Background
In the neocortex, information is represented by patterns of spike activity occurring over populations of neurons. A fundamental task in neuroscience is to understand how the information is encoded and transmitted in neural population activity. In comparison with the single unit activity, population activity is more information rich and robust in representation.With the advancement of multielectrode array and imaging technologies, neuroscientists have been able to record a large population of neurons at a fine temporal and spatial resolution. In the past few decades, probabilistic modeling and Bayesian methods have become increasingly popular in the analysis of neural codes (Ma et al. 2006; Yu et al. 2007, 2009; Kemere et al. 2008; Gerwinn et al. 2009; Pillow et al. 2011).
State space analyses (Chen et al. 2010, 2013) provides a powerful framework for modeling temporal neuronal dynamics and behavior. The state space model (SSM) consists of two basic equations. The state equation characterizes the dynamics of latent state variable, which is either known or modeled by prior knowledge. The observation equation captures the likelihood of the observations conditional on the latent state and other observed variables. Chapters 1 and 2 of this volume provide a detailed account of the mathematical framework.
In this chapter, we present two examples of state space analysis of rat hippocampal population codes. The first example is aimed to decode unsorted neuronal spikes, and the second example is aimed to uncover hippocampal population codes using a hidden Markov model (HMM). The common idea is to use probabilistic modeling and Bayesian inference to discover spatiotemporal structures of hippocampal ensemble spike activity.
Decode unsorted neuronal spikes from the rat hippocampus
Overview
Despite rapid progresses in the field of neural decoding, several challenges still remain: First, it is not clear how the spiking activity of individual neurons can reliably represent information. This is often reflected by complex neuronal tuning curves, which are poorly described by simple parametric models. Second, most population decoding methods are based on sorted single units, which will inevitably suffer from various spike-sorting errors, especially in the presence of few wires or probes (Wehr et al. 1999; Harris et al. 2000; Wood et al. 2004; Won et al. 2007).