Cumulant Based Inference of higher-order Correlation (CuBIC)

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:

  1. compute the population histogram (PSTH) with the desired bin size
    >>> binsize = 5 * pq.ms
>>> pop_count = elephant.statistics.time_histogram(sts, binsize)
  2. 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 H_0: k_3(data)<=k^*_{3,\xi} is iteratively tested with increasing correlation order \xi (correspondent to variable xi) until it is possible to accept, with a significance level alpha, that \hat{\xi} (corresponding to variable xi_hat) is the minimum order of correlation necessary to explain the third cumulant k_3(data).

k^*_{3,\xi} 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 \xi.

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 \hat{\xi} 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