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Figure 1 | BMC Neuroscience

Figure 1

From: Bayesian inference from single spikes

Figure 1

Simulation of prey detection by spiking sensors. The state x is the distance from predator to prey on a time step. The predator has a sensor that fires spikes with an intensity that depends on the strength of some stimulus produced by the prey; when x is small, the predator's sensor fires with higher intensity (and vice versa, left subplot). In general, we can approximate this intensity from the biophysics of some real sensor and stimulus, but for simplicity we assume that the intensity falls as 1 / x 2 . Pr(S = 1|X) and Pr(S = 0|X) are the probabilities of the sensor firing in some small window of time given x, and we consider sufficiently small time windows such that no more than one spike can occur in that window. Given these conditional pdfs, it is possible to infer prey location using the sensor's spikes by Bayes' rule (right subplot). The prior distribution of x is Pr(X). We can then calculate the posterior distribution of x given the output of a spiking sensor, Pr(X|S = 1) and Pr(X|S = 0). On the next time step, this posterior becomes the new prior and the process repeats. When spikes and non-spikes are streamed very quickly, these posterior pdfs are updated almost continuously and in real-time.

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