Separator-node conflict diagnostic
Algorithms AIMech:SeparatorNodeConflictDiagnostic DRAFT
A Bayesian graphical-model diagnostic that duplicates a selected separator node or node vector, partitions the information informing it, and compares the resulting partition-specific distributions on a declared scale. It assesses local incompatibility through explicitly chosen discrete agreement, signed-tail, radial or density-level scores, with nuisance dependence handled by a specified split or cut.
Identity Notes & Concept Scope
No normalized identity match for the proposed general separator-node and multiple-testing node conflict diagnostics across 442 pinned AIO records and 558 maintained IDs, names, aliases and scoped synonyms. Ignored- and hidden-inclusive fixed-string searches of the recovery, older discovery and original Documents checkouts returned 218, 0 and 0 lines. All 218 were assessed: 84 identical prior lines reused, 123 new short rows read, and 11 new long rows read or checked exactly against previously read record text and query results. Hits describe existing unit-level and Gaussian-message diagnostics, their mirrors, source metadata and pending general-method leads. Assessed 55 semantic AIO rows and 203 native names/definitions; all 55 and 202 were verified equal to earlier complete readings, and the new unit-level definition was read. Ten full AIO nodes, annotations, incident edges and generated records, plus six native context records, were read or verified unchanged. This identity denotes arbitrary selected separator information splits, including likelihood-versus-likelihood splits; it is broader in scope than the unit-level held-out prior/likelihood construction and differs from its Gaussian-message approximation. It does not denote generic DAG inference, cut-posterior fitting, every local conflict measure or the later simultaneous multiple-testing extension.
Claims & Grounded Evidence
7 Claims
Scope
#separator-and-partitions
Select a scalar or vector separator theta in a Bayesian DAG and specify which sources of information belong to partitions a and b. Replace the selected node by copies theta_a and theta_b and obtain proper partition-specific distributions p_a(theta_a|y_a) and p_b(theta_b|y_b). Depending on the split, these compare a prior with a likelihood contribution, one likelihood with the remaining prior and likelihood, or distinct likelihood contributions with explicit reference priors. Complete splitting requires removing shared dependence pathways, potentially by duplicating a vector of separator and nuisance nodes. Independent observed data sets alone do not prove that retained latent variables or priors leave the replicate distributions independent. The choice of partition is part of the diagnostic question.
Mechanism
#reference-prior-and-scale
A likelihood contribution must be combined with an explicit reference prior and normalized to define a distribution for its separator copy. The source proposes flat priors on a suitable transformed scale h(theta), or Jeffreys priors where appropriate, and calls for prior sensitivity assessment. In one dimension a prior flat in a differentiable one-to-one h corresponds to a density proportional to |h'(theta)| in theta; this is a change-of-variables statement, not a guarantee that every separator has a natural global flattening transformation. Improper priors are usable only if each required split posterior is proper. Weak identification, prior dominance and changes of parameter scale remain substantive choices rather than technical details.
Mechanism
#split-versus-cut
A full node split prevents feedback in both directions across the duplicated interface. A nuisance cut instead prevents a selected partition from updating a shared nuisance distribution while allowing that nuisance uncertainty to influence its separator copy. The cut therefore does not automatically make theta_a and theta_b independent. State the joint replication law, normalized conditional distributions and pairing of nuisance draws; use independent posterior draws only when independence is justified by the split. For vector differences, covariance terms from retained dependence must be included rather than automatically adding the marginal covariance matrices.
Mechanism
#discrete-agreement
For copies on the same discrete state space and independent partition posteriors, the source defines agreement as P(theta_a=theta_b)=sum_k p_a(k)*p_b(k). If the copies are dependent, equality instead uses their joint probabilities. This is a posterior agreement mass under the replication law, not the posterior probability of the entire model and not a generally uniform frequentist p-value. Its magnitude depends on concentration and state-space granularity: identical diffuse distributions can have small equality mass.
Mechanism
#continuous-scores
For a continuous scalar separator define delta=h(theta_a)-h(theta_b) on a declared common scale, and inspect its posterior distribution. A signed tail P(delta>0), its complement, or a stated two-sided equal-tail score 2*min(P(delta>0),P(delta<=0)) measures directional disagreement. The source also defines the density-level score P(p_delta(delta)<p_delta(0)); small values place zero in a low-density region. Under suitable continuous symmetric unimodal densities with no positive-probability density ties, the two-sided equal-tail and density-level scores coincide; they need not coincide for skewed or multimodal distributions. Density plateaus, mixed/discrete support and ties require an explicit convention. Kernel estimates introduce bandwidth, kernel and Monte Carlo uncertainty; a score is not a posterior point-null probability for a continuous difference.
Mechanism
#multivariate-score-options
For a k-dimensional continuous difference with finite mean m and positive-definite covariance S, one option under a justified multivariate Gaussian approximation is the upper chi-square_k reference tail at m^T*S^-1*m. Another uses samples to estimate P((delta-m)^T*S^-1*(delta-m)>m^T*S^-1*m), a posterior radial score. A third estimates P(p_delta(delta)<p_delta(0)) from a multivariate density. These are separate choices. In particular, symmetry and unimodality alone do not imply ellipsoidal density contours, so the radial and density-level scores are not interchangeable on those assumptions alone; this distinction is curator reasoning. Singular covariance, deterministic constraints or non-existent moments require a separately justified construction, not an unqualified inverse or chi-square_k calculation.
Limitation
#interpretation-and-calibration
A conflict score points to local incompatibility under a particular partition, prior and scale; it does not establish which evidence source or model component is wrong. Posterior Gaussianity alone does not establish repeated-data calibration, and the source explicitly presents a practical framework rather than a general proof of uniformity for every split. Density-level scores can change under nonlinear changes of separator scale, even where a common strictly increasing scalar transformation preserves the sign comparison. Repeated fits and high-dimensional density estimation can be costly. Scores from different splits may be dependent, and systematic searches or multiple testing require their own assessed correction and calibration assumptions. Conflicting evidence may be masked or coexist with apparent aggregate model fit; source exclusion or clinical conclusions require further analysis.
⚠️ Curated Limitations & Negative Results
- The split, reference priors, parameter scale and treatment of nuisance dependence define the comparison. Proper full-model inference does not guarantee proper or identifiable partition-specific distributions.
- Discrete equality mass, scalar equal-tail values, Gaussian reference tails, empirical radial tails and density-level scores have different meanings and assumptions. Density ties and singular covariance require explicit handling.
- The source suggests radial scoring under symmetry and unimodality; this does not establish equality with density-contour scoring for non-elliptical distributions. Its posterior-normality discussion is not imported as a universal frequentist calibration theorem.
- The generic two-partition method does not itself provide familywise or false-discovery error control across an adaptive collection of splits. The later multiple-testing framework is a separate pending concept.
- All 22 pages of the primary electronic reprint were read, including Figures 1–16, Table 1 and references. No author implementation, original application data analysis, MCMC, empirical calibration or benchmark was run. Constructed analytic and quadrature examples check distinctions between radial and density scores, nonlinear scale choices and discrete agreement; they are not reproductions of source experiments.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:BayesianNetwork
Bayesian Network
|
related_match | The method operates on Bayesian DAG information partitions and replicated separator nodes. BayesianNetwork supplies its defining directed-graph representation but is not the diagnostic algorithm itself; this is relatedness, not equivalence or subclass membership. The general separator can lie outside a random-effects hierarchy. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
presanis2013
|
Anne M. Presanis, David Ohlssen, David J. Spiegelhalter, Daniela De Angelis
|
primary paper
full_text
|
ID: https://doi.org/10.1214/13-STS426
sha256:9cff5092b47d…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-13T01:03:23Z
Updated: 2026-10-13T01:03:23Z
Source File:
data/curated/SeparatorNodeConflictDiagnostic.yaml