Assessing Goodness-of-Fit in Marked Point Process Models of Neural Population Coding via Time and Rate Rescaling.

Marked point process models have recently been used to capture the coding properties of neural populations from multiunit electrophysiological recordings without spike sorting. These clusterless models have been shown in some instances to better describe the firing properties of neural populations than collections of receptive field models for sorted neurons and to lead to better decoding results. To assess their quality, we previously proposed a goodness-of-fit technique for marked point process models based on time rescaling, which for a correct model produces a set of uniform samples over a random region of space. However, assessing uniformity over such a region can be challenging, especially in high dimensions. Here, we propose a set of new transformations in both time and the space of spike waveform features, which generate events that are uniformly distributed in the new mark and time spaces. These transformations are scalable to multidimensional mark spaces and provide uniformly distributed samples in hypercubes, which are well suited for uniformity tests. We discuss the properties of these transformations and demonstrate aspects of model fit captured by each transformation. We also compare multiple uniformity tests to determine their power to identify lack-of-fit in the rescaled data. We demonstrate an application of these transformations and uniformity tests in a simulation study. Proofs for each transformation are provided in the appendix.