Copolymerization Reactivity Ratio Inference: Determining Confidence Contours in Parameter Space via a Bayesian Hierarchical Approach

Confidence contours in parameter space are a helpful tool to compare and classify determined estimators. For more intricate parameter estimations of non-linear nature or complex error structures, the procedure of determining confidence contours is a statistically complex task. For polymer chemists, such particular cases are encountered in determination of reactivity ratios in copolymerization. Hereby, determination of reactivity ratios in copolymerization requires non-linear parameter estimation. Additionally, data may possess (possibly correlated) errors in both dependent and independent variables. A common approach for such non-linear estimations is the error-in-variables model yielding statistically unbiased estimators. Regarding reactivity ratios, to date published procedures neglect the non-Gaussian structure of the error estimates which is a consequence of the non-linearity of the model. In this publication, this issue is addressed by employing a Bayesian hierarchical model, which correctly propagates the errors of all variables. We detail the statistical procedure in chemist friendly language to encourage confident usage of our tool. Our approach is based on a \texttt{Python} program requiring minimal installation effort. A detailed manual of the code is included in the appendix of this work, in an effort to make this procedure available to all interested polymer chemists.