1—2 is linear with respect to the underlying spike trains {Ty(1‘)}.

Raw experimental data 3 Stimulus—a varying scalar value on each trial so Threshold stimulus value in the 2AFC task 0* Animal choice—binary report on each trial r,-(t) Spike train from neuron i in a given trial 02 Stimulus variance across trials

We describe the activity of this neural population on every trial as a multivariate point process r(t) = {Ty(1‘)},- = 1. , N“, where each r,(t) is the spike train for neuron i, and Ntot denotes the full population size, a very large and unknown number.

As is common in electrophysiological recordings, we will quantify the raw spike trains by their first and second order statistics.

Classic measures in decision-making experiments can be interpreted as estimates of the first-and second-order statistics of choice c and recorded spike trains ri(t), across all trials with a fixed stimulus value 5:

In practice, they are estimated by binning spike trains ri(t) with a finite temporal precision, depending on the amount of data available.

In addition, the neurometric sensitivities also depend on the time scale w that is used to integrate each neuron’s spike train in a given trial [3, 11—13].

Since the linear readout relies on the integrated spike trains , eq.

4—6, we find statistical quantities related to the percept E. On the right-hand sides of these equations, we find the model’s predictions, which are based on the neurons’ (measurable) response statistics, 19 and C. More specifically, the first line describes the average dependency of § on stimulus s, the second line expresses the resulting variance for the percept, and the third line expresses the linear covariance between each neuron’s spike train , and the animal’s percept § on the trial.

If the feedback depends linearly on per-cept§ (and thus, on the spike trains ), its effects are fully encompassed in our model.

One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons.

To determine whether an input of a certain amplitude can be “detected” given a specific set of spike trains we use the log likelihood ratio (LLR).

Both the history-only Model 1 and Model 2 with constant coupling capture statistics of the spike trains and predict spikes with reasonable accuracy.

On the other hand, methods for recording extracellular spike trains are advancing at a rapid pace [9,10] and allowing the simultaneous recording of hundreds of neurons.

Estimation of synaptic interactions from extracellularly recorded spike trains requires development of sensitive data analysis tools.

Although strong synapses are usually readily detectable using cross-correlation analysis [11—17], where they appear as asymmetric, short latency peaks on cross-correlograms [18,19], in general, it is difficult to link the statistical relationships between spike trains to specific synaptic processes [20,21].

Statistical inference of synaptic connections of different strength from spike trains .

D) Detectability of synaptic connections from spike trains : Dependence of the log likelihood ratio between Models M1 and M2 on the input amplitude.

Detectability of synaptic connections from spike trains depends strongly on how much data is available.

Comparison of the distributions obtained using the observed vs shuffled spike trains allows us to test whether an input has a statistically significant effect on the firing of the postsynaptic neuron (see Methods).