Concurrent measurements of neural activity at multiple scales, sometimes performed with multimodal techniques, become increasingly important for studying brain function. However, statistical methods for their concurrent analysis are currently lacking. Here we introduce such techniques in a framework based on vine copulas with mixed margins to construct multivariate stochastic models. These models can describe detailed mixed interactions between discrete variables such as neural spike counts, and continuous variables such as local field potentials. We propose efficient methods for likelihood calculation, inference, sampling and mutual information estimation within this framework. We test our methods on simulated data and demonstrate applicability on mixed data generated by a biologically realistic neural network. Our methods hold the promise to considerably improve statistical analysis of neural data recorded simultaneously at different scales.

The development of flexible methods to model the joint distribution between continuous and random variables is a important problem with many application areas, one of which, as the authors note, is neuroscience. Copula which allow for both discrete and continuous random variables are one means of approaching this problem, and the development of general and computationally tractable methods for fitting and performing inference with such models is of broad interest. The paper makes multiple methodological contributions, which I find valuable. The proposed family of models seems flexible and likely useful in practice. While others have previously proposed pair copula constructions as well as efficient algorithms for sampling from discrete copulas, the development of pair copula constructions and associated efficient algorithms for sampling and inference for mixed discrete and continuous data is valuable.

Concurrent measurements of neural activity at multiple scales, sometimes performed with multimodal techniques, become increasingly important for studying brain function. However, statistical methods for their concurrent analysis are currently lacking. Here we introduce such techniques in a framework based on vine copulas with mixed margins to construct multivariate stochastic models. These models can describe detailed mixed interactions between discrete variables such as neural spike counts, and continuous variables such as local field potentials. We propose efficient methods for likelihood calculation, inference, sampling and mutual information estimation within this framework.