Σ J^T ) ), where J = ( ∂f / ∂x ) and Σ is the input covariance.
• Bayesian / Monte Carlo (bayesian / montecarlo): Provide priors/likelihood or samples; report posterior mean/quantiles and the target_p coverage interval.
• Coverage factor: Expanded uncertainty U = ( k * u_c ); k≈2 for ~95% under normal assumptions.
• Units/dimensions: Normalize units before combination and pass check_dim.

VI. Correlation Handling

• Group-based: Common rho within a group or explicit pairwise correlations; cross-group assumed independent.
• Covariance-based: Provide Σ directly, or supply standard deviations and correlation matrix R with Σ = D R D.
• Reporting: State correlation sources (theory, calibration, concurrent measurements) and sensitivity of combined uncertainty.

VII. Coupling to Path-Dependent T_arr (when applicable)

1. Equivalent expressions:
   • T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • T_arr = ( ∫ ( n_eff / c_ref ) d ell )
2. Propagation: Discretize path γ(ell) into segments ℓ_k:
   u^2(T_arr) = ( Σ ( ( ∂T_arr / ∂n_eff,k )^2 u^2(n_eff,k) ) + 2 Σ_{i<j} ( ∂T_arr/∂n_i )( ∂T_arr/∂n_j ) cov(n_i,n_j) + ( ∂T_arr/∂c_ref )^2 u^2(c_ref ) ).
3. Registration: In path_dependence, register delta_form/path/measure; in uncertainty.components[], register sources and correlations for n_eff, c_ref, and medium-correction terms.

VIII. Reporting & Presentation Rules

• Numeric presentation: Follow Chapter 9’s sigfigs_default and rounding policy; uncertainty shares the same unit as the measurand.
• Interval posture: Explicitly label confidence/coverage (e.g., “expanded uncertainty at k=2 (~95%)”).
• Breakdown table: Provide systematic/random columns, percentage shares, and sensitivity ordering by |∂f/∂x_i|.

IX. Linkage to Quality Gates

• Set uncertainty thresholds in quality.gates (e.g., u_c ≤ u_max, bias ≤ b_max); failing these is blocking.
• Incorporate sampling-audit contributions (coverage, leakage, class imbalance) as components in the combined uncertainty.

X. Machine-Readable Fragment (Drop-in)

uncertainty:

model: "GUM"

components:

- {name:"thermal", type:"random", value:2.1, unit:"K", distribution:"normal", coverage:{k:1.0}}

- {name:"cal_gain", type:"systematic", value:0.8, unit:"%", distribution:"normal", coverage:{k:2.0}, corr_group:"instrument"}

correlation: {posture:"groups", groups:[{name:"instrument", pairwise:"rho=0.6"}]}

propagation: {rule:"linear", linearization:"first-order", samples:0}

coverage_policy: {target_p:0.95, k:2.0}

report: {significant_figures:3, unit_consistency:true}

path_dependence:

applies_to: ["T_arr"]

delta_form: "const-factor"

path: "gamma(ell)"

measure: "d ell"

see:

- "EFT.WP.Core.Equations v1.1:S20-1"

- "EFT.WP.Core.Metrology v1.0:check_dim"

(see[] syntax aligns with the export manifest and carries “Volume+Version+Anchor”.)

XI. Example Fragment (Report Table)

uncertainty_report:

combined:

u_c: 0.37

unit: "ms"

coverage: {k: 2.0, U: 0.74, target_p: 0.95}

breakdown:

- {name:"thermal", type:"random", contrib:0.29, unit:"ms", share:"61%"}

- {name:"cal_gain", type:"systematic", contrib:0.21, unit:"ms", share:"39%"}

sensitivity:

- {wrt:"n_eff", |df/dx|: "1.8e-9 s", note:"path-avg"}

- {wrt:"c_ref", |df/dx|: "1.2e-9 s", note:"const-factor"}

XII. Coupling with Export Manifest

export_manifest:

references:

- "EFT.WP.Core.DataSpec v1.0:EXPORT"

- "EFT.WP.Core.Metrology v1.0:check_dim"

- "EFT.WP.Core.Equations v1.1:S20-1"

artifacts:

- {path:"uncertainty/derivation.md", sha256:"..."}

- {path:"uncertainty/covariance.npy", sha256:"..."}

(Exported artifacts must be verifiable; no shortcodes/aliases; version and anchor are mandatory.)

XIII. Chapter Compliance Checklist

• uncertainty.components[] complete with type, unit, distribution, coverage; systematic vs. random clearly separated.
• Propagation rule (rss/linear/bayesian/montecarlo) and correlation posture (groups/covariance) chosen and recorded; units normalized prior to combination; check_dim passes.
• For T_arr, delta_form/path/measure registered and propagation path provided; one of the two equivalent expressions used for consistency checks.
• Report includes u_c, U=k*u_c, target coverage probability, breakdown table, and sensitivity ordering; significant figures and rounding follow Chapter 9.