  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 sensory cell
properties, that greatly facilitates the analysis of optimal encoding in
situations deviating from common assumptions of uniform coding. The analytic
framework leads to insights which are difficult to obtain from numerical
algorithms, and is consistent with experiments about the distribution of tuning
curve centers. Interestingly, we find that the information gained from the
absence of spikes may be crucial to performance.
