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REVIEW 3 major objections 5 minor 29 references

A computational framework for integrating Predictive processes with evidence Accumulation Models (PAM)

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read PAM couples Bayesian beliefs to decision models and recovers parameters accurately.

desk verdict Useful modular toolbox joining HGF to EAMs, with open code and honest recovery checks; the LNR/RDM validation rides on a Ter=0 assumption that real data will violate. read the letter →

arxiv 2411.13203 v2 pith:POZDY6GV submitted 2024-11-20 stat.AP

Antonino Visalli , Francesco Maria Calistroni , Margherita Calderan , Francesco Donnarumma , Marco Zorzi , Ettore Ambrosini This is my paper · ORCID
classification stat.AP
keywords EvidenceaccumulationmodelsPredictiveprocessingHierarchicalGaussianFilterDriftdiffusionmodelParameterrecoveryBayesianinferenceDecision-makingComputationalmodeling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

PAM is a computational framework for joining predictive, Bayesian accounts of learning with standard evidence-accumulation models of speeded choice. The paper's target is to show that the two modeling traditions can be coupled in a way that is both valid and practical: the trial-by-trial beliefs produced by a Hierarchical Gaussian Filter are used to modulate decision parameters of the Drift Diffusion Model, the Lognormal Race Model, and the Racing Diffusion Model. Parameter recovery simulations across fast and slow, easy and hard scenarios show highly accurate recovery of both learning and decision parameters. A tutorial with real random-dot-motion data illustrates the workflow and shows that models in which prior belief modulates drift rate outperform models in which it modulates starting point or boundary. If correct, PAM gives researchers a tool to estimate how predictions shape decisions from choice and response-time data alone.

What carries the argument

The load-bearing object is the trial-wise coupling equation between the perceptual model's inferred states and the EAM's parameters: predicted belief (and its precision) enters each decision parameter through centered linear terms, e.g. $v(t) = a_v + b_v(\hat{\mu}(t) - 0.5)$ for drift, with analogous expressions for start point, boundary, lognormal means, and racing-diffusion thresholds. The Hierarchical Gaussian Filter supplies the trial-wise belief trajectory and precision from the stimulus sequence; the EAM supplies the likelihood of the observed response time and choice. These pieces are optimized jointly with a quasi-Newton maximum-a-posteriori routine, which is what lets the framework estimate learning and decision parameters at the same time.

What would settle it

Simulate LNR and RDM datasets with a known nonzero non-decision time, for example 150 ms, and fit them with the framework's default Ter = 0; if the recovered belief slopes or drift and boundary intercepts shift systematically away from their true values, the central recovery claim fails for realistic data.

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Extended reading notes

Core claim

The central claim is that predictive processes can be integrated into evidence accumulation models without losing identifiability. In PAM, predicted belief about the stimulus, $\hat{\mu}(t)$, and the precision of that belief are inserted as linear modulators of the decision model's parameters: for the DDM they shift start point, boundary, and drift; for the LNR they shift the lognormal means of the two accumulators; for the RDM they shift both accumulator thresholds and drift rates. The perceptual and decision parameters are then estimated jointly by maximum a posteriori optimization. The paper reports that in every simulated scenario and with every decision model the recovery was highly accurate, with the belief-modulation slopes being the least precise but still within confidence intervals, and that the winning model on real data modulated drift rather than starting point.

Load-bearing premise

The recovery results for the LNR and RDM assume that non-decision time can be fixed at zero without bias, even though the model's own estimates show non-decision time highly correlated with LNR parameters, so a real participant's meaningful encoding or motor time could confound the recovered belief effects.

Editorial extensions

If this is right

  • Researchers can estimate a participant's Bayesian learning rate and decision parameters in a single fit from choice and response-time data.
  • The framework makes it possible to test competing hypotheses about where predictions act, since models that modulate start point, boundary, or drift can be compared with Bayesian model selection.
  • Because recovery was accurate across fast and slow, high- and low-accuracy scenarios, PAM can be applied to a wide range of two-choice speeded decision tasks.
  • The modular setup extends beyond the three demonstrated EAMs and beyond the Hierarchical Gaussian Filter, with other perceptual models already supported.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's claims, if the recovery results generalize, PAM could be used to re-examine existing expectation effects in diffusion-model studies, asking whether effects previously attributed to start-point shifts are better described as drift-rate modulations.
  • A testable extension the authors do not report is whether fixing non-decision time at zero for the LNR and RDM biases recovered belief slopes when real participants have non-negligible encoding or motor time; simulating nonzero non-decision time would settle this.
  • The centered linear coupling could be replaced by nonlinear or precision-weighted forms, and Bayesian model comparison across such variants would show whether the linear assumption is a real constraint or a harmless convenience.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript introduces PAM, a computational framework that couples a Hierarchical Gaussian Filter perceptual model with three evidence accumulation models (DDM, LNR, RDM), using trial-by-trial beliefs and belief precision to linearly modulate EAM parameters. The paper validates PAM through parameter recovery simulations across different accuracy and response-time scenarios, reports median recovery and confidence intervals for each model, and provides a step-by-step MATLAB tutorial applied to a random-dot kinematogram dataset, including Bayesian model selection among model variants. The central claim is that the framework yields highly accurate parameter recovery in all tested scenarios and with all three decision models, while remaining computationally efficient.

Significance. If the validation claims hold, PAM is a useful and timely contribution: it provides a concrete, open-source implementation bridging predictive-coding style belief models and standard EAMs, with a tutorial that lowers the barrier to adoption. The paper's strengths include the availability of code and data, the use of standard parameter-recovery methodology, and the demonstration of computational efficiency. However, the validation is an internal-consistency check (simulate from the same model, then recover), not a test against independent data, and the headline claim of highly accurate recovery is conditional on a strong auxiliary assumption about non-decision time for the LNR and RDM. The empirical tutorial is illustrative rather than confirmatory, which the authors acknowledge, but the main-text framing of the simulation results should be reconciled with the reported recovery accuracy.

major comments (3)
  1. [Parameter Recovery (LNR and RDM); Model fitting; Tutorial] The central claim that 'in all scenarios and with all the proposed decision models, the results showed highly accurate parameter recovery' is not supported for the LNR and RDM because Ter is fixed to zero in both the simulations and the tutorial default, and the manuscript itself reports that estimating Ter leads to |ρ| > .9 correlations with LNR parameters. Real response times include non-decisional encoding and motor components, as the DDM simulations acknowledge by adding Ter = 0.15 s. If real data contain nonzero Ter, an LNR or RDM that omits it can absorb the shift into location parameters, and because belief trajectories are correlated with the trial sequence, the belief-modulation slopes b and bv can be biased rather than merely shifted. The main text defers the nonzero-Ter analysis to Supplementary Information 1 but does not report its results; this is load-bearing for the quantitative claims of the framework. I request a main-text sensitivity analysis with realistic nonzero Ter values, or a clear restriction of the validation claim to the Ter = 0 case.
  2. [Results – LNR, Table 5] The reported recovery for the LNR slope parameter b contradicts the text's statement that recovery 'deviated by at most 15%.' For example, in the first row of Table 5, the simulated value is b = -1.04 and the median recovered value is listed as -0.63, a deviation of roughly 40% of the true value. Several subsequent rows appear misaligned (e.g., the second row lists an estimated a of 0.28 against a simulated a of -0.53, with what look like true values displaced into parentheses). This makes the LNR recovery results unreliable as reported and undermines the accuracy claim for that model. Please re-run or re-present the table with clearly aligned columns and report the actual deviation values.
  3. [Results – DDM, paragraph on omega2 recovery] The paper simultaneously claims highly accurate recovery and reports that the perceptual parameter ω2 deviates by up to 28% in the reduced model and 14% in the full model, with wide interquartile ranges (e.g., Table 4, first row, reduced model: median -3.14, IQR 1.17, for true ω2 = -4). Because ω2 drives the belief trajectories that modulate the EAM parameters, this imprecision is directly relevant to the joint-model recovery claim. The final remarks should either temper the 'highly accurate' wording to reflect the observed accuracy of the slope and perceptual parameters or provide additional diagnostics (e.g., bias, correlation, or root mean squared error) that justify the characterization.
minor comments (5)
  1. [Model Specifications, Eq. (4)] The sigmoid function s() used in the precision modulation of the boundary separation is not defined in the text; please define it explicitly (e.g., s(x) = 1/(1+exp(-x))).
  2. [Parameter Recovery, Table 7] Table 7's simulated-parameter row appears to contain four values while the header lists three (av, bval, bv), and the first value '-4' is inconsistent with the recovered aa shown as 2.00; please check the column alignment and the table caption (the caption says 'boundary (v)' but v is the drift rate, not the boundary).
  3. [Model fitting] The text states that 'on each dataset (excluding LNR), we carried out two analyses using full and reduced model configurations'; please clarify why the LNR was excluded from the full/reduced comparison and whether full-model LNR results exist in the supplement.
  4. [Introduction] In the sentence 'here we consider the DDR, LNR, and RDM', 'DDR' should be 'DDM'.
  5. [Perceptual model] The sentence 'The HGF, it is a generic computational model' contains a grammatical error; please remove 'it'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the framework's derivation is self-contained, and parameter recovery is a standard internal self-consistency check; the Ter=0 assumption is a robustness limitation, not a circular step.

full rationale

PAM's load-bearing derivation is not circular. The HGF belief trajectory is obtained by variational Bayesian inversion of the stimulus sequence with perceptual parameters (Perceptual model section), while the EAM trial parameters are separate quantities linked by explicit modulation equations (Eqs. 3-5 for the DDM, Eqs. 9-10 for the LNR, and Eqs. 15-18 for the RDM). The validation is a standard parameter-recovery simulation: synthetic data are generated from known parameters and refit, so the reported 'highly accurate parameter recovery' (Final Remarks) is a statement about the estimator's internal consistency, not a prediction against independent data. No fitted parameter is renamed as a prediction, and no equation is defined in terms of the quantity it supposedly derives. The self-citations (Visalli et al., 2023; Viviani et al., 2024) are illustrative empirical applications of the HGF and are not load-bearing premises; no uniqueness theorem from the authors' prior work is invoked to force the modeling choice. The Ter=0 default for the LNR and RDM, introduced because 'the estimated Ter parameter was highly correlated with all the LNR parameters (|ρ| > .9)', is a substantive identifiability limitation for real data with non-zero non-decision time, but it concerns external validity and robustness, not circularity: it does not make the derivation equivalent to its inputs.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The framework rests on standard distributional results (WFPT, lognormal race, Wald first-passage) and on domain assumptions that the HGF captures perceptual inference and that the linear modulation of EAM parameters is appropriate. The most fragile assumptions are the fixed-to-zero Ter for LNR and RDM and the choice of the two-level HGF with a Bayes-optimal prior mean for omega2. No invented entities are introduced.

free parameters (5)
  • HGF omega2 = -4 in simulations; prior mean -2.86 in tutorial
    Controls how quickly beliefs about the environment update; estimated from data jointly with decision parameters.
  • DDM slopes bw, ba, bv = simulated ranges: bw ~0.3 to 0.7, ba ~ -0.7 to -2.8, bv ~0.3 to 2.8
    Slopes of belief and precision effects on starting point, boundary, and drift; the main theoretical quantities.
  • DDM intercepts aa, av, Ter = simulated: aa ~1.1 to 2.0, av ~0.62 to 2.0, Ter 0.15 s
    Baseline boundary separation, drift, and non-decision time; estimated from data.
  • LNR parameters a, bval, b, sigma = simulated: a ~ -0.53 to 0.19, bval ~ -0.47 to -0.2, b ~ -1.04 to 0.53, sigma = 0.25
    Lognormal mean intercept, validity effect, belief slope, and variance; estimated from RT and choice data.
  • RDM parameters aa, av, bval, ba, bv = simulated: aa = 2 to 3, av = 2 to 3.55, bval = 1.16 to 2.5, ba ~ -1.2 to -4.2, bv ~ -1.43 to -4.75
    Boundary and drift intercepts plus belief modulation slopes; estimated from data.
assumptions (7)
  • standard math WFPT first-passage-time densities for the Wiener diffusion model are correct and the Navarro-Fuss approximation is accurate.
    Used in the DDM implementation via Equations 1 and 2.
  • standard math Lognormal race finishing time distributions and Wald first-passage densities are correct.
    Used for the LNR (Eq. 7) and the RDM (Eq. 13).
  • domain assumption HGF variational inversion under the mean-field approximation yields trial-by-trial posterior beliefs.
    The perceptual component; relies on Mathys et al. 2011 and 2014.
  • ad hoc to paper Prior beliefs and their precision linearly modulate EAM parameters (Eqs. 3-5, 9-10, 15-18).
    This is the core integration choice; no derivation or comparison to alternative mappings is given.
  • domain assumption The two-level HGF with kappa = 0 and prior mean omega2 = -2.86 is appropriate for the RDK task.
    Model configuration in the tutorial; assumes volatility is negligible.
  • ad hoc to paper Non-decision time Ter can be fixed to zero for LNR and RDM without biasing estimates.
    Reported Ter-LNR parameter correlations with absolute rho greater than 0.9; simulations and tutorial fix Ter to 0.
  • domain assumption BFGS quasi-Newton optimization converges to the MAP estimate in the joint parameter space.
    Estimation relies on standard optimization; no convergence guarantees for this nonconvex objective.

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Pith. "Pith review of A computational framework for integrating Predictive processes with evidence Accumulation Models (PAM)." pith.science (2026). https://pith.science/paper/POZDY6GV

@misc{pith2026241113203,
  author       = {Pith},
  title        = {Pith review of: A computational framework for integrating Predictive processes with evidence Accumulation Models (PAM)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/POZDY6GV}},
  note         = {Machine review of arXiv:2411.13203}
}
read the original abstract

Evidence Accumulation Models (EAMs) have been widely used to investigate speeded decision-making processes, but they have largely neglected the role of predictive processes emphasized by theories of the predictive brain. In this paper, we present the Predictive evidence Accumulation Models (PAM), a novel computational framework that integrates predictive processes into EAMs. Grounded in the "observing the observer" framework, PAM combines models of Bayesian perceptual inference, such as the Hierarchical Gaussian Filter, with three established EAMs (the Diffusion Decision Model, Lognormal Race Model, and Race Diffusion Model) to model decision-making under uncertainty. We validate PAM through parameter recovery simulations, demonstrating its accuracy and computational efficiency across various decision-making scenarios. Additionally, we provide a step-by-step tutorial using real data to illustrate PAM's application and discuss its theoretical implications. PAM represents a significant advancement in the computational modeling of decision-making, bridging the gap between predictive brain theories and EAMs, and offers a promising tool for future empirical research.

Figures

Figures reproduced from arXiv: 2411.13203 by the authors.

Figure 1
Figure 1. Infographic overview of PAM. PAM is grounded in the “Observing the Observer” framework, which posits that agents attempt to infer hidden environmental causes of their sensory inputs. In this example, participants perform a Random Dot Kinematogram task, where they are required to judge the leftward or rightward direction of dots moving coherently within background noise. To optimize behavior, participants infer the p… view at source ↗

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Reviewed August 12, 2026 · model on record in the stance chip above.