Statistics Domain Ontology

FLOW ALGEBRA
TITLE: Statistics Domain Ontology
DOMAIN: Domain Ontologies / Mathematical Domains / Statistics
SOURCE: https://kirethresearch.org/booksai-core/ontologies/domain-ontologies/mathematical-domains/statistics-domain-ontology.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "StatisticsDomainOntology" v1.0 {
  ontology:
    id: "statistics-domain-ontology"
    parent: "mathematical-domains"
    purpose: "Represent statistical data, designs, models, estimates, tests and evidence with explicit assumptions and uncertainty."

  types:
    Population: {id: string, definition: string, scope: string?}
    Sample: {id: string, population_id: string, sampling_method: string, size: integer, provenance: string}
    Variable: {id: string, measurement_scale: enum[nominal, ordinal, interval, ratio], unit: string?, missingness: string?}
    Dataset: {id: string, variables: string[], sample_id: string?, provenance: string, version: string}
    StudyDesign: {id: string, kind: enum[observational, experimental, survey, longitudinal, other], randomisation: boolean?, confounders: string[]}
    StatisticalModel: {id: string, family: string, parameters: string[], assumptions: string[], fitted_on: string?, version: string}
    Estimate: {id: string, estimand: string, value: number, standard_error: number?, interval: string?, method: string, evidence: string[]}
    HypothesisTest: {id: string, null_hypothesis: string, alternative: string, statistic: number?, p_value: number?, significance_level: number?, method: string, assumptions: string[]}
    Relationship: {id: string, subject: string, predicate: string, object: string, context: string?, confidence: number, evidence: string[]}

  predicates:
    sampled_from(sample: Sample, population: Population)
    contains_variable(dataset: Dataset, variable: Variable)
    generated_under(dataset: Dataset, design: StudyDesign)
    fitted_to(model: StatisticalModel, dataset: Dataset)
    estimates(estimate: Estimate, parameter: string)
    tests(test: HypothesisTest, hypothesis: string)
    associated_with(variable_a: Variable, variable_b: Variable)
    adjusted_for(model: StatisticalModel, variable: Variable)
    supported_by(relationship: Relationship, evidence_id: string)

  constraints:
    - "All references must resolve to typed entities with provenance."
    - "Sample size must be a non-negative integer; inferential analyses must justify effective sample size."
    - "Confidence values and p-values must lie within [0,1]."
    - "A p-value is not the probability that a null hypothesis is true."
    - "Distinguish confidence intervals, credible intervals and prediction intervals."
    - "Statistical association does not by itself establish causation."
    - "Record units, missing-data handling, sampling bias, model assumptions and multiplicity where relevant."
    - "Avoid treating statistical significance as practical importance."

  inference:
    rule descriptive_summary:
      if contains_variable(d,v) and valid_measurements(d,v)
      then eligible_for_descriptive_statistics(d,v)
      confidence: "dependent on data quality and missingness"
    rule model_estimation:
      if fitted_to(m,d) and assumptions_checked(m,d) and valid(d)
      then eligible_for_model_based_estimation(m,d)
      confidence: "retain uncertainty, design limitations and diagnostics"
    rule evidence_relation:
      if supported_by(r,e) and valid_evidence(e)
      then evidence_backed(r)
      confidence: "do not upgrade confidence without independent support"

  SEMANTIC_EQUIVALENCE:
    - "Normalise statistical terminology to versioned definitions and identifiers."
    - "Distinguish parameter from statistic, estimand from estimate, and population from sample."
    - "Preserve model specification, variable coding, units, population and study context."

  CONFIDENCE:
    range: [0,1]
    factors: [sampling_design, sample_size, measurement_quality, model_fit, assumption_validity, uncertainty, replication, source_reliability]
    policy: "Represent epistemic confidence separately from frequentist confidence levels and Bayesian posterior probabilities."

  VALIDATION:
    - "Validate types, identifiers, data ranges, missingness, units and provenance."
    - "Check model assumptions, diagnostics, study design and reproducibility."
    - "Flag data leakage, selection bias, multiple testing and unsupported causal interpretation."
    - "Record competing models and contradictory findings rather than silently overwriting them."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, rules, data references and provenance"
    note: "Compute hash at execution; no hash value is claimed here."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental update"
    steps: [ingest, normalise, validate, assess_assumptions, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed statistical knowledge graph with uncertainty and evidence-backed relationships"
    outputs: [dataset_links, model_descriptions, estimates, test_results, uncertainty_annotations, provenance_records]
    safeguards: [no_unsupported_causal_claims, preserve_study_context, distinguish_significance_from_effect_size, report_uncertainty]
}

END FLOW ALGEBRA