Bayesian and Frequentist Methods for Estimating Joint Uncertainty of Freundlich Adsorption Isotherm Fitting Parameters

This paper presents methods for estimating Freundlich isotherm fitting parameters (K and N) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyses and subsequently compared with a commonly applied method in which the Freundlich parameter uncertainty is treated independently. By accounting for joint uncertainty in K and N, smaller uncertainty regions resulted compared with independent uncertainty estimates, with this effect becoming more pronounced as the degree of nonlinearity increased (i.e., as N decreased from 1). To illustrate the impact when considering uncertainty in adsorption system design, an example is provided in which, at a 95% confidence level, considering joint uncertainty decreased the required sorbent by 57-72% (depending on equilibrium liquid concentration, C-W) relative to the commonly applied independent uncertainty treatment of K and N. DOI: 10.1061/(ASCE)EE.1943-7870.0000634. (C) 2013 American Society of Civil Engineers.