- Spike Trains as Event Sequences: Fundamental Implications

Abstract

In some parts of the nervous system, especially in the periphery, spike timing in response to a stimulus, or in production of muscle activity, is highly precise and reproducible. Elsewhere, neural spike trains may exhibit substantial variability when examined across repeated trials. There are many sources of the apparent variability in spike trains, ranging from subtle changes in experimental conditions to features of neural computation that are basic objects of scientific interest. When variation is large enough to cause potential confusion about apparent timing patterns, careful statistical analysis can be critically important. In this chapter we discuss statistical methods for analysis and interpretation of synchrony, by which we mean the approximate temporal alignment of spikes across two or more spike trains. Other kinds of timing patterns are also of interest [2, 57, 74, 69, 23], but synchrony plays a prominent role in the literature, and the principles that arise from consideration of synchrony can be applied in other contexts as well. The methods we describe all follow the general strategy of handling imperfect reproducibility by formalizing scientific questions in terms of statistical models, where relevant aspects of variation are described using probability. We aim not only to provide a succinct overview of useful techniques, but also to emphasize the importance of taking this fundamental first step, of connecting models with questions, which is sometimes overlooked by non-statisticians. More specifically, we emphasize that (i) detection of synchrony presumes a model of spiking without synchrony, in statistical jargon this is a null hypothesis, and (ii) quantification of the amount of synchrony requires a richer model of spiking that explicitly allows for synchrony, and in particular, permits statistical estimation of synchrony