  In a constantly changing world, animals must account for environmental
volatility when making decisions. To appropriately discount older, irrelevant
information, they need to learn the rate at which the environment changes. We
develop an ideal observer model capable of inferring the present state of the
environment along with its rate of change. Key to this computation is an update
of the posterior probability of all possible changepoint counts. This
computation can be challenging, as the number of possibilities grows rapidly
with time. However, we show how the computations can be simplified in the
continuum limit by a moment closure approximation. The resulting
low-dimensional system can be used to infer the environmental state and change
rate with accuracy comparable to the ideal observer. The approximate
computations can be performed by a neural network model via a rate-correlation
based plasticity rule. We thus show how optimal observers accumulate evidence
in changing environments, and map this computation to reduced models which
perform inference using plausible neural mechanisms.
