Abstract
This chapter focuses on the discrete-time detection and classification of action potentials (APs)—or spikes—in extracellular neural recordings. These spikes are usually recorded over a finite number of time instants in the presence of noise. The theories of detection and estimation play a crucial role in processing neural signals, largely because of the highly stochastic nature of these signals and the direct impact this processing has on any subsequent information extraction. Detection theory is rooted in statistical hypothesis testing, in which one needs to decide which generative model, or hypothesis, among many possible ones, may have generated the observed signals. Detection theory is rooted in statistical hypothesis testing, in which one needs to decide which generative model, or hypothesis, among many possible ones, may have generated the observed signals. The degree of complexity of the detection task can be viewed as directly proportional to the degree of “closeness” of the candidate generative models (i.e., the detection task becomes more complex as the models get closer together in a geometrical sense). Estimation theory can then be used to estimate the values of the parameters underlying each generative model.
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