  The process of dynamic state estimation (filtering) based on point process
observations is in general intractable. Numerical sampling techniques are often
practically useful, but lead to limited conceptual insight about optimal
encoding/decoding strategies, which are of significant relevance to
Computational Neuroscience. We develop an analytically tractable Bayesian
approximation to optimal filtering based on point process observations, which
allows us to introduce distributional assumptions about sensor properties, that
greatly facilitate the analysis of optimal encoding in situations deviating
from common assumptions of uniform coding. Numerical comparison with particle
filtering demonstrate the quality of the approximation. The analytic framework
leads to insights which are difficult to obtain from numerical algorithms, and
is consistent with biological observations about the distribution of sensory
cells' tuning curve centers.
