Explicit models for UP and DOWN state duration distributions.

<p><b>A</b>) The distribution of DOWN state durations inferred by the HMM algorithm for an example LFP recording. The green trace shows the maximum-likelihood geometric distribution fit. The red and orange traces are the maximum likelihood fits for the gamma and inverse Gaussian distributions respectively, showing much better fits to the empirical distribution than the geometric distribution. <b>B</b>) Same as A for the UP state durations. <b>C</b>) DOWN (blue) and UP (red) state duration distributions averaged across all (n = 21) LFP recordings. Error bars indicate mean ± standard error of the mean. <b>D</b>) The maximized log-likelihood per sample <i>L_n</i> for the geometric distribution is plotted against <i>L_n</i> for the inverse Gaussian distribution across all LFP recordings for the DOWN (blue dots) and UP (red dots) state duration distributions. The inverse Gaussian distribution was a much better model for the data than the geometric distribution for both the DOWN (inverse Gaussian: median: −4.97, inter-quartile range: −5.14–4.82; geometric: −5.22, −5.39–5.16; <i>p</i> = 6.0e-5, two-sided Wilcoxon signed rank test), and UP (inverse Gaussian: −4.33, −4.47–4.27; geometric: −5.01, −5.11–4.95; <i>p</i> = 6.0e-5) states. <b>E</b>) Same as D for the gamma distribution. The gamma distribution also produced higher normalized log-likelihoods than the geometric distribution for both DOWN (−5.10, −5.21–4.87; <i>p</i> = 6.0e-5) and UP (−4.51, −4.37–4.25; <i>p</i> = 6.0e-5) state duration distributions. <b>F</b>) The inverse Gaussian distribution produced significantly better fits than the gamma distribution for the DOWN (p = 6.0e-5), as well as the UP (p = 0.027) states.