A managed pressure drilling (MPD) operation may use an inverse model in conjunction with a hydraulic model and real-time drilling conditions and parameters as inputs to determine a wellhead pressure set point corresponding to a desired bottomhole pressure. For example, while drilling a wellbore penetrating a subterranean formation with a drilling system, measured data including a wellhead pressure may be acquired. A model may then be executed that applies a hydraulic model to an a priori model estimate vector to produce predicted data; converts the measured data to a measured data vector; applies a randomized maximum likelihood algorithm to the a priori model estimate vector, the predicted data, and the measured data vector to produce an a posterioiri model estimates; and applies the hydraulic model to the a posterioiri model estimates to produce an a posteriori prediction and a calculated wellhead pressure set point corresponding to a desired bottomhole pressure.