Calcium imaging is a critical tool for measuring the activity of large neural populations. Much effort has been devoted to developing ``pre-processing" tools applied to calcium video data, addressing the important issues of e.g., motion correction, denoising, compression, demixing, and deconvolution. However, computational modeling of deconvolved calcium signals (i.e., the estimated activity extracted by a pre-processing pipeline) is just as critical for interpreting calcium measurements. Surprisingly, these issues have to date received significantly less attention. To fill this gap, we examine the statistical properties of the deconvolved activity estimates, and propose several density models for these random signals. These models include a zero-inflated gamma (ZIG) model, which characterizes the calcium responses as a mixture of a gamma distribution and a point mass which serves to model zero responses. We apply the resulting models to neural encoding and decoding problems. We find that the ZIG model outperforms simpler models (e.g., Poisson or Bernoulli models) in the context of both simulated and real neural data, and can therefore play a useful role in bridging calcium imaging analysis methods with tools for analyzing activity in large neural populations.
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