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Nonconvergence in logistic and Poisson models for neural spiking. (English) Zbl 1187.92029
Summary: Generalized linear models are an increasingly common approach for spike train data analysis. For the logistic and Poisson models, one possible difficulty is that iterative algorithms for computing parameter estimates may not converge because of certain data configurations. For the logistic model, these configurations are called complete and quasi-complete separation. We show that these features are likely to occur because of refractory periods of neurons. We use an example to study how standard software deals with this difficulty. For the Poisson model, we show that the same difficulties arise, this time possibly due to bursting or specifics of the binning. We characterize the nonconvergent configurations for both models, show that they can be detected by linear programming methods, and discuss possible remedies.

92C20 Neural biology
90C05 Linear programming
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J12 Generalized linear models (logistic models)
65C20 Probabilistic models, generic numerical methods in probability and statistics
Full Text: DOI
[1] DOI: 10.1093/biomet/71.1.1 · Zbl 0543.62020 · doi:10.1093/biomet/71.1.1
[2] Allison P., Numerical issues in statistical computing for the social scientists (2004)
[3] Azzalini A., Statistical analysis based on the likelihood (1996) · Zbl 0871.62001
[4] Barndorff-Nielsen O., Information and exponential families in statistical theory (1978) · Zbl 0387.62011
[5] DOI: 10.1007/BF00318010 · Zbl 0646.92007 · doi:10.1007/BF00318010
[6] DOI: 10.1214/08-STS275 · Zbl 1329.62274 · doi:10.1214/08-STS275
[7] DOI: 10.1162/neco.2008.09-07-606 · Zbl 1178.68407 · doi:10.1162/neco.2008.09-07-606
[8] Eubank R. L., Nonparametric regression and spline smoothing, 2. ed. (1999) · Zbl 0936.62044
[9] DOI: 10.1162/08997660152469314 · Zbl 0985.92017 · doi:10.1162/08997660152469314
[10] Luenberger D. G., Linear and nonlinear programming, 2. ed. (1984) · Zbl 0571.90051
[11] DOI: 10.1088/0954-898X/15/4/002 · doi:10.1088/0954-898X/15/4/002
[12] DOI: 10.1093/biomet/73.3.755 · Zbl 0655.62022 · doi:10.1093/biomet/73.3.755
[13] Silvapulle M., J. Royal Statistical Society, B 43 pp 310– (1981)
[14] Stevenson I. H., IEEE TNSRE 17 pp 203– (2009)
[15] DOI: 10.1152/jn.00697.2004 · doi:10.1152/jn.00697.2004
[16] DOI: 10.1093/biomet/63.1.27 · Zbl 0329.62027 · doi:10.1093/biomet/63.1.27
[17] Zhao M., Logistic regression model with -regularization for detecting neural connectivity (2009)
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