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The reliability of the mercury spallation target is mission-critical for the neutron science program of the spallation neutron source at the Oak Ridge National Laboratory. We present an inverse uncertainty quantification (UQ) study using the Bayesian framework for the mercury equation of state model parameters, with the assistance of polynomial chaos expansion surrogate models. By leveraging high-fidelity structural mechanics simulations and real measured strain data, the inverse UQ results reveal a maximum-a-posteriori estimate, mean, and standard deviation of $6.5\times 10^4$ ($6.49\times 10^4 \pm 2.39\times 10^3$) Pa for the tensile cutoff threshold, $12112.1$ ($12111.8 \pm 14.9$) kg/m$^3$ for the mercury density, and $1850.4$ ($1849.7 \pm 5.3$) m/s for the mercury speed of sound. These values do not necessarily represent the nominal mercury physical properties, but the ones that fit the strain data and the solid mechanics model we have used, and can be explained by three reasons: The limitations of the computer model or what is known as the model-form uncertainty, the biases and errors in the experimental data, and the mercury cavitation damage that also contributes to the change in mercury behavior. Consequently, the equation of state model parameters try to compensate for these effects to improve fitness to the data. The mercury target simulations using the updated parametric values result in an excellent agreement with 88% average accuracy compared to experimental data, 6% average increase compared to reference parameters, with some sensors experiencing an increase of more than 25%. With a more accurate simulated strain response, the component fatigue analysis can utilize the comprehensive strain history data to evaluate the target vessel's lifetime closer to its real limit, saving tremendous target costs.