## Maximum likelihood estimation of a stochastic
integrate-and-fire neural encoding model*

Neural Computation 16:
2533-2561 (2004).

We examine a cascade encoding model for neural response in which a
linear filtering stage is followed by a noisy, leaky,
integrate-and-fire spike generation mechanism. This model provides a
biophysically more realistic alternative to models based on Poisson
(memoryless) spike generation, and can effectively reproduce a variety
of spiking behaviors seen {\it in vivo}. We describe the maximum
likelihood estimator for the model parameters, given only
extracellular spike train responses (not intracellular voltage data).
Specifically, we prove that the log likelihood function is concave and
thus has an essentially unique global maximum that can be found using
gradient ascent techniques. We develop an efficient algorithm for
computing the maximum likelihood solution, demonstrate the
effectiveness of the resulting estimator with numerical simulations,
and discuss a method of testing the model's validity using
time-rescaling and density evolution techniques.

**Note: we recently re-examined the proof of theorem 1 in the
paper, and we have found a questionable step. The statement of
log-concavity in all variables except for the membrane conductance g
remains unchanged (ie, the likelihood is unimodal in all the other
variables if g is held fixed); however, we are no longer sure whether
the statement about unimodality in g holds. We'll publish an update
once the situation is more clear.

Reprint (600K, pdf) | Liam
Paninski's research page

Related work on likelihood-based
estimation of neural models| on
the integrate-and-fire cell

*A short version of this work appeared in the NIPS 2003 proceedings.