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In the neuroscience literature, periods during which pop-ulations of neurons are either simultaneously depolarizedor hyperpolarized are often classified as "UP" and"DOWN" states, respectively [1]. No particular attentionhas been devoted to accurately characterize the transitionbetween these two states within a statistical framework[2]. We propose two (semi-) Markov probabilistic models,in both discrete- and continuous-time domains, aiming toinfer a discrete two-state (UP vs. DOWN) latent processbased on multi-unit spike train observations. The simulta-neously recorded spike trains, treated as stochastic pointprocesses, are modulated by the discrete hidden state andthe firing history of ensemble neurons. To jointly estimatethe hidden state and the unknown parameters of theprobabilistic models, we develop statistical inferencealgorithms within the maximum likelihood estimationframework.

Probabilistic models and inference algorithms for neuronal decoding of UP and DOWN states