On the basis of the evident ability of neuronal olfactory systems to evaluate the intensity of an odorous stimulus and at the same time also recognise the identity of the odorant over a large range of concentrations, a few biologically-realistic hypotheses on some of the underlying neural processes are made. In particular, it is assumed that the receptor neurons mean firing-rate scale monotonically with odorant intensity, and that the receptor sensitivities range widely across odorants and receptor neurons hence leading to highly distributed representations of the stimuli. The mathematical implementation of the phenomenological postulates allows for inferring explicit functional relationships between some measurable quantities. It results that both the dependence of the mean firing-rate on odorant concentration and the statistical distribution of receptor sensitivity across the neuronal population are power-laws, whose respective exponents are in an arithmetic, testable relationship. In order to test quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature. The values of the free parameters of the model are estimated by an info-geometric Bayesian maximum-likelihood inference which keeps into account the prior distribution of the parameters. The eventual goodness of fit is quantified by means of a distribution-independent test. The probabilistic model results to be accurate with high statistical significance, thus confirming the theoretical prediction of a power-law dependence on odorant concentration. The experimental data available about the distribution of sensitivities also agree with the other predictions, though they are not statistically sufficient for a very stringent verification. Furthermore, the theory suggests a potential evolutionary reason for the exponent of the sensitivity power-law to be significantly different from the unit. The power-law dependence on concentration is consistent with the psychophysical Stevens Law. On the whole, from the formalisation of just a few phenomenological observations a compact model is derived that may fit experimental findings from several levels of research on olfaction.
