A common goodness-of-fit framework for neural population models using marked point process time-rescaling

Abstract

A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.

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

“…While the marked point process framework has the potential to provide holistic models of the coding properties of a neural population while avoiding a computationally expensive spike-sorting procedure, until recently methods for assessing their goodness-of-fit have been lacking. Our preceding work to extend the time-rescaling theorem [5] to marked point process neural models has provided a preliminary approach to address this problem [6] but further work was necessary to make the approach computationally efficient in higher dimensions, to enable the use of more statistically powerful test methods, and to understand which tests are most useful for capturing different aspects of model misspecification.…”

“…In equation (A.20), the denominator defines the joint probability distribution of observing ݊ events independent of their temporal order. Given the history dependence of the events, the joint probability distribution of temporally ordered events [6] is defined by We utilize the simulation data described in section (4-1) to assess the mapping result of MRCI. Figure A1 shows the mapping results for this algorithm.…”

“…For point process models of sorted spike train data, effective goodness-of-fit methods have been developed based on the time-rescaling theorem [4,5]. Previously, we developed an extension of the time-rescaling theorem for marked point processes, which given the correct model, rescales the observed spike and mark data to a uniform distribution in a random subset of a space of the marks and rescaled times [6]. We can then use established statistical tests for uniformity to assess whether the model used for rescaling is consistent with the observed data.…”

“…However, several challenges still limit the efficient application of these methods to marked point process models, in some cases. For models with high-dimensional marks representing the waveform features, computing the space in which the rescaled data should be uniform can be computationally expensive [6]. Since this space is random and typically not convex, the number of statistical tests for uniformity is limited to those that can be applied in general spaces.…”

In vivo flow cytometry reveals a circadian rhythm of circulating tumor cells

“…To test whether CTC occurrence was a Poisson process, we first determined whether the ICIs were exponentially distributed. The empirical cumulative density function (CDF) was compared with a model CDF of the exponential based on the KS test 63 . The CDF of the exponential distribution was where is the intensity of CTC occurrence, was estimated by the maximum log-likelihood where C is the number of ICIs.…”