Attribution Uncertainty Under Cross-Channel Identity Loss: A Bayesian Provenance Protocol

1. Introduction: causal attribution when commercial identity is fragmented across channels

Commercial exposure increasingly reaches consumers through embedded entertainment content, direct messages, and data-driven targeting. In such environments, the practical attribution problem is not whether an exposure occurred, but whether the consumer can identify which commercial source, format, or delivery pathway produced the response. Cross-channel identity loss refers to this ambiguity: the same brand, offer, or persuasive cue appears under different degrees of disclosure and traceability, so observed behavior cannot be assigned to a single channel without a model of source identity. The problem is methodologically distinct from general exposure measurement because the causal estimand concerns attribution under uncertain channel identity, not simply the average effect of contact. A useful protocol must therefore combine evidence on format-sensitive persuasion, direct causal manipulation where available, and probabilistic modeling for settings where direct manipulation is infeasible. [1] [2] [3]

The available material supports this shift in emphasis, but not all sources contribute the same kind of support. Research comparing brand placement and television advertising provides experimental evidence that persuasive format matters and that responses vary with attitude toward advertising, so identical commercial content can produce different effects depending on how it is embedded in the media environment. Gambling marketing research provides randomized field evidence that removing a direct-marketing channel can reduce betting, expenditure, and short-term harms even when the full message sequence is complex. By contrast, theoretical work on targeted advertising and consumer information search predicts that search can interact with advertising performance under stated model assumptions; this source informs mechanism specification rather than offering empirical confirmation. The methodological implication is to model attribution at the level of channel identity and consumer interpretation, while keeping empirical findings, theoretical predictions, and belief-based modeling distinct. [1] [2] [4]

2. Evidence scope and narrative synthesis strategy

This manuscript uses a targeted narrative synthesis rather than a systematic review. The purpose is not to estimate a pooled effect or enumerate all relevant studies, but to extract transferable causal structure from a small set of directly relevant sources. Three source clusters are prioritized. First, format-dependent persuasion evidence is taken from studies comparing brand placement, television advertising, and combined exposure because those designs isolate how disclosure and interruption alter persuasion. Second, direct-marketing evidence from gambling is used because the opt-out intervention creates a clean contrast between continued exposure and exposure removal in a real-world communication channel. Third, Bayesian-network methodology is used as a belief-based approach for uncertainty-aware attribution in data-poor settings; this source contributes modeling logic and do-operator semantics, not empirically validated treatment effects. [1] [2] [3]

The stem-cell marketing archiving paper is relevant for a different reason. It shows how commercial actors can use persuasive legitimacy cues across digital platforms and how archiving is needed when claims change over time. That literature does not identify causal effects of exposure on behavior, but it is useful for framing identity ambiguity: when commercial representations shift across websites, social media, video, print, and other channels, the same actor may be legible as authoritative in one format and obscure in another. In this protocol, that paper informs the need to preserve channel traces, disclosure text, and message provenance, not the estimation of treatment effects. [5]

3. Conceptual model: channel identity, exposure, and attribution

Let X denote an observed exposure event, C the latent commercial source, F the persuasive format, D the disclosure profile, T the timing relative to the consumer task, and Y the downstream outcome. Cross-channel identity loss occurs when the posterior distribution P(C | X, F, D, T, Z) remains too diffuse for credible assignment to a single attribution class, where Z denotes any auxiliary provenance data such as identifiers, archived creative material, or account metadata. In this protocol, an attribution class is a joint construct defined by source identity and disclosure regime, not source identity alone. The proposed causal question is therefore conditional: under what conditions should an observed outcome Y be attributed to a source-disclosure class rather than to undifferentiated commercial exposure? Framing the problem this way permits the analyst to distinguish same-source exposures that remain causally different because their disclosure conditions differ materially. [1] [2] [4] [5]

The protocol distinguishes three exposure mechanisms. Embedded persuasion is a format in which commercial content appears inside entertainment or informational material; its persuasive force depends partly on whether audiences recognize the commercial intent. Direct marketing is a solicited or unsolicited message delivered through email, text, push notification, or similar contact that can be turned off or restricted. Targeted advertising is a matching process that uses consumer data or search behavior to allocate message delivery, so the relevant causal unit is not only the ad itself but the consumer state that makes the ad more or less effective. These mechanisms can coexist in one consumer trajectory, which is why channel identity loss is not a measurement nuisance but the central object of inference. [1] [2] [4]

4. Proposed variables and operational definitions

The protocol defines four variable blocks. First, channel-identity variables: source legibility (the degree to which the commercial source is explicitly disclosed), format salience (the extent to which the message interrupts versus blends into surrounding content), provenance certainty (the analyst’s posterior probability that two exposures share a commercial source), and disclosure discrepancy (the absolute difference between the disclosure profile of two exposures). Second, consumer-state variables: attitude toward advertising, baseline receptivity to persuasion, search intensity, and prior exposure history. Third, implementation-context variables: organizational readiness for channel tracking, measurement capability, and regulatory literacy. Fourth, outcomes: brand attitude, purchase intention, betting frequency, gambling expenditure, short-term harm, and any channel-specific behavioral response judged relevant to the application domain. [1] [2] [6] [4]

Primary operational rule. Two exposure events x1 and x2 are assigned to the same attribution class only if both conditions hold: (i) P(C1 = C2 | x1, x2, Z) >= theta and (ii) |D1 - D2| <= 1, where theta is fixed prospectively before outcome analysis. The default preregistered value is theta = 0.80; sensitivity analyses may repeat the full analysis at theta = 0.70 and theta = 0.90 without changing any other specification. The disclosure scale D is coded ordinally as 0 = no observable disclosure of commercial source, 1 = indirect or weak disclosure, 2 = clear disclosure embedded within content or interface, and 3 = explicit stand-alone commercial communication. For a mixed-format exposure in which multiple disclosure cues appear during one encounter, coding proceeds by time segmentation rather than by a single highest or lowest cue. Let the encounter be partitioned into contiguous segments k = 1,...,K, each with duration wk and disclosure level dk. The primary encounter-level disclosure score is D* = round(sum_k wk dk / sum_k wk), with standard half-up rounding to the nearest integer; if durations are unavailable, segments are weighted equally by count under a prespecified fallback rule. In addition, any encounter that contains both dk <= 1 and dk >= 3 is flagged as disclosure-heterogeneous. A same-class assignment is permitted only when both encounters satisfy the posterior threshold and either neither encounter is disclosure-heterogeneous or both have the same D* and the same heterogeneity flag. Sensitivity analyses may replace D* with the maximum segment disclosure and the minimum segment disclosure, respectively, while keeping all other rules fixed. If source identifiers are tied or contradictory, the event pair is classified as unresolved regardless of a high model posterior; verified contradictory identifiers cannot be overridden probabilistically. This rule is proposed in this manuscript; it is not attributed to prior literature. [3] [1]

Consumer information search is represented as a latent intensity parameter that may be estimated from observed query frequency, time spent on comparison pages, number of cross-brand comparisons, and self-reported search effort. In applications that include a survey extension, implementation-context covariates enter the model only under a prespecified selection rule: organizational readiness is measured and modeled when event logging depends on internal tracking infrastructure or staff procedures, and regulatory literacy is measured and modeled when disclosure compliance or opt-out rights vary in ways that could alter either exposure definition or reporting accuracy. If neither condition is met, these covariates are excluded from the primary model and reserved for descriptive context. This restriction is intended to prevent post hoc covariate inclusion in attribution analysis. [4] [6]

5. Proposed causal model and algorithm

The primary provenance model is a finite categorical Bayesian classifier for the pair state same-source versus different-source. Freeze a joint pattern vocabulary covering verified identifier agreement, disclosure profile and archived source cues; include missingness as explicit categories. On a consented, independently labeled calibration partition, estimate the joint pattern probability within each class using symmetric Dirichlet-one smoothing, and class priors from smoothed class counts. Bayes’ rule then yields the same-source posterior. Unseen patterns use the registered smoothed vocabulary rather than an improvised independent-feature factorization. This is a predictive provenance model, not a causal graph. Expert beliefs may be reported as a separate sensitivity specification, never as empirically calibrated accuracy. A known contradictory verified source identifier forces unresolved status regardless of the model score. Freeze all vocabulary, counts and thresholds before the held-out evaluation. [3] [2] [1]

Algorithmic sequence. Step 1: define all exposure events with timestamps, provisional channel labels, disclosure features, and source identifiers where available. Step 2: archive or otherwise preserve mutable channel traces when feasible so that provenance coding can be audited later. Step 3: for each encounter, segment the exposure timeline whenever disclosure status, source cue, or format changes; record each segment's duration where available, then compute the encounter-level disclosure score and heterogeneity flag under the preregistered rule. Step 4: encode each event into the channel-identity graph and specify whether format is modeled as a single categorical state or as concurrent binary components. Step 5: obtain structured priors for uncertain edges; if priors come from expert elicitation, record the elicitation protocol and retain those priors as belief-based inputs. Step 6: compute posterior provenance certainty for each event pair. Step 7: apply the preregistered attribution rule to classify pairs as same class, different class, or unresolved. Step 8: estimate the target causal contrast separately within each application: randomized contrasts when assignment is available, opt-out contrasts when channel removal is randomized, and posterior counterfactual simulation only when its identifying assumptions are explicitly accepted. Step 9: report estimates separately for directly observed classes, probabilistically assigned classes, and unresolved cases, with resolved-only descriptive analyses explicitly conditional on resolution and accompanied by resolution coverage; a randomized intention-to-treat channel contrast retains all assigned units, including unresolved provenance. [3] [2] [5]

The model assumes stable channel semantics over the observation window, meaning that a channel labeled as direct marketing or brand placement retains a relatively consistent disclosure structure within the study period. It also assumes that consumer search is not fully determined by the exposure under study, because search can mediate, moderate, or confound targeting effects depending on timing. These assumptions are testable through sensitivity analysis: if disclosure varies too sharply over time or if search reacts immediately to exposure in a way that destroys temporal ordering, attribution should be downgraded to descriptive association. [4] [1]

6. Comparator logic and evidence transfer across the three source domains

The relevant comparator is not a single control condition across all applications, but the best available contrast for each channel class. For embedded persuasion, the comparator is conventional television advertising or control exposure, because the question is whether format alters persuasion under similar brand content. For direct marketing, the comparator is continued receipt of messages, because the causal estimand is the effect of removal through opt-out. For targeted advertising, the comparator is lower search intensity or different search environments, because the issue is how consumer information behavior modifies ad performance. These comparators are not interchangeable, and the protocol preserves that distinction rather than forcing all channels into one summary effect. [1] [2] [4]

The transfer from prior work is therefore structural. The persuasion study contributes a moderation logic: format effects depend on audience predispositions, so attribution should include consumer-level receptivity rather than assuming a uniform channel effect. The gambling study contributes a causal-manipulation logic: removing one channel can reveal whether that channel is causally relevant in a live environment. The Bayesian-network study contributes uncertainty handling: when data are sparse or causally mixed, expert belief can be formalized and updated instead of being treated as a vague narrative. The AI-adoption survey adds a limited but useful lesson about covariates: if channel identity recovery depends on organizational readiness or regulatory literacy, those constructs should be measured directly rather than inferred. [1] [2] [3] [6]

7. Validation design, outcome measures, and failure cases

Validation is prospective and should proceed in three stages with explicit success criteria. First, internal coherence asks whether the fitted model reproduces prespecified directional patterns that match prior source logic: lower outcomes under direct-marketing opt-out than under continued direct marketing, audience-by-format moderation in persuasion, and theoretically predicted search-related shifts only as qualitative sign checks rather than empirical benchmarks. Second, construct validity asks whether independent coders and respondents can apply the channel-identity scale consistently; failure is defined in advance as persistent disagreement that prevents stable assignment of disclosure levels or attribution classes. Third, counterfactual validity requires a prospective study in which at least one channel state can be randomized or disabled while the remaining channels are observed with timestamps adequate for provenance coding. This manuscript specifies the test conditions and failure criteria as a design proposal only; no empirical validation is claimed. [1] [2] [4] [3]

Primary outcome measures should differ by domain but remain comparable at the level of attribution. In persuasion settings, the main outcomes are brand attitude and purchase intention. In gambling settings, the main outcomes are betting count, expenditure, and short-term harm. In targeted-advertising settings, the main outcomes are conversion, choice efficiency, and any shift in ad effectiveness conditional on search intensity. A cross-domain secondary outcome is attribution certainty, defined as the posterior probability mass assigned to the independently known channel class on a consented ground-truth or synthetic benchmark; without such a reference, report posterior concentration rather than accuracy. This is essential because a model that predicts outcomes well but mislabels the channel cannot answer the causal question posed by cross-channel identity loss. [1] [2] [4]

Failure cases are expected. The model will underperform when channels converge too closely in disclosure, for example when a placement is heavily branded, a direct message is highly personalized, and targeted ads are delivered immediately after consumer search. It will also fail when the analyst lacks event-level timestamps or source provenance, when consumer self-reports cannot distinguish recall from attribution, or when organizational readiness is so weak that channel logging is incomplete. Generalization is limited to settings where commercial channels are observable enough to define a provenance graph. It does not generalize automatically to fully opaque recommendation systems, covert influence operations, or historical archives in which metadata are missing and only residual traces remain. [5] [3] [6]

Identification and validation boundary

A high same-source posterior is evidence of model confidence, not proof of the correct commercial channel. Evaluate calibration, discrimination and resolution coverage on held-out pairs with independent source truth. In real traffic without that truth, correctness is unavailable. A behavioral comparison limited to resolved events can be selected by disclosure or logging quality and is not an unbiased causal effect. Causal claims require an independently justified randomized assignment or an observational identification design; posterior graph simulation alone does not supply one. Expected effect directions from persuasion, gambling or search studies are hypotheses, not validation labels. Report those domains separately. The protocol’s testable contribution is a reproducible provenance-and-uncertainty workflow, with an explicit unresolved state and audit trail, rather than a demonstrated solution to cross-channel causal attribution.

8. Discussion: what the protocol establishes and what remains untested

This manuscript does not establish an empirical conclusion about cross-channel attribution; it proposes a framework for studying that problem. The cited literature contributes different inputs to the proposal. Experimental persuasion research indicates that embedded and explicit advertising can differ in effect because format shapes interpretation and because attitude toward advertising moderates that contrast. Randomized gambling-marketing research indicates that removing direct marketing can change short-term behavior and harm in a live environment. The targeted-advertising/search source contributes a theoretical mechanism in which consumer search may alter advertising performance under stated assumptions, which justifies modeling search as part of attribution even though the relationship has not been empirically validated by that source. The archiving literature adds a practical requirement: when commercial claims move across channels and change over time, provenance preservation is necessary for later causal analysis. [1] [2] [4] [5]

What remains untested is the full protocol itself. The proposed threshold rule, Bayesian network, survey constructs, and validation sequence have not yet been evaluated in a unified cross-channel study. In particular, the manuscript does not claim that the 0.80 provenance threshold is optimal, that the suggested channel-identity scale is sufficient for every market, or that expert elicitation can replace direct experimental evidence. Those are hypotheses for prospective testing. The bounded contribution of this paper is to define a falsifiable framework for attribution under identity loss and to specify how evidence from persuasion, gambling marketing, targeted advertising, and legitimacy-cue archiving can be assembled without collapsing their methodological differences. [3] [1] [2] [4] [5]

References

1. Li, Linshang (2026). From entertainment to persuasion: how attitudes toward advertising shape responses to brand placement and television advertising. Frontiers in Psychology. 17, 1963379. doi:10.3389/fpsyg.2026.1963379.
2. Rockloff, Matthew; Browne, Matthew; Hing, Nerilee; Russell, Alex M. T.; Rawat, Vijay; Newall, Philip (2026). Direct gambling marketing, direct harm: A randomised experiment. Addiction. 121(7), 1907-1919. doi:10.1111/add.70369.
3. Albtoush, Faten; Al-Btoosh, Ja’far A. Aldiabat; Rawashdeh, Taiseer Mustafa; Al-Btoush, Mohammed A. K. A. (2026). Assessing the impact of AI-enabled BIM digital twins on construction risks: a Bayesian Network of Jordanian expert beliefs. Frontiers in Artificial Intelligence. 9, 1846388. doi:10.3389/frai.2026.1846388.
4. Dan, Wu; Jiang, Zhao (2026). The complementary-competitive interplay of consumer information search and experience sharing: Implications for targeted advertising and firm performance. PLOS One. 21(10), e0340849. doi:10.1371/journal.pone.0340849.
5. Turner, Leigh (2026). Digital Archiving of Direct-to-Consumer Marketing Claims Made by Businesses Selling Unproven Stem Cell Interventions. Journal of Medical Internet Research. 28, e95156-e95156. doi:10.2196/95156.
6. Boruga, Veronica Madalina; Bratu, Melania Lavinia; Puenea, George; Popa, Daniel; Popa, Cristina Annemari; Bogdan, Iulia Georgiana; Savencu, Cristina Elena (2026). Organizational Readiness, Perceived Usefulness, and Determinants of Artificial Intelligence Adoption in Romanian Medical Management and Pharmaceutical Marketing. Healthcare. 14(12), 1714. doi:10.3390/healthcare14121714.