mcmc_temkinNLM {adsoRptionMCMC}R Documentation

MCMC Analysis for Temkin Isotherm Non-linear Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) for the non-linear Temkin isotherm model: Qe = (R * T / b_T) * ln(A_T * 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.

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:

AT_mean

Posterior mean estimate of Temkin constant (AT).

bT_mean

Posterior mean estimate of Temkin constant (bT).

logAT_mean

Posterior mean of (log(AT)).

bT_sd

Posterior standard deviation for (bT).

logAT_sd

Posterior standard deviation for (log(AT)).

logAT_ci

95% credible interval for (log(AT)).

bT_ci

95% credible interval for (bT).

gelman_diag

Gelman-Rubin diagnostics (only if multiple chains).

mcmc_summary

Summary statistics for each parameter.

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_temkinNLM(Ce, Qe, 298, burnin = 1000, mcmc = 5000, thin = 10,
               verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

[Package adsoRptionMCMC version 0.1.0 Index]