Is this diffusion of particles or heat?

No. x is a psychological decision variable. The mathematics is the same Wiener process, but the absorbing bounds are “choose A” versus “choose B”, and the hitting time is reaction time.

How does starting bias z change behavior?

Starting closer to +a shortens correct RTs and raises the correct-choice rate even when v=0. It models prior expectation or payoff imbalance.

What is the speed–accuracy tradeoff here?

Raising a (or lowering σ) increases accuracy toward 1 but lengthens mean RT roughly like (a/v) tanh(av/σ²) for v≠0. Lowering a does the reverse — fast, error-prone choices.

Drift-Diffusion Reaction Time

Evidence accumulator to ±a bounds: drift, noise, starting bias, RT histograms, accuracy, and speed–accuracy tradeoff.

About this model

The drift–diffusion model accumulates noisy evidence x with dx=v dt+σ dW until it hits absorbing bounds +a (correct) or −a (error). A starting point z encodes bias. Drift v is stimulus strength; bound height a sets the speed–accuracy tradeoff: larger a means slower, more accurate choices. The page runs a live trial and a Monte-Carlo histogram of reaction times, and can overlay the closed-form accuracy and mean decision time for the unbiased Wiener process.

Who it's for: Cognitive psychology, computational neuroscience, and decision-science courses on reaction time.

Key terms

Drift-diffusion model
Evidence accumulation
Decision bound
Bias
Reaction time
Speed-accuracy tradeoff

How it works

Cognitive drift–diffusion: evidence x races to absorbing bounds ±a. Drift, noise, and starting bias set accuracy and reaction time; bound height a is the speed–accuracy tradeoff.

Key equations

dx = v dt + σ dW · x(0) = z, |z| < a · absorb at ±a

P(+a | z=0) = 1 / (1 + exp(−2 a v / σ²)) · v = 0 → 1/2

|v| > 0: T = (a / v) tanh(a v / σ²) · v ≈ 0: T = a² / σ²

Displayed RT = T + Tnd (Tnd ≥ 0 non-decision time)

Frequently asked questions

Is this diffusion of particles or heat?: No. x is a psychological decision variable. The mathematics is the same Wiener process, but the absorbing bounds are “choose A” versus “choose B”, and the hitting time is reaction time.
How does starting bias z change behavior?: Starting closer to +a shortens correct RTs and raises the correct-choice rate even when v=0. It models prior expectation or payoff imbalance.
What is the speed–accuracy tradeoff here?: Raising a (or lowering σ) increases accuracy toward 1 but lengthens mean RT roughly like (a/v) tanh(av/σ²) for v≠0. Lowering a does the reverse — fast, error-prone choices.

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