e060824spont_1_lambda

A nearly step by step analysis is presented on a dedicated web page for the second neuron of e060517spont 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: e060824spont_1.R. Then start R from the directory where the file was downloaded and type:

> source("e060824spont_1.R", verbose=TRUE)

The "renewal test plot" (second plot) of the automatic analysis of the spontaneous activity of neuron 1 shows that the discharge is tstrongly bursty and cannot be described by a renewal process. We therefore try models depending not only on the elapsed time since the last spike but also on the duration of the last inter-spike intervals (isi).

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 20th or 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 (<= 10) of the statistic (the 10 is arbitrary). In the present case we use the 9th root for the elapsed time since the last spike (TmO.9th) and the 10th root transform for the duration of the last inter spike interval (d.1Oth).

As usual we split the data into two parts, fit the model to the last 30 seconds and test it (by time transformation) on the first 30 seconds.

We first consider model: event ~ TmO.9th * d.10th

And get the following extended Ogata's test plots:

Based on these tests we accept the model. Notice how simple the model turns out to be with only two variables involved given the pattern of discharge (first plot).

Before going further we can try a simpler model, an additive model:

event ~ TmO.9th + d.10th

Fitting again the last 30 s and time transforming the first we get:

It does very slightly worse for the Berman's test but it still looks good. We therefore go ahead and estimate the functional form of the 2 terms by refitting the last model on the whole data set to get:

The top row shows the effect of the elapsed time since the last spike. It has an early negative part (refractory period) 7 ms long, it peaks at 34 ms and remains positive until 253 ms. It becomes afterwards significantly negative for more than 3 s.

The effect of the last inter spike interval (ISI) is positive up to 120 ms and negative afterwards (bottom row). 89% of the ISIs are smaller or equal to 120 ms. Notice that the peak effect of the previous ISI (~ 1.5) is of the same order of magnitude than the peak effect of the ellapsed time since the last spike (~ 2).