mcmc_temkinLM: MCMC Analysis for Temkin Isotherm Linear Model

In adsoRptionMCMC: Bayesian Estimation of Adsorption Isotherms via MCMC

MCMC Analysis for Temkin Isotherm Linear Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Temkin isotherm based on its linearized form: Qe = aT + bT * 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.
Temp	Numeric value of temperature in Kelvin.
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.

aT_mean

Posterior mean estimate of Temkin constant (aT).

bT_mean

Posterior mean estimate of Temkin constant (bT).

aT_raw_mean

Posterior mean of the intercept (aT) from the linear model.

bT_raw_mean

Posterior mean of the slope (b_T) from the linear model.

aT_sd

Posterior standard deviation of (aT).

bT_sd

Posterior standard deviation of (bT).

aT_ci

95% credible interval for (aT).

bT_ci

95% credible interval for (bT ).

gelman_diag

Gelman-Rubin convergence diagnostic.

mcmc_summary

Summary statistics from the first 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_temkinLM(Ce, Qe, 298, 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.