mcmc_langmuirLM1 {adsoRptionMCMC}R Documentation

MCMC Analysis for Langmuir Isotherm Linear (Form 1) Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Langmuir isotherm based on its first linear form: Ce / Qe = 1 / (Qmax * b) + Ce / Qmax 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.

Qmax_mean

Posterior mean estimate of (Qmax).

b_mean

Posterior mean estimate of Langmuir constant (b).

slope_mean

Posterior mean of the slope ((1/Qmax)).

intercept_mean

Posterior mean of the intercept ((1/(Qmax*b))).

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_langmuirLM1(Ce, Qe, burnin = 1000, mcmc = 5000, thin = 10,
                 verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

[Package adsoRptionMCMC version 0.1.0 Index]