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The human heart rate is influenced by different internal systems of the body and can reveal valuable information about health and disease conditions. In this paper, we analyze the instantaneous heart rate signal using a Bayesian method, inferring in real time a probabilistic distribution that approximates the real distribution of this signal. The best model is chosen after an experimental analysis of real data collected within our framework. The parameters of this distribution can reveal interesting insights on the influences of the sympathetic and parasympathetic divisions of the autonomic nervous system (ANS) in real time.