Bayesian Information Criterion for Event-based Multi-trial Ensemble data
This work provides a method for researchers in fields like neuroscience and meteorology to better analyze transient recurring phenomena, but it is incremental as it adapts an existing criterion to a specific data type.
The authors tackled the problem of selecting optimal model orders for time-inhomogeneous Vector Autoregressive Models (VAR) in multi-trial ensemble data, which is not addressed by standard AIC/BIC methods, and showed that their derived multi-trial BIC recovers the real model order in simulations and estimates sufficiently small orders in both simulated and real data.
Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such phenomena, and can be learned by exploiting multi-dimensional data gathering samples of the evolution of the system in multiple time windows comprising, each associated with one occurrence of the transient phenomenon, that we will call "trial". However, optimal VAR model order selection methods, commonly relying on the Akaike or Bayesian Information Criteria (AIC/BIC), are typically not designed for multi-trial data. Here we derive the BIC methods for multi-trial ensemble data which are gathered after the detection of the events. We show using simulated bivariate AR models that the multi-trial BIC is able to recover the real model order. We also demonstrate with simulated transient events and real data that the multi-trial BIC is able to estimate a sufficiently small model order for dynamic system modeling.