CuBIC - Cumulant Based Inference of higher-order Correlation¶
CuBIC is a statistical method for the detection of higher order of correlations in parallel spike trains based on the analysis of the cumulants of the population count. Given a list sts of SpikeTrains, the analysis comprises the following steps:
- compute the population histogram (PSTH) with the desired bin size
>>> binsize = 5 * pq.ms >>> pop_count = elephant.statistics.time_histogram(sts, binsize)
- apply CuBIC to the population count
>>> alpha = 0.05 # significance level of the tests used >>> xi, p_val, k = cubic(data, ximax=100, alpha=0.05, errorval=4.):
-
elephant.cubic.
cubic
(data, ximax=100, alpha=0.05)[source]¶ Performs the CuBIC analysis [1] on a population histogram, calculated from a population of spiking neurons.
The null hypothesis is iteratively tested with increasing correlation order (correspondent to variable xi) until it is possible to accept, with a significance level alpha, that (corresponding to variable xi_hat) is the minimum order of correlation necessary to explain the third cumulant .
is the maximized third cumulant, supposing a Compund Poisson Process (CPP) model for correlated spike trains (see [1]) with maximum order of correlation equal to .
Parameters: - data : neo.AnalogSignal
The population histogram (count of spikes per time bin) of the entire population of neurons.
- ximax : int
The maximum number of iteration of the hypothesis test: if it is not possible to compute the before ximax iteration the CuBIC procedure is aborted. Default: 100
- alpha : float
The significance level of the hypothesis tests perfomed. Default: 0.05
Returns: - xi_hat : int
The minimum correlation order estimated by CuBIC, necessary to explain the value of the third cumulant calculated from the population.
- p : list
The ordred list of all the p-values of the hypothesis tests that have been performed. If the maximum number of iteration ximax is reached the last p-value is set to -4
- kappa : list
The list of the first three cumulants of the data.
- test_aborted : bool
Wheter the test was aborted because reached the maximum number of iteration ximax
References
[1]Staude, Rotter, Gruen, (2009) J. Comp. Neurosci