🧠 neuroscience

Non-decision time-informed collapsing threshold diffusion model: A joint modeling framework with identifiable time-dependent parameters

This paper proposes a joint modeling framework that links non-decision time to external EEG measurements to resolve parameter estimation unreliability in time-dependent threshold diffusion models, thereby enabling robust inference of individual differences in decision dynamics.

Original authors: Hadian Rasanan, A. H., Schumacher, L., D Nunez, M., Weindel, G., Rieskamp, J.

Published 2026-06-05

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CC BY 4.0

Original authors: Hadian Rasanan, A. H., Schumacher, L., D Nunez, M., Weindel, G., Rieskamp, J.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine your brain as a busy courtroom where a jury is trying to decide a verdict. For decades, scientists have used a specific "rulebook" to understand how this jury works. The rulebook says the jury gathers noisy, confusing clues (evidence) and keeps adding them up until they hit a fixed "guilty" or "not guilty" line. Once that line is crossed, a decision is made.

However, new research suggests this rulebook is a bit too rigid. In real life, juries don't wait for a fixed line; they get impatient or more cautious as time passes, meaning the "line" they need to cross actually moves up and down. This is called a time-dependent threshold.

The Problem: A Foggy Mirror
The trouble is, when scientists try to measure exactly how this moving line behaves, the results are like looking at a reflection in a foggy mirror. The numbers come out unreliable and shaky. Because of this, researchers have mostly stopped trying to interpret what those numbers mean for individual people, focusing instead on just comparing which model looks better on paper.

The Solution: A New Detective Tool
This paper introduces a clever new way to clear up that fog. The authors propose a "joint modeling" approach. Think of it like this:

Imagine the jury's decision process is a race. Part of the race is the actual thinking (gathering evidence), and another part is the time it takes to get the verdict written down and announced (called non-decision time).

In the past, scientists had to guess how long that "writing down" part took, which made the whole race time hard to calculate accurately. In this new study, the researchers brought in an outside witness: EEG brain scans.

They used a special digital method to "listen" to the brain's electrical signals and extract a noisy, but real-time measurement of exactly how long that "writing down" part took for every single trial. They then fed this information directly into their mathematical model.

The Result: A Sharper Picture
By telling the model, "Hey, we know exactly how long the writing took for this specific trial," the model no longer has to guess. It can focus its energy on figuring out how the moving decision line actually behaves.

The authors tested this in two ways:

Simulations: They created fake data to prove that adding these brain-scan measurements makes the math much more reliable and stable.
Real Experiments: They re-analyzed data from two real experiments where people made visual decisions. By using the brain signals to pin down the "writing time," they found two things:
- They could finally get reliable numbers for how the decision threshold changes over time.
- The model fit the actual human behavior much better than before.

In Short
The paper doesn't claim to cure diseases or predict the future. It simply says: "If you want to understand how our decision-making 'moving line' works, stop guessing the time it takes to finish the paperwork. Use brain scans to measure that time directly, and your math will finally make sense."

Technical Summary: Non-decision time-informed collapsing threshold diffusion model

Problem Statement
Evidence accumulation models have served as a dominant framework for sixty years in explaining the neural and behavioral mechanisms of decision-making, frequently acting as measurement instruments for latent cognitive constructs. A foundational assumption of these models is that decision-makers accumulate noisy evidence until a fixed decision threshold is reached. However, behavioral, neuroscientific, and theoretical optimality considerations suggest that decision thresholds are not static but vary over time. While time-dependent threshold models often provide superior accounts of empirical data compared to fixed-threshold models, they suffer from a critical limitation: the unreliable estimation of their parameters. This estimation instability has forced researchers to prioritize model-fitting comparisons over the interpretation of specific parameter values or the analysis of individual differences in decision threshold dynamics.

Methodology
To address the reliability issues inherent in time-dependent threshold diffusion models, the authors propose a joint modeling framework that integrates external observations of non-decision time ( $t_{nd}$ ) directly into the model. The core innovation lies in linking the diffusion model to trial-level, noisy measurements of non-decision time derived from electroencephalography (EEG) recordings. These non-decision time measurements were extracted using the hidden multivariate pattern method. By constraining the non-decision time parameter with these external EEG-based observations, the framework aims to stabilize the estimation of the remaining time-dependent threshold parameters.

Key Contributions and Results
The paper presents two primary lines of evidence supporting the proposed framework:

Parameter Recovery Simulations: The authors conducted simulations demonstrating that informing the diffusion model with trial-level noisy measurements of non-decision time substantially improves the reliability of parameter estimation for time-dependent threshold models. This approach effectively mitigates the estimation instability that has historically plagued such models.
Empirical Reanalysis: The framework was applied to reanalyze experimental data from two perceptual decision-making tasks. The results confirmed the feasibility of the approach, showing that constraining non-decision time not only enables reliable parameter estimation but also improves the absolute fit to behavioral data.

Significance
The paper claims that this joint modeling approach resolves a long-standing barrier in the application of time-dependent threshold models. By enabling reliable parameter estimation, the framework allows researchers to move beyond simple model-comparison metrics and begin interpreting specific parameter values. Furthermore, it opens the door to investigating individual differences in the dynamics of the decision threshold, a capability that was previously hindered by estimation unreliability. The work demonstrates that integrating neurophysiological data (EEG) with behavioral modeling can enhance both the statistical robustness and the explanatory power of evidence accumulation models.

Technical Summary: Non-decision time-informed collapsing threshold diffusion model

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