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

A) Model fits for a typical neuron (top), and results for N = 10 cells (bottom). Model 1 (M1, No Coupling) describes only the effects of prior spikes in the postsynaptic cell on the generation of future spikes (Post-Spike Gain). Model 2 (M2, Constant Coupling) describes both the post-spike history effects (Post-Spike Gain) as well as the coupling effects following a pre-synaptic spike (Coupling Gain). Gray lines show parameters estimated from bootstrap samples; solid colored lines show their averages. B) Model accuracy: Receiver operating characteristic (ROC) curves for the example cell and area under the curve (AUC) for all cells from A. Curves show the cross-validated false positive rate (FPR) *vs* true positive rate (TPR) for spike detection in 1ms bins. Error bars denote standard deviation across cells. Note that the accuracy of Model 2, with constant-gain coupling, (M2) increases with increasing input amplitude. C) Cross- and auto-correlations for the typical cell with the model predictions. D) Detectability of synaptic connections from spike trains: Dependence of the log likelihood ratio between Models M1 and M2 on the input amplitude. Each dot represents data for one cell and one input amplitude. Black dots denote trials where M2 significantly outperforms M1 (Chi-squared test, p<0.05). E) The true amplitude of aEPSCs *vs* the estimated amplitude (coupling coefficient) using Model 2 with all data (length varies across cells 216–720s). Colors denote different cells recorded with inputs of different amplitudes, and error bars denote bootstrap standard error. F) Dependence of the log likelihood ratios of models M1 and M2 relative to a homogeneous Poisson process on the length of data used for analysis. Input amplitude of 1σ, data for N = 10 cells. Error bands denote standard deviation across cells. “*Detection time*” is defined as minimal data-length at which Model 2 with constant-gain coupling starts to out-perform the Model 1 with no connection (marked by the red point). Also note that for <50s of data the models tend to over-fit (the accuracy on training data is higher than the accuracy on test data). G) Detection time as a function of input amplitude. The dependence is well-approximated by the black curve c/x^{2}. Gray dots denote recording length for those cells where no change was detected. If it exists the detection time must be longer than the recording length, as indicated by the arrow.