  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.
