Technique(s) for Spike - Sorting
  Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons that can ultimately improve classification performance. In this chapter, after illustrating the spike-sorting problem with real data, we propose a more realistic spike train generation model. It incorporates both a description of "non trivial" (ie, non Poisson) neuronal discharge statistics and a description of spike waveform dynamics (eg, the events amplitude decays for short inter-spike intervals). We show that this spike train generation model is analogous to a one-dimensional Potts spin glass model. We can therefore use the computational methods which have been developed in fields where Potts models are extensively used. These methods are based on the construction of a Markov Chain in the space of model parameters and spike train configurations, where a configuration is defined by specifying a neuron of origin for each spike. This Markov Chain is built such that its unique stationary density is the posterior density of model parameters and configurations given the observed data. A Monte Carlo simulation of the Markov Chain is then used to estimate the posterior density. The theoretical background on Markov chains is provided and the way to build the transition matrix of the Markov Chain is illustrated with a simple, but realistic, model for data generation . Simulated data are used to illustrate the performance of the method and to show that it can easily cope with neurons generating spikes with highly dynamic waveforms and/or generating strongly overlapping clusters on Wilson plots. 
Christophe Pouzat