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Multiple-testing node conflict diagnostic

Algorithms AIMech:MultipleTestingNodeConflictDiagnostic DRAFT

A Bayesian evidence-synthesis diagnostic that partitions information at replicated separator nodes, stacks declared contrasts between transformed copies, and uses their joint covariance and a multivariate reference distribution to assess global and multiplicity-adjusted local conflict. Its single-step max-absolute-statistic adjustment accounts for correlation within an explicitly selected family of comparisons.

Identity Notes & Concept Scope No normalized identity match for the proposed multiple-testing conflict, INLA group-conflict and general parametric maxT candidates among all 442 pinned AIO and 559 maintained IDs, labels, aliases and scoped synonyms. Ignored- and hidden-inclusive searches of the recovery, older discovery and original Documents checkouts returned 132, 0 and 0 lines: 39 identical previous lines reused, 90 new short rows read, two identical generated separator-record search rows checked and read, and one previous query row verified exact against its earlier reading. Hits concern existing diagnostics, mirrors, metadata and pending leads. Assessed 61 semantic AIO rows and 213 native names/definitions: 55 and 203 prior rows verified equal, all 6 and 10 additions read. Ten full AIO nodes, annotations, incident edges and generated records plus seven native context records were read or verified unchanged. This identity adds a joint contrast family and multiplicity adjustment to general separator splitting. It is not generic maxT inference for arbitrary estimators, a single unit-level conflict score, Gaussian-message screening, INLA fitting, or every method called node splitting.

Claims & Grounded Evidence

7 Claims

Scope #partition-family

Specify the data partitions, separator copies, common parameter transformations and family of comparisons before interpreting adjusted conflict. The source partitions the evidence into Q submodels and compares separator quantities informed by more than one partition. Proper partition posteriors are required to define these distributions. Poor identification can make comparisons prior-driven or uninformative even when a score is computable; calibrated testing requires the separately stated regularity and sampling assumptions. Weak data and reference priors can materially determine the result. Multiarm trial information must retain its joint structure. Separate observed data subsets do not by themselves ensure independent fitted partitions when latent or estimated nuisance quantities are shared.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Sections 2–3.2, PDF pp. 2–6; network meta-analysis, pp. 8–9; discussion, pp. 12–13

Mechanism #signed-contrasts

Let phi stack the declared separator copies, u=h(phi), and K be a fixed matrix whose rows encode comparisons. Define Delta=K*u; a pairwise difference row contains +1 and -1. K may be rectangular and pairwise comparisons may be redundant. From joint draws of u, compute m=E(Delta) and S=Cov(Delta)=K*Cov(u)*K^T. Block-diagonal partition covariance requires justified independence. If instead applying a local delta approximation on the original phi scale, include the transformation Jacobian J: S approximately equals K*J*Cov(phi)*J^T*K^T. A plug-in K*h(E(phi)) approximates, rather than generally equals, E(Delta).

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Sections 3.2–3.3, PDF pp. 6–7; Appendix B, p. 28
supports Source: Simultaneous Inference in General Parametric Models · Locator: Section 2, PDF pp. 4–5 / printed pp. 2–3; redundant Tukey contrasts, PDF p. 9 / printed p. 7

Mechanism #standardization-and-support

For a p-component contrast vector with positive finite diagonal variances, set D=diag(S), T=D^(-1/2)*m and R=D^(-1/2)*S*D^(-1/2). Correlation R may be singular because comparisons are redundant. Zero-variance or deterministic contrasts require an explicit support check and separate handling; they cannot be standardized by division by zero. A null vector outside the posterior affine support is not rescued by a pseudoinverse. Numerical rank thresholds and covariance approximation affect the resulting diagnostics.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Sections 3.3–3.4, PDF p. 7; Appendix B, p. 28
supports Source: Simultaneous Inference in General Parametric Models · Locator: Sections 2–3, PDF pp. 4–7 / printed pp. 2–5

Mechanism #wald-global-score

One global option is W=m^T*S^+*m, equivalently T^T*R^+*T when the mean lies in the covariance range, with + denoting the Moore–Penrose pseudoinverse. Under a justified Gaussian null reference on an r-dimensional contrast subspace, use the upper chi-square_r tail, where r is the covariance rank. This quadratic global assessment differs from max-absolute-statistic testing and does not itself identify the inconsistent component. Its reference law needs support and calibration assumptions beyond computing a posterior mean and covariance.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Section 3.4, PDF p. 7
supports Source: Simultaneous Inference in General Parametric Models · Locator: Section 3, PDF pp. 5–6 / printed pp. 3–4

Mechanism #single-step-maxt

For a centered joint normal reference Z with covariance R, define M=max_j |Z_j| and G_R(c)=P(-c<=Z_j<=c for all j). The global maxT score is 1-G_R(max_j |T_j|); a single-step adjusted score for component j is 1-G_R(|T_j|), using the same declared comparison family. This is an absolute maximum for two-sided tests, not the maximum of signed components. The rectangle probability incorporates correlation and can accommodate redundant coordinates under a valid singular normal law. Under the same continuous reference, each adjusted score is at least its corresponding marginal two-sided normal tail. This comparison does not automatically hold between differently approximated or sampled raw and adjusted scores.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Section 3.4, PDF p. 7; distinct adjustment families in Table 2, PDF p. 19
supports Source: Simultaneous Inference in General Parametric Models · Locator: Section 3, PDF pp. 6–7 / printed pp. 4–5

Limitation #error-control-conditions

The joint reference construction targets familywise error, not a false-discovery-rate guarantee. Exact or asymptotic repeated-data control requires a valid joint null law for the true-null comparisons, an appropriately estimated covariance and a declared testing family; posterior Gaussianity alone is insufficient. Hothorn and colleagues state a multivariate sampling limit and consistent covariance estimation for their general parametric procedure. Applying that reasoning to split Bayesian summaries requires verifying the relevant regularity and prior-dominance conditions, rather than assuming every split satisfies them. Adaptive partition searches, incompatible priors, shared nuisance fitting, weak identification and nonnormal posteriors need further assessment.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Sections 3.4 and 5, PDF pp. 7 and 12–13; Appendix B, p. 28
supports Source: Simultaneous Inference in General Parametric Models · Locator: Sections 2–3, PDF pp. 4–7 / printed pp. 2–5

Limitation #interpretation-and-source-boundaries

An adjusted continuous tail is not the posterior probability that two quantities are exactly equal. The choice of split, reference prior, scale and testing family changes the diagnostic; masking can remain, and a small score does not establish which source is wrong or authorize its exclusion. The record uses signed contrast matrices, proper normalized posteriors, explicit transformation Jacobians and max-absolute tails. It does not import the 2017 source expressions that apply a second two-tail transform to an already two-sided density-level score, describe difference matrices with only 1s and 0s, or require an invertible contrast matrix. These qualifications preserve the method without treating source notation as a general theorem.

supports Source: Conflict diagnostics for evidence synthesis in a multiple testing framework · Locator: Section 3.1, PDF p. 6; Sections 3.2–3.4, pp. 6–7; examples/discussion, pp. 9–13; Appendix B, p. 28
supports Source: Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis · Locator: Section 3.2.2, PDF p. 9
supports Source: Simultaneous Inference in General Parametric Models · Locator: Sections 2–3, PDF pp. 4–7 / printed pp. 2–5

⚠️ Curated Limitations & Negative Results

Only a specified collection of partitions and contrasts is assessed. Broad exploratory searches, dependence introduced by shared nuisance estimates, and changes in the selected family require separate validity analysis.
A singular covariance due to redundant contrasts differs from a zero-variance coordinate or a null outside the affine support. Positive diagonal variances, support, numerical rank and the joint reference law must be assessed explicitly.
The source contains density-score, contrast-sign, rank and normalization ambiguities; the record states its mathematical convention and uses the earlier node-splitting paper and primary simultaneous-inference report for clarification. No universal frequentist control follows from a normal-looking posterior.
The inspected arXiv v2 margin is dated 13 September 2017 while its title page says July 9, 2021; both observations are retained without explaining the discrepancy. The Hothorn source is the February 15, 2008 LMU technical report, not an assumed identical journal PDF.
All 28 pages of the multiple-testing paper, all 25 PDF pages of the technical report and all 22 pages of the earlier general diagnostic paper were read. No multcomp/OpenBUGS implementation, original application fit, MCMC, benchmark or repeated-data calibration experiment was run. Constructed Gaussian contrasts check rank, covariance, correlation-adjusted tails and support boundaries; they do not reproduce the source applications.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:BayesianNetwork` Bayesian Network	related_match	The algorithm forms joint conflict comparisons from separator copies in Bayesian directed acyclic evidence-synthesis graphs. BayesianNetwork supplies this representation context; it is not the diagnostic or its simultaneous testing procedure, so this is relatedness rather than equivalence or subclass membership.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`presanis2017`	Conflict diagnostics for evidence synthesis in a multiple testing framework Anne M. Presanis, David Ohlssen, Kai Cui, Magdalena Rosińska, Daniela De Angelis	primary paper full_text	ID: https://arxiv.org/abs/1702.07304v2 sha256:20326bded40d…
`hothorn2008`	Simultaneous Inference in General Parametric Models Torsten Hothorn, Frank Bretz, Peter Westfall	primary paper full_text	ID: https://doi.org/10.5282/ubm/epub.2120 sha256:e5a1a1e1790b…
`presanis2013`	Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis 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: 2026-10-13T01:15:37Z

Updated: 2026-10-13T01:21:23Z

Source File: data/curated/MultipleTestingNodeConflictDiagnostic.yaml