mcmc_freundlichLM: MCMC Analysis for Freundlich Isotherm Linear Model

In adsoRptionMCMC: Bayesian Estimation of Adsorption Isotherms via MCMC

MCMC Analysis for Freundlich Isotherm Linear Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Freundlich isotherm based on its linearized form: log(Qe) = log(Kf) + (1/n)log(Ce) This method provides a probabilistic interpretation of the model parameters and accounts for their uncertainties. It supports multiple MCMC chains and computes convergence diagnostics (Gelman-Rubin).

Arguments

Ce	Numeric vector of equilibrium concentrations.
Qe	Numeric vector of adsorbed amounts.
burnin	Integer specifying the number of burn-in iterations (default is 1000).
mcmc	Integer specifying the total number of MCMC iterations (default is 5000).
thin	Integer specifying the thinning interval (default is 10).
verbose	Integer controlling the frequency of progress updates (default is 100).
plot	Logical; if TRUE, trace and density plots of the MCMC chains are shown (default is FALSE).
n_chains	Number of independent MCMC chains (default = 2).
seed	Optional integer for reproducibility.

Value

A list containing:

mcmc_results

An object of class mcmc.list containing posterior samples from all MCMC chains. Each chain includes samples of the intercept and slope.

Kf_mean

Posterior mean estimate of the Freundlich constant (Kf).

n_mean

Posterior mean estimate of the Freundlich exponent (n).

logKf_mean

Posterior mean of (log(Kf)) from the first MCMC chain.

inv_n_mean

Posterior mean of (1/n) (the slope) from the first MCMC chain.

logKf_sd

Posterior standard deviation of (log(Kf)), quantifying uncertainty in the intercept estimate.

inv_n_sd

Posterior standard deviation of (1/n), quantifying uncertainty in the slope estimate.

logKf_ci

95% credible interval for (log(Kf)) from the first MCMC chain, representing the posterior uncertainty in the intercept.

inv_n_ci

95% credible interval for (1/n) from the first MCMC chain, representing the posterior uncertainty in the slope.

gelman_diag

Gelman-Rubin diagnostic output from coda::gelman.diag(), used to assess convergence of the multiple MCMC chains. A potential scale reduction factor (PSRF) close to 1 indicates good convergence.

mcmc_summary

Summary statistics of the first MCMC chain, including means, standard deviations, quantiles, and sample sizes for each parameter.

Author(s)

Paul Angelo C. Manlapaz

References

Gilks, W. R., Richardson, S., & Spiegelhalter, D. J. (1995). Markov Chain Monte Carlo in Practice. Chapman and Hall/CRC.

Examples

Ce <- c(0.01353, 0.04648, 0.13239, 0.27714, 0.41600, 0.63607, 0.80435, 1.10327, 1.58223)
Qe <- c(0.03409, 0.06025, 0.10622, 0.12842, 0.15299, 0.15379, 0.15735, 0.15735, 0.16607)
mcmc_freundlichLM(Ce, Qe, burnin = 1000, mcmc = 5000, thin = 10,
                  verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

adsoRptionMCMC documentation built on June 8, 2025, 10:36 a.m.