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Submitted by Assigned_Reviewer_1 Q1 This paper extends Poisson linear dynamical systems (PLDS) to account for the non-stationarity in neural spike trains. Their method (NPLDS) uses a hierarchical framework to find the latent variables for each trial, and also scale those latent variables multiplicatively for each trial. The latent variables are found with a linear dynamical system, and the inter-trial modulators are enforced to be smooth across trials with a Gaussian process. To fit the model, the authors devised the Bayesian Laplacian propagation and used an iterative procedure, which may be of interest to those outside the neuroscience field. The results are shown to be more predictive than the previous PLDS method, which suggests the added complexity helps performance.