  Mud is a suspension of fine-grained particles (sand, silt, and clay) in
water. The interaction of clay minerals in mud gives rise to complex
rheological behaviors, such as yield stress, thixotropy and viscoelasticity.
Here, we experimentally examine the flow behaviors of kaolinite clay
suspensions, a model mud, using steady shear rheometry. The flow curves exhibit
both yield stress and rheological hysteresis behaviors for various kaolinite
volume fractions ($\phi_k$). Further understanding of these behaviors requires
fitting to existing constitutive models, which is challenging due to numerous
fitting parameters. To this end, we employ a Bayesian inference method, Markov
chain Monte Carlo (MCMC), to fit the experimental flow curves to a
microstructural viscoelastic model. The method allows us to estimate the
rheological properties of the clay suspensions, such as viscosity, yield
stress, and relaxation time scales. The comparison of the inherent relaxation
time scales suggests that kaolinite clay suspensions are strongly viscoelastic
and weakly thixotropic at relatively low $\phi_k$, while being almost inelastic
and purely thixotropic at high $\phi_k$. Overall, our results provide a
framework for predictive model fitting to elucidate the rheological behaviors
of natural materials and other structured fluids.
