dorsal/arxiv
View SchemaSampling Properties of the Spectrum and Coherency of Sequences of Action Potentials
| Authors | M. R. Jarvis, P. P. Mitra |
|---|---|
| Categories | |
| ArXiv ID | physics/0002053 |
| URL | https://arxiv.org/abs/physics/0002053 |
Abstract
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper 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 which 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 which is 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. While the material discussed is of general applicability to point processes attention will be confined to sequences of neuronal action potentials (spike trains) which were the motivation for this work.
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"abstract": "The spectrum and coherency are useful quantities for characterizing the\ntemporal correlations and functional relations within and between point\nprocesses. This paper begins with a review of these quantities, their\ninterpretation and how they may be estimated. A discussion of how to assess the\nstatistical significance of features in these measures is included. In\naddition, new work is presented which builds on the framework established in\nthe review section. This work investigates how the estimates and their error\nbars are modified by finite sample sizes. Finite sample corrections are derived\nbased on a doubly stochastic inhomogeneous Poisson process model in which the\nrate functions are drawn from a low variance Gaussian process. It is found\nthat, in contrast to continuous processes, the variance of the estimators\ncannot be reduced by smoothing beyond a scale which is set by the number of\npoint events in the interval. Alternatively, the degrees of freedom of the\nestimators can be thought of as bounded from above by the expected number of\npoint events in the interval. Further new work describing and illustrating a\nmethod for detecting the presence of a line in a point process spectrum is also\npresented, corresponding to the detection of a periodic modulation of the\nunderlying rate. This work demonstrates that a known statistical test,\napplicable to continuous processes, applies, with little modification, to point\nprocess spectra, and is of utility in studying a point process driven by a\ncontinuous stimulus. While the material discussed is of general applicability\nto point processes attention will be confined to sequences of neuronal action\npotentials (spike trains) which were the motivation for this work.",
"arxiv_id": "physics/0002053",
"authors": [
"M. R. Jarvis",
"P. P. Mitra"
],
"categories": [
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"physics.data-an",
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],
"title": "Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials",
"url": "https://arxiv.org/abs/physics/0002053"
},
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