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Rapid strides are being made to bring to reality the technology of wearable sensors for monitoring patients' physiological data. We study the problem of automatically detecting anomalies in the measured blood glucose levels. The normal daily measurements of the patient are used to train a hidden Markov model (HMM). The structure of the HMM-its states and output symbols-are selected to accurately model the typical transitions in blood glucose levels throughout a 24-hour period. The learning of the HMM is done using historic data of normal measurements. The HMM can then be used to detect anomalies in blood glucose levels being measured, if the inferred likelihood of the observed data is low in the world described by the HMM. Our simulation results show that our technique is accurate in detecting anomalies in glucose levels and is robust (i.e., no false positives) in the presence of reasonable changes in the patient's daily routine.