| Detection of artificial EPSCs immersed in fluctuating noise | 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). |
| Prediction of spikes | Log likelihood ratios (relative to a homogeneous Poisson model) increase monotonically with the increasing fraction of observed inputs (Fig. |
| Quantifying accuracy and detecting functional connections | In general, if we have two models H1 and Hz with Poisson observations the log likelihood ratio is given by where the two models have conditional intensities defined by 11 and 12 (log base 2 is used LLR (H 1,H2) * log2 when reporting bits). |
| Quantifying accuracy and detecting functional connections | Importantly, the log likelihood ratio quantifies the relative accuracy of the two models. |
| Quantifying accuracy and detecting functional connections | For instance, when H2 is a homogeneous Poisson model that only describes the mean firing rate, the log likelihood ratio quantifies how much more accurately spikes are predicted by the model H1 over just predicting the mean. |
| U | D) Detectability of synaptic connections from spike trains: Dependence of the log likelihood ratio between Models M1 and M2 on the input amplitude. |
| U | 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. |
| U | As in previous analysis, we use the likelihood ratio to determine whether the synaptic weight has changed. |
| input experiments. | They have less impact on the postsynaptic firing, and thus are less accurate in predicting output spikes compared to excitatory inputs of the same magnitude (the log likelihood ratios comparing Model 2 with coupling to Model 1 with spike-history alone are 58i2% smaller for inhibitory inputs). |
| Ordinary differential equation model selection | We applied an adaptation of a likelihood ratio test (LRT) with a threshold of 95%, which takes into account the different degrees of freedom for each model structure (Materials and Methods). |
| Ordinary differential equation modeling | The result of each pairwise likelihood ratio test is then used to obtain the ranking of the corresponding model structures. |
| Supporting Information | The models are sorted according to the Likelihood ratio test value as 81 Fig. |
| Supporting Information | Values of the likelihood ratio test with the threshold of 95% are shown under each corresponding model. |
| Supporting Information | P-Values were computed using either a Score test (A) or a Likelihood Ratio test (B). |
| Supporting Information | Because the Likelihood Ratio test appeared to have significantly more power than both the Score test and the MAGMA F-test, empirical p-Values for the Likelihood Ratio test were computed by generating up to 10,000 permutations of the Likelihood Ratio statistic. |
| Supporting Information | This was compared to the asymptotic Likelihood Ratio test p-Values (C), revealing a downward bias in the asymptotic p-Values. |