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Bivariate cumulative probit model for the comparison of neuronal encoding hypotheses



Understanding the way stimulus properties are encoded in the nerve cell responses of sensory organs is one of the fundamental scientific questions in neurosciences. Different neuronal coding hypotheses can be compared by use of an inverse procedure called stimulus reconstruction. Here, based on different attributes of experimentally recorded neuronal responses, the values of certain stimulus properties are estimated by statistical classification methods. Comparison of stimulus reconstruction results then allows to draw conclusions about relative importance of covariate features. Since many stimulus properties have a natural order and can therefore be considered as ordinal, we introduce a bivariate ordinal probit model to obtain classifications for the combination of light intensity and velocity of a visual dot pattern based on different covariates extracted from recorded spike trains. For parameter estimation, we develop a Bayesian Gibbs sampler and incorporate penalized splines to model nonlinear effects. We compare the classification performance of different individual cell covariates and simple features of groups of neurons and find that the combination of at least two covariates increases the classification performance significantly. Furthermore, we obtain a non-linear effect for the first spike latency. The model is compared to a naïve Bayesian stimulus estimation method where it yields comparable misclassification rates for the given dataset. Hence, the bivariate ordinal probit model is shown to be a helpful tool for stimulus reconstruction particularly thanks to its flexibility with respect to the number of covariates as well as their scale and effect type.