In the dynamic hospital setting, decision support can be a valuable tool for improving patient outcomes. Data-driven inference of future outcomes is challenging in this dynamic setting, where long sequences such as laboratory tests and medications are updated frequently. This is due in part to heterogeneity of data types and mixed-sequence types contained in variable length sequences. In this work we design a probabilistic unsupervised model for multiple arbitrary-length sequences contained in hospitalization Electronic Health Record (EHR) data. The model uses a latent variable structure and captures complex relationships between medications, diagnoses, laboratory tests, neurological assessments, and medications. It can be trained on original data, without requiring any lossy transformations or time binning. Inference algorithms are derived that use partial data to infer properties of the complete sequences, including their length and presence of specific values. We train this model on data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The results are evaluated against held-out data for predicting the length of sequences and presence of Intensive Care Unit (ICU) in hospitalization bed sequences. Our method outperforms a baseline approach, showing that in these experiments the trained model captures information in the sequences that is informative of their future values.