Fig. 3.

Statistical tests of space-time separability. The measured space-time receptive field is plotted using ordinal position along the spiral (see Fig. 1), instead of azimuth and elevation, so that space can be treated as a single dimension. The test statistic used in this study was that of the power-divergence (PD) statistic, which unifies χ² and log-likelihood ratio. The PD statistic reflects the magnitude of the difference between the observed joint-frequency distribution f_s,τ (shown on the left) and the frequency distributionf_sf_τexpected under the assumption of independence (shown on theright):

$$PD=\frac{2}{\ell (\ell +1)}\sum _{\text{s}=1}^S \sum _{\tau =1}^T f_{\text{s},\tau }\left[{\left(\frac{f_{\text{s},\tau }}{f_{\text{s}}{f}_{\tau }}\right)}^{\ell }-1\right].$$ Equation 4

ℓ specifies membership of the power-divergence family, and in our case ℓ = 2/3 was chosen to maximize the power of the statistical test (Read and Cressie, 1988). Ncorresponds to the total number of observed output spikes. This neuron evidences a space-time inseparable kernel with a large PD statistic (PD =  23,788; df = 20,493; p < 0.01), resulting from a large difference between f_s,τ andf_s f_τ.