One of the main goals of the project is the development of novel stochastic methods for the analysis of concurrent measurements of neural activity at multiple scales. To this end, we introduced a novel framework for constructing multivariate stochastic models based on vine copulas with mixed margins. These models can describe detailed mixed interactions between discrete variables such as neural spike counts, and continuous variables such as local field potentials. We developed a software toolbox for MATLAB implementing the complete framework. The toolbox includes functions for parameter fitting, probability density calculation, sampling, entropy and information estimation. We implemented a wide range of flexible pairwise copula families for building canonical vines and D-vines and also provide the most commonly encountered discrete and continuous single element distributions. We then validated the toolbox on simulated data. To test probability density calculation and sampling, we build small 3-dimensional and 4-dimensional mixed vine-based models and compared 2-dimensional margin density and sample scatter plots. To test fitting and entropy estimation, we fitted and compared mixed vine-based models, corresponding mixed independent models and corresponding fully continuous vine-based models and showed superior performance of mixed vine-based models in terms of the likelihood ratio statistics and entropy estimates. To generate more realistic neural activity, we applied the VERTEX simulator. Using this tool, we simulated a neural network of 5000 adaptive exponential neuron models with two different input current conditions and recorded spike counts as well as local field potentials from this artificial network. We then fitted mixed vine-based models, mixed independent models and fully continuous vine-based models and demonstrated superior fit of mixed vine-based models. We also showed that information estimated with the mixed vine-based models substantially differs from information estimates obtained from best-fitting mixed independent models and fully continuous vine-based models. We then developed additional important methodological extensions for validating the appropriateness of mixed vine copula-based models for information-theoretic quantities. We derived a bias corrected estimator for entropy and mutual information of mixed discrete and continuous distributions that can be used to confirm entropy estimates of copula-based models on small subsets of variables. Moreover, we developed pre-processing steps for identifying compact parts-based data representations that can tremendously improve performance of the models. The project led to five peer-reviewed scientific article publications, three conference poster presentations and four invited talks. We also disseminated a free and open source MATLAB toolbox, set up a project website and wrote a blog post targeted at the general public.
