e060517spont_1_lambda

A nearly step by step analysis is presented on a dedicated web page for the second neuron of this 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: e060515spont_1.R. Then start R from the directory where the file was downloaded and type:

> source("e060517spont_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 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) 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. In the present case we use the 8th root for the elapsed time since the last spike (TmO.hr) and the 10th root transform for the duration of the last inter spike interval (d.tr).

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.hr * d.tr

And get the following extended Ogata's test plots:

We apply next a projection test:

> project(GF0,include=c("TmO.hr","d.tr"))

$ratio

[1] 0.02170837

$kl

[1] 6.821997e-05

$check

[1] 0.9997514

suggesting that the interaction term is not necessary.

We therefore fit (to the last 30 s) an additive model:

event ~ TmO.hr + d.tr

Time transform the first 30 s and get:

Which is still satifying.

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

We see that the elapsed time to the last spike as a negative effect (refractory period) up to 4 ms, it peaks at 30 ms and remains positive until 200 ms. The previous isi has a positive effect if it was less than 87 ms long, 62% of the isi have therefore an excitatory effect.