# Technical Report 109, c4e-Preprint Series, Cambridge

## Bayesian parameter estimation for a jet-milling model using Metropolis-Hastings and Wang-Landau sampling

ref: Technical Report 109, c4e-Preprint Series, Cambridge

Associated Themes: Numerics and Particle Processes

Bayesian parameter estimates for a computationally expensive multi-response jet-milling model are computed using the Metropolis-Hastings and Wang-Landau Markov Chain Monte Carlo sampling algorithms. The model is accompanied by data obtained from 74 experiments at different process settings which is used to estimate the model parameters. The experimentally measured quantities are the 10th, 50th and 90th quantiles of the resulting particle size distributions. Parameter estimation is performed on a population balance jet-milling model comprised of three subprocesses: jet expansion, milling and classification. The model contains eight parameters requiring estimation and can compute the same quantities that are determined in the experiments. As the model is computationally expensive to solve, the sampling algorithms are applied to a surrogate model to establish algorithm specific parameters and to obtain model parameter estimates. The resulting parameter estimates are given with a discussion of their reliability and the observed behaviour of the two sampling algorithms. Comparison of the autocorrelation function between samples generated by the two algorithms shows that the Wang-Landau algorithm exhibits more rapid decay. Trace plots of the parameter samples from the two algorithms appear to be analogous and encourage the supposition that the Markov Chains have converged to the distribution of interest. One- and two-dimensional density plots indicate a unimodal distribution for all parameters, which suggests that the obtained estimates are unique. The two-dimensional density plots also suggest correlation between at least two of the model parameters. The realised distribution generated by both algorithms produced consistent results and demonstrated similar behaviour. For the application considered in this work, the Wang-Landau algorithm is found to exhibit superior performance with respect to the correlation and equivalent performance in all other respects.

Material from this preprint has been published in: Chemical Engineering Science 89, 244-257, (2013)

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