AUTHOR=Gerwinn Sebastian , Macke Jakob H., Bethge Matthias TITLE=Bayesian population decoding of spiking neurons JOURNAL=Frontiers in Computational Neuroscience VOLUME=Volume 3 - 2009 YEAR=2009 URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/neuro.10.021.2009 DOI=10.3389/neuro.10.021.2009 ISSN=1662-5188 ABSTRACT=The timing of action potentials in spiking neurons depends on the temporal dynamics of their inputs and contains information about temporal fluctuations in the stimulus. Leaky integrate-and-fire neurons constitute a popular class of encoding models, in which spike times depend directly on the temporal structure of the inputs. However, optimal decoding rules for these models have only been studied explicitly in the noiseless case. Here, we study decoding rules for probabilistic inference of a continuous stimulus from the spike times of a population of leaky integrate-and-fire neurons with threshold noise. We derive three algorithms for approximating the posterior distribution over stimuli as a function of the observed spike trains. In addition to a reconstruction of the stimulus we thus obtain an estimate of the uncertainty as well. Furthermore, we derive a `spike-by-spike' online decoding scheme that recursively updates the posterior with the arrival of each new spike. We use these decoding rules to reconstruct time-varying stimuli represented by a Gaussian process from spike trains of single neurons as well as neural populations.