mcmc_langmuirLM2: MCMC Analysis for Langmuir Isotherm Linear (Form 2) Model

In adsoRptionMCMC: Bayesian Estimation of Adsorption Isotherms via MCMC

MCMC Analysis for Langmuir Isotherm Linear (Form 2) Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Langmuir isotherm using its second linear form: 1 / Qe = 1 / Qmax + (1 / (Qmax * b)) * (1 / 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 with posterior samples from all chains.

Qmax_mean

Posterior mean estimate of (Qmax).

b_mean

Posterior mean estimate of (b).

slope_mean

Posterior mean of slope (1 / (Qmax * b)).

intercept_mean

Posterior mean of intercept ((1/Qmax)).

slope_sd

Posterior standard deviation of the slope.

intercept_sd

Posterior standard deviation of the intercept.

slope_ci

95% credible interval for the slope.

intercept_ci

95% credible interval for the intercept.

gelman_diag

Gelman-Rubin convergence diagnostic.

mcmc_summary

Summary statistics of the first MCMC chain.

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_langmuirLM2(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.