mcmc_langmuirNLM {adsoRptionMCMC}R Documentation

MCMC Analysis for Langmuir Isotherm Non-linear Model

Description

This function performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) simulation to estimate the parameters of the Langmuir isotherm using the non-linear model: Qe = (Qmax * KL * Ce) / (1 + KL * Ce) This approach is applied to obtain a probabilistic distribution of the model parameters, capturing uncertainties and potential correlations between them.

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:

Qmax_mean

Posterior mean estimate of the Langmuir maximum adsorption capacity (Qmax).

Kl_mean

Posterior mean estimate of the Langmuir constant (Kl).

Qmax_sd

Posterior standard deviation for (Qmax).

Kl_sd

Posterior standard deviation for (Kl).

Qmax_ci

95% credible interval for (Qmax).

Kl_ci

95% credible interval for (Kl).

gelman_diag

Gelman-Rubin diagnostics (only if multiple chains).

mcmc_summary

Summary statistics for each parameter.

Author(s)

Paul Angelo C. Manlapaz

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

[Package adsoRptionMCMC version 0.1.0 Index]