Characterizing Complex, Multi-Scale Neural Phenomena Using State-Space Models

In the past three decades, we have seen a massive expansion in our ability to record neural activity: from many more neurons, from multiple brain areas, and across multiple spatial and temporal scales. As a result, scientific investigation is limited in many cases not by the availability of data but by the availability of statistical and analysis tools. In particular, making use of such complex datasets to understand the mechanisms and effects of neural phenomena requires integration of multiple information sources. The state-space approach, whose application to complex neural phenomena has been pioneered by Emery Brown and his colleagues, provides a natural statistical modeling approach for integrating information across multiple sources and scales, for discovering low-dimensional representations of behavioral and cognitive states, and for expressing confidence about estimates and inferences. In this chapter, we will review the fundamental features of the state-space paradigm, discuss successful applications of the paradigm to various neural data analysis problems, and present a novel extension of these methods to better understand the phenomenon of hippocampal “ripple-replay” events. These events are defined by high-frequency oscillations in the local field potential (LFP), called ripples, during which neural spike sequences correspond to those seen during previous experience, or replay; their analysis therefore requires integration of neural information at multiple scales. Specifically, we will discuss a semi-latent state-space model that combines information from a rat’s movement, LFP, and ensemble hippocampal spiking to simultaneously identify periods of ripple-replay and decode its content in real time.