Estimating reaction model parameter uncertainty with Markov Chain Monte Carlo

Predicting the performance of chemical reactions with a mechanistic model is desired during the development of pharmaceutical and other high value chemical syntheses. Model parameters usually must be regressed to experimental observations. However, experimental error may not follow conventional distributions and the validity of common statistical assumptions used for regression should be examined when fitting mechanistic models.This paper compares different techniques to estimate parameter confidence for reaction models encountered in pharmaceutical manufacturing, simulated with either normally distributed or experimentally measured noise. Confidence intervals were calculated following standard linear approaches and two Markov Chain Monte Carlo algorithms utilizing a Bayesian approach to parameter estimation: one assuming a normal error distribution, and a new non-parametric likelihood function. While standard frequentist approaches work well for simpler nonlinear models and normal distributions, only MCMC accurately estimates uncertainty when the system is highly nonlinear, and can account for any measurement bias via customized likelihood functions.

► Non-parametric error distributions are used to regress model parameters.
► Chemical reaction models common to pharmaceutical process engineering are examined.
► Improved estimates are made for nonlinear models and biased error distributions.
► Selecting proper error distribution critical to accurate regression and credibility.