Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed. 1. Introduction Neuronal action potentials or spikes are the basic language that neurons use to represent and transmit information. Understanding neuronal representations of spike trains remains a fundamental task in computational neuroscience [1, 2]. 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 [3]. To extract (“read out”) information from or inject/restore (“write in”) signals to neural circuits [4], there are emerging needs for modeling and analyzing neural spike trains recorded directly or extracted indirectly from neural signals, as well as building closed-loop brain-machine interfaces (BMIs). Many good examples and applications can be found in the volumes of the current or other special issues [5, 6]. In recent years, cutting-edge Bayesian methods have gained increasing attention in the analysis of neural data and neural spike trains. Despite its well-established theoretic principle since the inception of Bayes’ rule [7], Bayesian machinery has not been widely used in large-scaled data analysis until very recently. This was partially ascribed to two facts: first, the development of new methodologies and effective algorithms; second, the ever-increasing computing power. The major theoretic or methodological development has been reported in the field of statistics, and numerous algorithms were developed in applied statistics and machine learning for successful real-world applications [8]. It is time to push this research frontier to
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