The problem faced by an animal using sensory information to find out about its environment may be suited to Bayesian analysis. The animal will be most accurate if it guesses that the event occurring is the event for which the probability of event given neural responses, p(e|r), is maximum. In order to estimate p(e|r), an organism must know the probabilities of occurrence of events p(e) (the priors), and the probabilities of neural responses given events p(r|e). Given these, one can apply Bayes’ formula:
p(e|r) = p(r|e).p(e)/p(r).
Yet it is difficult to see how the statistical formalism could be implemented in the brain. We examined the problem, developing a computer model of contrast identification in which 16 simplified V1 neurons must infer, from their noisy responses (variance = 2 X mean, Tolhurst et al. 1983), the value of stimulus contrast presented. The contrast response function is modelled by the Naka-Rushton equation (Albrecht & Hamilton, 1982). An important parameter is the level of contrast at which the neuron attains half of its maximum response (ρ). We ran simulations in which the ρ distribution was taken from cat (D.J. Tolhurst, unpublished data) and monkey (D. Ringach, personal communication) neurophysiology and found performance in contrast identification to be different from that of a control population with a uniform ρ distribution. For the animal ρ simulations performance peaked at the mid contrast range, corresponding to the peak in the distribution of contrasts in natural scenes, as estimated by an equivalent contrast method (Peli, 1990). This would give the animal the advantage of being best at coding the contrasts most frequently occurring in the natural world.
This observation was supported by calculations of mutual information between a set of natural contrasts (c) and model contrast estimates (Æöc):
I(c;Æöc) = ·{special}·{special} p(c;Æöc).log2[p(c;Æöc)/p(c).p(Æöc)],
which found I to be greater for cat and monkey populations (2.4 and 2.2 bits, respectively) than the control set (2.1 bits), when measured with a flat p(e) distribution.
Measurement with a natural scenes p(e) did not increase I for the control population, but did shift peak accuracy closer to the peak of the natural contrast distribution – an effect analogous to making the ρ set more like that of the cat or monkey populations. The finding that the effect of a probability distribution can be mimicked by adjusting a neuronal parameter is relevant to the issue of biological implementation of Bayesian analysis. It suggests that by setting ρ values, V1 is able to encode prior information.
This work was supported by the MRC.