Nowadays, hospitals are ubiquitous and integral to modern society. Patients flow in and out of a veritable whirlwind of paperwork, consultations, and potential inpatient admissions, through an abstracted system that is not without flaws. One of the biggest flaws in the medical system is perhaps an unexpected one: the patient alarm system. One longitudinal study reported an 88.8% rate of false alarms, with other studies reporting numbers of similar magnitudes. These false alarm rates lead to deleterious effects that manifest in a lower standard of care across clinics. This paper discusses a model-based probabilistic inference approach to estimate physiological variables at a detection level. We design a generative model that complies with a layman's understanding of human physiology and perform approximate Bayesian inference. One primary goal of this paper is to justify a Bayesian modeling approach to increasing robustness in a physiological domain. In order to evaluate our algorithm we look at the application of heart beat detection using four datasets provided by PhysioNet, a research resource for complex physiological signals, in the form of the PhysioNet 2014 Challenge set-p1 and set-p2, the MIT-BIH Polysomnographic Database, and the MGH/MF Waveform Database. On these data sets our algorithm performs on par with the other top six submissions to the PhysioNet 2014 challenge. The overall evaluation scores in terms of sensitivity and positive predictivity values obtained were as follows: set-p1 (99.72%), set-p2 (93.51%), MIT-BIH (99.66%), and MGH/MF (95.53%). These scores are based on the averaging of gross sensitivity, gross positive predictivity, average sensitivity, and average positive predictivity.