Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

By M. Jarvis, Partha P. Mitra. Neural Computation, 2000

425 citations recorded by the source corpus.

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This article begins with a review of these quantities, their interpretation, and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low-variance gaussian process. It is found that in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus. Although the material discussed is of general applicability to point processes, attention will be confined to sequences of neuronal action potentials (spike trains), the motivation for this work.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience

View Paper: https://www.semanticscholar.org/paper/c56b0539c07a33912185918d1bb611c360421ad2

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In Cellular and Molecular Neuroscience

In Cognitive Neuroscience

Citations in the corpus

Localizing human visual gamma-band activity in frequency, time and space (2006, methodology): “We achieved this by using multi-taper spectral analysis techniques (Mitra and Pesaran, 1999; Jarvis and Mitra, 2001; Pesaran et al., 2002).”
Correcting for the sampling bias problem in spike train information measures. (2007, methodology): “To analyze prediction accuracy on different timescales, we used spectral coherence (Jarvis and Mitra 2001).”
Neurophysiological and Computational Principles of Cortical Rhythms in Cognition (2010, background): “In the cortex, especially in awake behaving conditions, even when a synchronous oscillation is detected in LFP, it is often not readily discernable in highly irregular spike trains of single units (468, 706).”
Nonlinear multivariate analysis of neurophysiological signals. (2005, methodology): “Additionally, specific methods have been derived for the reliable estimation of the coherence function as well as its confident limits in point processes such as sequences of neural action potentials (Jarvis and Mitra, 2001; Pesaran et al., 2002).”
Different Origins of Gamma Rhythm and High-Gamma Activity in Macaque Visual Cortex (2011, methodology): “Details and properties of this method can be found here [21,22].”
Spike Synchrony Reveals Emergence of Proto-Objects in Visual Cortex (2015, methodology): “…between pairs of spikes, or between spikes and LFPs, was measured in the period from 400 to 1050 ms after stimulus onset using the multitaper method (Mitra and Pesaran, 1999; Jarvis and Mitra, 2001), with functions modified from the Chronux data analysis toolbox for Matlab (www.chronux.org).”
Oscillatory synchronization in large-scale cortical networks predicts perception. (2011, positive): “Thus, before statistical testing, we applied a nonlinear transform (Jarvis and Mitra, 2001) that renders the distribution approximately Gaussian.”
Gamma and beta bursts underlie working memory (2016, positive): “…et al., 1996) as well as multi-taper analysis (with a family of orthogonal tapers produced by Slepian functions; Slepian, 1978; Thomson, 1982; Jarvis and Mitra, 2001) and bandpass filtering techniques (Butterworth filter of order 4-6 applied in the forward and reverse directions to obtain…”
Mechanisms of Gamma Oscillations (2012, background): “…are needed to distinguish between a power increase resulting from genuine oscillations and an increase resulting from greater spiking activity ( Jarvis & Mitra 2001, Crone et al. 2006, Montgomery et al. 2008, Whittingstall & Logothetis 2009, Quilichini et al. 2010, Belluscio et al. 2012, Ray &…”
Odor representations in olfactory cortex: "sparse" coding, global inhibition, and oscillations. (2009, methodology): “spectra with confidence limits were calculated using multitapered methods (Jarvis and Mitra, 2001) and the Chronux package (NIMH).”
The Natural Statistics of Audiovisual Speech (2009, background): “Coherence is a metric, which estimates the relationships between two time series as a function of frequency and does not have normalization problems [10,29].”
Temporal structure in neuronal activity during working memory in macaque parietal cortex (2000, background): “Correlation functions are often estimated in the time domain to detect temporal structure but are well known to suffer serious problems of bias and variance which are exacerbated in the context of a behaving animal (Jarvis and Mitra, 2000).”