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Contact mode Atomic Force Microscopy (AFM) is popularly used by the biophysics community to study mechanical properties of cells and tissue due to its ability to quantify biological processes like disease proliferation and stem cell differentiation. While AFM indentation experiments are relatively straightforward, interpretation of the AFM data is subject to some debate. Three factors make the AFM force data prone to incorrect interpretation, namely, the appropriate contact model to use to fit the post-contact AFM data, identifying the point when the AFM probe contacts the cell, and variability in the stiffness of the probe used to estimate material properties of cells. A lot of research has been directed towards developing constitutive models based on sample material property assumptions, however, variability in the AFM probe stiffness and contact point uncertainty has received limited attention. This suggests the need to have an integrated probabilistic model to estimate mechanical properties from the AFM force data which can account for errors contributed from these two sources. In this work, we have developed an Error-In-Variables (EIV) based Bayesian Changepoint model to estimate the contact point and the Young's Modulus from AFM force curves on fixed mouse Embryonic Stem cells (mESC) in the indentation range of 1-1.5 μm. Our results indicate that the EIV-based Bayesian Approach can be used to obtain robust estimates of material properties of biomaterials.