---
slug: model_uncertainty
name: Model Uncertainty
one_liner: "Second-order uncertainty over which distributional family or functional form is right in the first place — a distribution of doubt ranging over the hypothesis-space STRUCTURE itself, as opposed to parameter uncertainty within a fixed family."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, statistical, epistemic]
origin_domain: statistics
alternate_origin_domains: [machine_learning, econometrics, decision_theory, climate_science, epidemiology]
aliases: [structural_uncertainty, model_class_uncertainty, specification_uncertainty, bayesian_model_averaging_uncertainty, uncertainty_over_the_model]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-02 self-application, route M / machinery) — the SECOND-ORDER prime obtained by applying `distributional_assumption` to itself: uncertainty not about the parameters WITHIN an assumed family but about WHICH family or functional form to assume in the first place. Surfaced in the op-02 self-application pilot (from distributional_assumption) and confirmed in the sweep, 2026-07-03. MODERATE hold (verified absent from corpus; established construct — model / structural uncertainty, Bayesian model averaging). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "META-UNCERTAINTY CLUSTER MERGE FLAG (PROMINENT): model_uncertainty sits in a tight cluster of four op-02 self-application holds that all concern uncertainty/probability/risk about one's own uncertainty apparatus — `second_order_uncertainty` (from uncertainty), `second_order_probability` (from probability), `model_risk` (from risk), and this one. model_uncertainty is specifically the 'which MODEL FAMILY / STRUCTURE' flavor. OWNER MUST DECIDE at curation whether these are one prime, a genus + species (plausibly `second_order_uncertainty` as genus with `model_uncertainty` as the model-family species), or four distinct primes. Resolve the cluster TOGETHER, not piecemeal."
- "Phase-C action: re-similarity-check vs `distributional_assumption` (the input / parent) and the three cluster siblings `second_order_uncertainty` / `second_order_probability` / `model_risk`, plus `uncertainty`; confirm it is the genuine second-order lift (doubt ranging over the hypothesis-space STRUCTURE, not points within a fixed family) and not a restatement of parameter uncertainty or of plain `uncertainty`; resolve the genus/species split before drawing edges — likely a subsumption edge `second_order_uncertainty` → `model_uncertainty` (if kept as species) plus `distributional_assumption` → `model_uncertainty`; write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 4
  structural_abstraction: 4
  transfer_evidence: 4
  reasoning: 'The bare structure — a doubt/distribution that ranges over WHICH hypothesis-space structure (family, functional form, model class) to adopt, as opposed to over points within an already-fixed structure — is a genuinely substrate-neutral second-order form. It recurs wherever an inference commits to a structural choice before doing parameter work: model selection / Bayesian model averaging / ensembling in statistics and ML, specification uncertainty in econometrics, structural model spread across climate and epidemiological models, and ambiguity (as distinct from risk) in decision theory. These are structurally-similar siblings sharing the same abstract move — lift uncertainty up from parameters-within-a-family to the choice-of-family itself — which supports domain_breadth 4 (broad within the quantitative/inferential world but less cross-substrate than the most physical primes). Structural abstraction is 4 because the core is a clean statement about a level-2 object (the hypothesis-space structure) distinct from the level-1 object (parameters inside it), requiring no particular substance; it stays short of 5 because the notion leans on the machinery of distributions/models and reads most naturally in an inferential frame. Transfer evidence is strong (independently named as model uncertainty, structural uncertainty, and specification uncertainty across statistics, econometrics, and the climate/epidemiology modeling literatures).'
similarity_to_nearest_existing_prime:
  slug: distributional_assumption
  similarity: 0.58
structural_framed:
  label: structural
  aggregate: 0.41
  criteria: {vocab_travels: 0.7, evaluative_weight: 0.3, institutional_origin: 0.2, human_practice_bound: 0.4, import_vs_recognize: 0.45}
  rationale: 'Reads structural-to-mixed. The core claim — a doubt ranging over which model family / functional form is right, distinct from parameter uncertainty within a fixed family — is recognized rather than imported, and travels cleanly across statistics, ML, econometrics, and climate/epidemiological modeling without carrying any one field''s substance. The frame residue is moderate: the construct presupposes a modeling PRACTICE (someone chose a family and could have chosen another), which lifts human_practice_bound and import_vs_recognize off the floor and pushes the aggregate above the surrounding structural-stratum candidates; but the underlying second-order structure — uncertainty over hypothesis-space STRUCTURE versus over points within it — is substrate-neutral. Comparable framing to its parent `distributional_assumption`.'
phase_b_passes_completed: []
---
# Model Uncertainty

## Core Idea

Model uncertainty is a *second-order* uncertainty: the object of doubt is not the parameters of an assumed model but the *choice of model itself* — which distributional family, functional form, or model class is right in the first place. Base-level `distributional_assumption` commits to a specific family (normal, power-law, Poisson, some structural equation) and then does inference *within* that commitment, quantifying uncertainty over its parameters. Model uncertainty is reached from `distributional_assumption` by applying uncertainty to the assumption itself: a distribution of doubt ranging over *which family or form* generated the data, as opposed to a distribution over parameter values inside one fixed family. It is the uncertainty you have *before* — and orthogonally to — the uncertainty you quantify once a family is chosen.

The load-bearing anatomy is a distinction the base object does not name: *parameter uncertainty* (spread over points inside a fixed hypothesis space) versus *structural / model uncertainty* (spread over which hypothesis space to use). These are logically independent — one can be nearly certain of a family's parameters yet deeply unsure the family is correct, or confident in the family while its parameters remain vague. The feature present at the meta level but absent at the base is precisely the NEW object over which uncertainty ranges: the *hypothesis-space structure*, not points within it. Within a single `distributional_assumption` the family is a fixed background — there is no vocabulary for "the family itself might be wrong," because the family is presupposed. Lift uncertainty up one level and that background becomes the foreground: the model class is now the thing that is uncertain, averaged over, selected among, or hedged against. This is exactly the object that drives *model averaging* (Bayesian model averaging), *model selection*, *ensembling*, and *robustness-to-misspecification* behaviors — none of which fixed-family inference can express, because none of them are moves you can make while the family stays presupposed.

Read structurally, the same second-order shape appears wherever an inference must first commit to a structural choice and could have chosen otherwise. In *machine learning*, it is model-class / architecture uncertainty handled by model selection, Bayesian model averaging, and ensembling. In *econometrics*, it is *specification uncertainty* — doubt over which regressors, functional form, or structural equation to adopt, distinct from uncertainty over the coefficients once specified. In *climate science and epidemiology*, it is the *structural model spread* across whole models, treated as its own error budget alongside parameter and scenario uncertainty. In *decision theory*, it is *ambiguity* — uncertainty about the probability model itself, as opposed to risk quantified within a known model. Across these, the shared abstract move is the same lift: from uncertainty over points-within-a-family to uncertainty over the choice-of-family, with the hypothesis-space structure as the new selectable, averageable, hedgeable object.

## Notes

**Provenance.** Produced by operator 02 (self-application), route M (machinery), as the second-order prime obtained by applying `distributional_assumption` to itself — uncertainty not about parameters within an assumed family but about *which family or functional form to assume in the first place*. Surfaced in the op-02 self-application pilot (from `distributional_assumption`) and re-confirmed in the full-corpus sweep on 2026-07-03. Established construct: *model uncertainty* / *structural uncertainty* in statistics and ML (Bayesian model averaging, model selection, ensembling), *specification uncertainty* in econometrics, *structural model spread* in climate/epidemiological modeling, and *ambiguity* (Knightian, à la Ellsberg) in decision under uncertainty. Verified absent from the corpus. Manifest: MODERATE hold.

**META-UNCERTAINTY CLUSTER — read before keep/cut.** model_uncertainty does not stand alone: it is one of *four* op-02 self-application holds that all concern uncertainty/probability/risk about one's own uncertainty apparatus — `second_order_uncertainty` (uncertainty applied to uncertainty), `second_order_probability` (probability of a probability), `model_risk` (risk applied to risk / the risk that the model is wrong), and this one. model_uncertainty is specifically the *"which MODEL FAMILY / STRUCTURE"* flavor of that family. The dominant curation question is therefore NOT "keep or cut model_uncertainty in isolation" but *how to carve the cluster*: are these one merged prime, a genus + species arrangement (the plausible reading is `second_order_uncertainty` as the genus, with `model_uncertainty` the *model-family species*, `second_order_probability` the probability species, and `model_risk` the risk species), or four genuinely distinct primes? The proposer's lean is *genus/species*: `second_order_uncertainty` as parent, `model_uncertainty` as the specific case where the second-order object is the hypothesis-space structure. Kurt should resolve all four TOGETHER at curation, not piecemeal, so the split is coherent.

**For owner evaluation (keep/cut).** The case FOR: model uncertainty is an *established, named construct* (Bayesian model averaging, structural / specification uncertainty), verified absent, with a clean second-order anatomy — uncertainty over the hypothesis-space *structure* versus over parameters *within* it — and siblings spanning statistics, ML, econometrics, climate/epidemiology, and decision theory. It names a real, load-bearing distinction (parameter vs. structural uncertainty) that `distributional_assumption` presupposes-away. The case AGAINST is dominated by the cluster question above: model_uncertainty is arguably the *model-family species* of a general `second_order_uncertainty` genus, in which case it should be admitted (if at all) as a child under that genus rather than as an independent node — and the owner should settle the genus and its species split as a unit. Also screen for collapse against `distributional_assumption` (the parent — is this just "doubt about the assumption" restated?) and plain `uncertainty`. Sharp keep/cut question: *is model_uncertainty a distinct prime, or a species under `second_order_uncertainty` — and is either that or `distributional_assumption` the right parent?*

**At incorporation.** Re-run similarity against `distributional_assumption` (input / parent), the three cluster siblings `second_order_uncertainty`, `second_order_probability`, and `model_risk`, and plain `uncertainty`, to confirm no collapse and to fix the carve. If kept as a species, draw a subsumption edge `second_order_uncertainty` → `model_uncertainty` plus a subsumption/derivation edge `distributional_assumption` → `model_uncertainty`; if kept as an independent node, draw sibling edges across the cluster and to the specification-uncertainty / model-spread / ambiguity instances (or the primes carrying them). Add a missing-edge note flagging the cluster relationship explicitly so the four are not adjudicated in isolation. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
