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Autonomous execution of robot tasks requires the ability to deal online with uncertainties such as partially unknown environments, inaccurate models, and measurement noise. This is especially true for the execution of motions maintaining stiff contacts ("compliant motions"), as contact forces become very high even for small position errors. The autonomy during compliant motion tasks is based on i) a force controller, dealing with small misalignments and keeping the contact forces within safe limits, and ii) an estimator, which recognizes the model (e.g., the type of contact) and estimates the system state (e.g., the relative position of the contacting objects). This paper focuses on Bayesian model-based solutions to the model recognition problem. We discuss Bayesian hypothesis testing and practical approximations. Experimental results are provided for two autonomous-compliant motion tasks by applying consistency testing and likelihood ratio testing. The system state is estimated simultaneously with the model recognition. This estimation is performed by the Iterated Extended Kalman filter for (approximate) linear problems and by the nonminimal state Kalman filter for nonlinear problems.