9 Noisy Output: Escape Rate and Soft Threshold


The Spike Response Model with exponential escape noise has been introduced in (180; 182), but closely related models had already been applied to neuronal data by Brillinger (69) and have an obvious link to Generalized Linear Models which were used in statistics already in the 1970’s (361) and have been repeatedly applied to neuronal data (521; 399). The choice of an exponential escape rate for experimental data has been demonstrated in Jolivet et al. (247).

The term escape noise has been chosen in analogy to the Arrhenius formula which describes the escape of a particle (or a chemical process) across an energy barrier in the presence of thermal energy (529).

The relation of diffusive noise in the input to escape noise has been studied in Plesser and Gerstner (403); Herrmann and Gerstner (214) and Mensi et al. (339). Stochastic resonance has been a popular topic of research for many years, starting in 1989 (336; 132; 308; 101). A nice review on stochastic resonance can be found in Gammaitoni et al. (167).