0.1 Bound optimization; auxiliary functions . . . . . . . . . . . . . . . . . . . . . 2 0.2 The EM algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.3 EM may be used to optimize the log-posterior instead of the log-likelihood . . 5 0.4 Example: Mixture models and spike sorting . . . . . . . . . . . . . . . . . . . 5 0.5 Example: Spike sorting given stimulus observa...

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical t...

I review a class of hybrid models of neurons that combine continuous spike-generation mechanisms and a discontinuous 'after-spike' reset of state variables. Unlike Hodgkin-Huxley-type conductance-based models, the hybrid spiking models have a few parameters derived from the bifurcation theory; instead of matching neuronal electrophysiology, they match neuronal dynamics. I present a method of af...

Electrical source imaging of interictal spikes observed in EEG recordings of patients with refractory epilepsy provides useful information to localize the epileptogenic focus during the presurgical evaluation. However, the selection of the time points or time epochs of the spikes in order to estimate the origin of the activity remains a challenge. In this study, we consider a Bayesian EEG sourc...

The ability to detect and sort overlapping spike waveforms in extracellular recordings is key to studies of neural coding at high spatial and temporal resolution. Most spike-sorting algorithms are based on initial spike detection (e.g. by a voltage threshold) and subsequent waveform classification. Much effort has been devoted to the clustering step, despite the fact that conservative spike det...

It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as s...