Response variability, as measured by fluctuating responses upon repeated performance of trials, is a major component of neural responses, and its characterization is key to interpret high dimensional population recordings. Response variability and covariability display predictable changes upon changes in stimulus and cognitive or behavioral state, providing an opportunity to test the predictive power of models of neural variability. Still, there is little agreement on which model to use as a building block for population-level analyses, and models of variability are often treated as a subject of choice. We investigate two competing models, the Doubly Stochastic Poisson (DSP) model assuming stochasticity at spike generation, and the Rectified Gaussian (RG) model that traces variability back to membrane potential variance, to analyze stimulus-dependent modulation of response statistics. Using a model of a pair of neurons, we demonstrate that the two models predict similar single-cell statistics. However, DSP and RG models have contradicting predictions on the joint statistics of spiking responses. In order to test the models against data, we build a population model to simulate stimulus change-related modulations in response statistics. We use unit recordings from the primary visual cortex of monkeys to show that while model predictions for variance are qualitatively similar to experimental data, only the RG models predictions are compatible with joint statistics. These results suggest that models using Poisson-like variability might fail to capture important properties of response statistics. We argue that membrane potential-level modelling of stochasticity provides an efficient strategy to model correlations.
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