# Bayesian regression explains how human participants handle parameter uncertainty

## TL;DR

This study demonstrates that humans perform Bayesian regression when predicting a parabola from noisy data, effectively incorporating prior knowledge and likelihood, aligning with the optimal Bayesian solution.

## Contribution

It provides empirical evidence that humans utilize Bayesian regression in a parameter uncertainty task, advancing understanding of human probabilistic reasoning.

## Key findings

- Humans perform Bayesian regression in the task.
- Participants' behavior aligns with sophisticated Bayesian models.
- Humans incorporate prior knowledge and likelihood in predictions.

## Abstract

The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter uncertainty into account in a regression task. Participants extrapolated a parabola from a limited number of noisy points, shown on a computer screen. The quadratic parameter was drawn from a prior distribution, unknown to the observers. We tested whether human observers take full advantage of the given information, including the likelihood function of the observed points and the prior distribution of the quadratic parameter. We compared human performance with Bayesian regression, which is the (Bayes) optimal solution to this problem, and three sub-optimal models, namely maximum likelihood regression, prior regression and maximum a posteriori regression, which are simpler to compute. Our results clearly show that humans use Bayesian regression. We further investigated several variants of Bayesian regression models depending on how the generative noise is treated and found that participants act in line with the more sophisticated version.