Bias-free estimation of information content in temporally sparse neuronal activity
Fig 4
Correcting the upward bias in the naïve SI using the BAE method.
(A) Demonstration of the asymptotic extrapolation (AE) method. Using an unbounded function of the form a+b/t+c/t2 (solid orange curve) to fit the naïve SI as a function of sample duration (blue) yields an inaccurate estimation (dashed orange curve) of the true SI (cyan). (B) Demonstration of the bounded asymptotic extrapolation (BAE) method. Using a bounded function of the form a+b/(1+ct) (solid green curve) to fit the naïve SI as a function of sample duration (blue) yields an accurate estimation (dashed green curve) of the true SI (cyan). The extrapolation of the fitted curve to an infinite sample duration is the estimated SI. Data in A-B show the mean across 100 cells from one example simulation. (C) Estimated SI (mean ± SEM) as a function of the sample duration for the naïve calculation (blue), AE (orange), BAE (green), and the true SI (cyan). (D) Absolute bias in the estimated SI (mean ± SEM) as a function of sample duration for the naïve calculation (blue), SR (red), SSR (magenta), AE (orange) and BAE (green). Data in C-D were averaged across N = 9 simulations. Each simulation corresponds to behavioral data from a different mouse and consists of 100 simulated place cells. ***p < 0.001.