The fluorescence observations at the time frame and trial: , are noisy surrogates of the intracellular calcium concentrations: . The calcium concentration at time is a function of the spiking activity , and the calcium activity at the previous time point . The spiking activity is driven by two independent mechanisms: latent trial-dependent covariates , and contributions from the known external stimulus , which we model by (in which the receptive field is unknown). Then, we model as a Gaussian process with constant mean , and unknown covariance . Finally, we assume the covariance to have an inverse Wishart prior distribution with hyper-parameters and . Based on this forward model, the inverse problem amounts to recovering the signal and noise correlations by directly estimating and (top layer) from the fluorescence observations (bottom layer).