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Some sampling properties of common phase estimators. (English) Zbl 1269.92021
Summary: The instantaneous phase of neural rhythms is important to many neuroscience-related studies. We show that the statistical sampling properties of three instantaneous phase estimators commonly employed to analyze neuroscience data share common features, allowing an analytical investigation of their behavior. These three phase estimators, the Hilbert, complex Morlet, and discrete Fourier transform, are each shown to maximize the likelihood of the data, assuming the observation of different neural signals. This connection, explored with the use of a geometric argument, is used to describe the bias and variance properties of each of the phase estimators, their temporal dependence, and the effect of model misspecification. This analysis suggests how prior knowledge about a rhythmic signal can be used to improve the accuracy of phase estimates.

92C20 Neural biology
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] DOI: 10.1002/hbm.21000 · doi:10.1002/hbm.21000
[2] DOI: 10.1109/TSP.2011.2144589 · Zbl 1392.94078 · doi:10.1109/TSP.2011.2144589
[3] DOI: 10.1016/j.jneumeth.2004.03.002 · doi:10.1016/j.jneumeth.2004.03.002
[4] DOI: 10.1093/acprof:oso/9780195301069.001.0001 · doi:10.1093/acprof:oso/9780195301069.001.0001
[5] DOI: 10.1016/S0306-4522(02)00669-3 · doi:10.1016/S0306-4522(02)00669-3
[6] DOI: 10.1126/science.1099745 · doi:10.1126/science.1099745
[7] DOI: 10.1126/science.1128115 · doi:10.1126/science.1128115
[8] DOI: 10.1016/j.tics.2010.09.001 · doi:10.1016/j.tics.2010.09.001
[9] DOI: 10.1016/j.jneumeth.2007.10.012 · doi:10.1016/j.jneumeth.2007.10.012
[10] DOI: 10.1038/338334a0 · doi:10.1038/338334a0
[11] DOI: 10.1385/NI:3:4:301 · doi:10.1385/NI:3:4:301
[12] DOI: 10.1038/nature01834 · doi:10.1038/nature01834
[13] DOI: 10.1111/j.1460-9568.2007.05779.x · doi:10.1111/j.1460-9568.2007.05779.x
[14] Hogg, R. V., McKean, J. W. & Craig, A. T. (2005). Introduction to mathematical statistics (6th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
[15] DOI: 10.1152/jn.00853.2003 · doi:10.1152/jn.00853.2003
[16] Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory. Upper Saddle River, NJ: Prentice Hall PTR. · Zbl 0803.62002
[17] DOI: 10.1126/science.1154735 · doi:10.1126/science.1154735
[18] DOI: 10.1523/JNEUROSCI.4250-04.2005 · doi:10.1523/JNEUROSCI.4250-04.2005
[19] DOI: 10.1016/j.pneurobio.2005.10.003 · doi:10.1016/j.pneurobio.2005.10.003
[20] Priestly M. B., Spectral analysis and time series (1981)
[21] DOI: 10.1016/j.newideapsych.2010.11.001 · doi:10.1016/j.newideapsych.2010.11.001
[22] DOI: 10.1016/j.tins.2007.05.006 · doi:10.1016/j.tins.2007.05.006
[23] DOI: 10.1016/S0165-0270(01)00372-7 · doi:10.1016/S0165-0270(01)00372-7
[24] DOI: 10.1016/j.neuroimage.2006.01.009 · doi:10.1016/j.neuroimage.2006.01.009
[25] DOI: 10.1073/pnas.0732061100 · doi:10.1073/pnas.0732061100
[26] DOI: 10.1038/nature08860 · doi:10.1038/nature08860
[27] DOI: 10.1016/j.tins.2008.09.012 · doi:10.1016/j.tins.2008.09.012
[28] DOI: 10.1016/j.neuron.2008.09.014 · doi:10.1016/j.neuron.2008.09.014
[29] DOI: 10.1073/pnas.0810524105 · doi:10.1073/pnas.0810524105
[30] DOI: 10.1038/35067550 · doi:10.1038/35067550
[31] DOI: 10.1111/1467-9892.00175 · Zbl 0974.62082 · doi:10.1111/1467-9892.00175
[32] DOI: 10.1126/science.1139597 · doi:10.1126/science.1139597
[33] DOI: 10.1016/j.pneurobio.2009.06.002 · doi:10.1016/j.pneurobio.2009.06.002
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