Regression of binary interaction parameters for thermodynamic models using an inside-variance estimation method (IVEM)

An inside-variance estimation method (IVEM) for binary interaction parameter regression in thermodynamic models is proposed. This maximum likelihood method involves the re-computation of the variance for each iteration of the optimization procedure, automatically re-weighting the objective function. Most of the maximum likelihood approaches currently used to regress the parameters of thermodynamic models fix the variances, converting the problem into a traditional weighted least squares minimization. However, such approaches lead to residual variances (between measured and calculated values) that are inconsistent with the fixed variances and, thus, do not necessarily produce optimum parameters for prediction purposes. The new method (IVEM) substantially improves fluid phase equilibria predictions (as shown by the examples presented) by maintaining consistency between the residual variances and the variance used in the objective function. This results in better parameter estimation and to a direct measure of the uncertainty in the model prediction.