Conclusions Bayesian updating of the force coefficients using the Markov chain Monte Carlo (MCMC) method was presented. The single component Metropolis Hastings (MH) algorithm of MCMC was used. Bayesian inference provides a formal way of belief updating when new experimental data is available. It gives a posterior distribution that incorporates the uncertainty in variables as compared to traditional methods, such as the linear regression which yields a deterministic value. By combining prior knowledge and experimental results, Bayesian inference reduces the number of experiments required for uncertainty quantification. Using Bayesian updating, a single test can provide distributions for force coefficients. The posterior distribution samples provide the covariance of the joint distribution as well. Experimental milling results showed that the linear regression did not give consistent results at 50% RI due to a poor quality of fit in the x direction mean forces, whereas Bayesian updating yielded consistent results at both radial immersions tested. Also, since Bayesian updating does not rely on a least squares fit, mean force data at different feed per tooth values is not required

Finally, the Metropolis Hastings algorithm is a powerful tool for updating multiple variables. A grid-based method would require Nm computations, where m is the number of variables and N is the size of the grid. To illustrate, for a joint pdf of four variables with a grid size equal to 300, the grid-based method would require at least

8.1 × 109computations. The MH algorithm would require only approximately 1 × 104iterations for the value to converge to the posterior pdf mean values. The single component MH algorithm for MCMC facilitates updating of joint distributions without significant computational expensive.