  To make informed decisions in natural environments that change over time,
humans must update their beliefs as new observations are gathered. Studies
exploring human inference as a dynamical process that unfolds in time have
focused on situations in which the statistics of observations are
history-independent. Yet temporal structure is everywhere in nature, and yields
history-dependent observations. Do humans modify their inference processes
depending on the latent temporal statistics of their observations? We
investigate this question experimentally and theoretically using a change-point
inference task. We show that humans adapt their inference process to fine
aspects of the temporal structure in the statistics of stimuli. As such, humans
behave qualitatively in a Bayesian fashion, but, quantitatively, deviate away
from optimality. Perhaps more importantly, humans behave suboptimally in that
their responses are not deterministic, but variable. We show that this
variability itself is modulated by the temporal statistics of stimuli. To
elucidate the cognitive algorithm that yields this behavior, we investigate a
broad array of existing and new models that characterize different sources of
suboptimal deviations away from Bayesian inference. While models with 'output
noise' that corrupts the response-selection process are natural candidates,
human behavior is best described by sampling-based inference models, in which
the main ingredient is a compressed approximation of the posterior, represented
through a modest set of random samples and updated over time. This result comes
to complement a growing literature on sample-based representation and learning
in humans.
