A Bayesian Model Explains Why Order Changes What Touch Feels Like

If two vibrations arrive in a row, the first one can change how strong the second feels. That order effect has long been a puzzle in haptic perception, where people judge pairs of sequential stimuli differently depending on which comes first. This paper introduces a dynamical Bayesian model, meaning a model that blends noisy sensory input with an internal estimate that keeps evolving over time. Tested on vibrotactile discrimination experiments, it reproduced both the direction and the size of these time-order effects across subjects, along with the differences between individuals, using only a small number of parameters. The fitted parameters also gave a compact readout of each person’s prior expectations and noise characteristics. Beyond matching the data, the model reshaped stimulus space itself, revealing a subject-dependent geometry of perceived touch. In that transformed space, the judgments showed approximate symmetries that are missing in the raw physical stimulus coordinates, suggesting that temporal bias is built into how the mind infers touch.

Two vibrations in a row can feel different just because of order. A first pulse can make the second seem stronger or weaker, even when the physical signal stays the same. If you have ever used a phone that buzzes twice, you know the first buzz can set the tone. The next buzz may feel different. This paper asks why that happens in haptic perception, the sense of touch. It treats the brain as a guess-making system. That guess changes after each pulse and keeps drifting in between. The surprise is that the order effect can come from that moving guess, not from the touch itself.

When the first buzz sets the rules

The model matched real vibrotactile data, the kind where people compare two brief buzzes. Vibrotactile means touch through vibration. Time-order effects mean the first stimulus changes how the second feels. The model used a noisy first readout of each stimulus. It then updated an internal level of expected intensity. Expected intensity means the brain's built-in guess about strength. It also let that guess drift between pulses. With that setup, the same framework reproduced the direction and size of time-order effects across subjects. It also captured how people differed from one another. It did this with a small number of parameters, the knobs the model tunes to fit data. Those fitted knobs gave a compact readout of prior expectations and noise. The model also bent stimulus space. Stimulus space means the map of possible touch values. That map became subject-specific. In that new shape, judgments became nearly symmetric. The raw physical values lacked that symmetry.

How a moving guess turns into bias

Bayesian means the model starts with a guess and revises it with evidence. Here, that guess is the expected touch strength. Each incoming vibration gives a noisy measurement, like a blurry reading on a cheap scale. The model updates its guess after each reading. Then it lets that guess move on its own between events. That moving part is the dynamical piece. It matters because the second stimulus does not meet a blank slate. It meets a brain state already changed by the first one. The fit used psychophysical data, meaning choice data from human perception tests. Once fit, it could predict order bias for different people with the same small set of knobs.

Why a new map of touch matters

This matters because the model does more than fit a curve. It gives a clean way to talk about bias as a mix of expectation and noise. That helps explain why two people can feel the same inputs and still disagree. The fitted knobs separate a person's guess about touch from the roughness of the signal itself. The transformed stimulus space is also useful. It shows that judgments can look messy in raw values, then become nearly regular after the model bends them. So the strange order effect is not just error. It is part of the map the brain uses to compare touch.

What to test next

The same idea points to a practical test for haptic design. A touch cue is not just a value. It is a sequence. That means the order of pulses may matter as much as their strength. A pattern that feels clear one way may not feel clear in reverse. So touch interfaces should be tested as sequences, not single taps. That surprise comes back here. The brain does not read touch like a frozen number. It keeps a moving guess, and that guess bends what comes next.