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Sequential score-discrepancy conflict diagnostic

Algorithms AIMech:SequentialScoreDiscrepancyConflictDiagnostic DRAFT

Aliases: Sequential score-based node conflict check, Two-stage parent-child score conflict diagnostic

A two-stage Bayesian directed acyclic graph (DAG) node-conflict diagnostic algorithm that partitions observed data around a selected separator parameter block into parent-linked data and child-linked data, propagates parent-submodel posterior draws to define conditional priors for the separator parameter, evaluates a prior-expansion score discrepancy on the child submodel for each parent draw, and aggregates the resulting dependent conditional conflict p-values via order-statistic bounds or the Half-Cauchy Combination Test.

Identity Notes & Concept Scope No normalized identity match for the sequential score-discrepancy conflict diagnostic across all 442 pinned AIO records and 562 maintained IDs, names, aliases and scoped synonyms. Fixed-string searches across data, sources, research, history, and reviews returned only references in the Round 167 discovery report and prior-expansion record noting Yang, Nott, & Presanis (2026) Section 3.1 (Algorithm 1) as a separate pending concept. Distinct from AIMech:PriorExpansionScoreConflictDiagnostic, which defines the general prior-expansion Fisher-score prior-data conflict check on a baseline prior or hierarchical stage without two-stage parent-to-child DAG posterior propagation, single-draw conditional score approximation, and dependent p-value combination across parent posterior draws. Distinct from AIMech:SeparatorNodeConflictDiagnostic, AIMech:MultipleTestingNodeConflictDiagnostic, and AIMech:INLAGroupNodeConflictDiagnostic, which duplicate separator or latent group nodes into split copies and compare split posteriors via density-level, Mahalanobis, or Gaussian-cut discrepancy tails rather than evaluating prior-expansion score statistics sequentially from parent posterior draws to a child submodel.

Claims & Grounded Evidence

5 Claims

Mechanism #two-stage-dag-parent-child-partition

For a selected separator parameter block theta_2 in a Bayesian directed acyclic graph with ancestor parameter block theta_1 and partitioned data y = (y_pa, y_ch), the first stage fits the parent submodel to y_pa_obs alone to draw M samples theta_1^(1), ..., theta_1^(M) from p(theta_1 | y_pa_obs), so that each parent draw induces a conditional prior p(theta_2 | theta_1^(m)) for theta_2 in the child submodel.

supports Source: Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies · Locator: Section 3.1, PDF pp. 13–14; Algorithm 1 Step 1, PDF p. 16
supports Source: Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis · Locator: Section 2.1–2.2, PDF pp. 3–5

Mechanism #conditional-prior-expansion-score-discrepancy

In the second stage, the conditional prior p(theta_2 | theta_1) is embedded into a smooth expansion family p(theta_2 | theta_1, alpha) with baseline alpha = alpha_0, and for each parent draw theta_1^(m) the child-stage conflict score S_alpha^(m)(y_ch) is defined via Fisher's identity as the conditional posterior expectation of d/d_alpha log p(theta_2 | theta_1^(m), alpha) at alpha = alpha_0 under p(theta_2 | y_ch, theta_1^(m)), combined for vector alpha into the quadratic form S_alpha^(m)(y_ch)^T V_{S^(m)}^-1 S_alpha^(m)(y_ch).

supports Source: Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies · Locator: Section 2.3, Equations 6–8, PDF pp. 11–12; Section 3.1, Equations 10–12, PDF pp. 14–15

Mechanism #single-draw-posterior-score-approximation-and-scaling

To avoid running a full inner Markov chain Monte Carlo chain for each parent posterior draw theta_1^(m), Algorithm 1 approximates the conditional posterior expectation by drawing a single sample theta_2^(m) ~ p(theta_2 | y_ch, theta_1^(m)) and evaluating d/d_alpha log p(theta_2^(m) | theta_1^(m), alpha) at alpha_0 for both the observed child data y_ch_obs and conditional prior-predictive replicates y_ch_rep^(m); because a single posterior draw adds conditional posterior variance relative to the exact posterior expectation, observed and replicate discrepancies must use a matched estimator or explicit variance scaling.

supports Source: Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies · Locator: Section 3.1, Equation 13 and Algorithm 1 Step 2, PDF pp. 15–16; Appendix D.2, PDF p. 43

Mechanism #dependent-pvalue-aggregation

Because the conditional conflict p-values p^(1), ..., p^(M) evaluated across parent posterior draws theta_1^(1), ..., theta_1^(M) all condition on the same observed child dataset y_ch_obs, they are statistically dependent and are combined into an overall conflict summary using either order-statistic bounds such as min(1, M * min_m p^(m)) or the Half-Cauchy Combination Test statistic T_HCCT = (1/M) * sum_{m=1}^M tan((pi/2) * (1 - p^(m))) with upper-tail reference probability 1 - (2/pi) * arctan(T_HCCT).

supports Source: Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies · Locator: Section 2.4, Equation 9, PDF p. 13; Section 3.1, Equations 14–15 and Algorithm 1 Step 3, PDF pp. 15–16

Application #avoidance-of-split-posterior-density-estimation

Evaluating conflict through conditional prior-expansion scores and scalar p-value aggregation avoids estimating a multivariate posterior difference density across duplicated separator nodes when the separator parameter block theta_2 has moderate or high dimension.

supports Source: Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies · Locator: Section 1, PDF pp. 3–4; Section 3.1, PDF pp. 13–16; Section 4, PDF pp. 21–28

⚠️ Curated Limitations & Negative Results

Requires an explicit directed acyclic graph partition into parent-linked data y_pa and child-linked data y_ch around the selected separator block theta_2 such that the parent submodel p(theta_1 | y_pa_obs) and conditional child submodel p(theta_2 | y_ch, theta_1) are well-defined and proper.
When Algorithm 1 uses a single conditional posterior draw theta_2^(m) ~ p(theta_2 | y_ch, theta_1^(m)) rather than the exact conditional posterior expectation of the prior score, the single-draw score includes additional conditional posterior Monte Carlo variance; comparing an exact observed score to single-draw replicate scores (or vice versa) without the Appendix D.2 variance scaling factor distorts the reference tail probability.
Order-statistic p-value bounds can be conservative under strong positive dependence across parent posterior draws, whereas the Half-Cauchy Combination Test relies on heavy-tail asymptotic approximation and does not guarantee exact finite-threshold Uniform(0,1) calibration under arbitrary finite-sample dependence structures.
All 52 pages of Yang, Nott, & Presanis (2026, arXiv:2511.02977v2) and 22 pages of Presanis et al. (2013, arXiv:1310.0628v1) were read. No author MCMC implementation, epidemic model fit, or empirical repeated-data calibration benchmark was executed; constructed numerical checks in research/discovery/sequential-score-conflict-boundaries.py verify analytical variance scaling and dependent p-value combination boundaries only.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:BayesianNetwork` Bayesian Network	related_match	The sequential score-discrepancy conflict diagnostic operates on a parent-child partition of a Bayesian directed acyclic graph (Bayesian network), propagating posterior draws from the parent subgraph to conditional prior-expansion score checks in the child subgraph. AIO:BayesianNetwork provides the graphical model representation context rather than an algorithmic superclass.

Evidence Sources & Primary Literature

2 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`yang2026`	Detecting Conflicts in Evidence Synthesis Models Using Score Discrepancies Fuming Yang, David J. Nott, Anne M. Presanis	primary paper full_text	ID: https://doi.org/10.48550/arXiv.2511.02977 sha256:4829e0d63d56…
`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…

Ontology & Grounding Topology

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Curation Provenance

Curator: Antigravity

Method: ai_assisted

Model: Gemini 3

Created: 2026-10-17T08:46:00Z

Updated: 2026-10-17T08:46:00Z

Source File: data/curated/SequentialScoreDiscrepancyConflictDiagnostic.yaml · Schema: curated_concept.yaml

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