mcmc_langmuirLM3: MCMC Analysis for Langmuir Isotherm Linear (Form 3) Model

In adsoRptionMCMC: Bayesian Estimation of Adsorption Isotherms via MCMC

MCMC Analysis for Langmuir Isotherm Linear (Form 3) Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Langmuir isotherm using its third linear form: Qe = Qmax - (1 / b) * (Qe / 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

Combined posterior samples (mcmc.list).

Qmax_mean

Posterior mean of Qmax.

b_mean

Posterior mean of b.

slope_mean

Posterior mean of slope (-1/b).

intercept_mean

Posterior mean of Qmax.

slope_sd

Standard deviation of slope.

intercept_sd

Standard deviation of intercept.

slope_ci

95% credible interval for slope.

intercept_ci

95% credible interval for intercept.

gelman_diag

Gelman-Rubin convergence diagnostic.

mcmc_summary

Summary of main 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_langmuirLM3(Ce, Qe, burnin = 1000, mcmc = 10000, thin = 10,
                 verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

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