e060817spont_1_lambda

A nearly step by step analysis is presented on a dedicated web page for the second neuron of the e060517 data set. We only provide an outline of the analysis with the key results here. The analysis presented in the sequel can nevertheless be automatically replicated by downloading the R script file attached at the bottom of this page: e060817spont_1.R. Then start R from the directory where the file was downloaded and type:

> source("e060817spont_1.R", verbose=TRUE)

The "renewal test plot" (second plot) of the automatic analysis of the spontaneous activity of neuron 1 suggest that the discharge can be described by a renewal process. We therefore try first a model depending only on the elapsed time since the last spike.

Before embarking into fitting a candidate model it is a good idea to look at the distribution of the variables we will include in it and , if necessary, to try to transform them in order to have a uniform distribution of the model's variables on their definition domains. We are now trying to make this transformation selection slightly more automatic (than in the step by step example) by performing systematic root transform (from the 1st to the 40th) and by computing the Kolmogorov statistic associated with each transform (comparing to the target uniform distribution). We then select for each variable of the model the transform giving the smallest value of the statistic if the root is equal or smaller to the tenth one and we (arbitrarily) select the 10th one otherwise. In the present case we use the 10th root for the elapsed time since the last spike (TmO.tr). The ECDF obtained with root 10, 20, 30 and 40 are shown next:

The 10th does not look much worse the higher order roots and is kept for simplicity.

We therefore first consider model: event ~ TmO.tr

And get the following extended Ogata's test plots:

It looks good but the Berman's test almost fails. The cross-correlogram obtained with neuron 1 as a reference and neuron 2 as a test (see the automatic analysis of the spontaneous activity of neuron 1) shows a pronounced correlation around 0. We therefore modify our model to include the elapsed time since the last spike of neuron 2: TmO2.

The automatic study of the TmO2 variable transformation suggests that the 5th root is the best we therefore use as a next model (fitted to the last 30 s of data):

event ~ TmO.tr + TmO2.5th

Time transform the first 30 s and get:

The Berman's test looks now better.

We next look at the functional form of the 2 terms:

We see that the elapsed time to the last spike as a negative or null effect (not well defined refractory period) up to 40 ms, it peaks at 179 ms and remains positive until 680 ms. The elapsed time since the last spike of neuron 2 as a positive effect between 0 and ~ 25 ms and is negative afterwards.