Type:	Package
Title:	Bayesian Estimation of Adsorption Isotherms via MCMC
Version:	0.1.0
Author:	Paul Angelo C. Manlapaz [aut, cre]
Maintainer:	Paul Angelo C. Manlapaz <pacmanlapaz@gmail.com>
Description:	Provides tools for Bayesian parameter estimation of adsorption isotherm models using Markov Chain Monte Carlo (MCMC) methods. This package enables users to fit non-linear and linear adsorption isotherm models—Freundlich, Langmuir, and Temkin—within a probabilistic framework, capturing uncertainty and parameter correlations. It provides posterior summaries, 95% credible intervals, convergence diagnostics (Gelman-Rubin), and visualizations through trace and density plots. With this R package, researchers can rigorously analyze adsorption behavior in environmental and chemical systems using robust Bayesian inference. For more details, see Gilks et al. (1995) <doi:10.1201/b14835>, and Gamerman & Lopes (2006) <doi:10.1201/9781482296426>.
License:	GPL-3
Encoding:	UTF-8
Imports:	MCMCpack, coda, stats, graphics
Suggests:	testthat
Config/testthat/edition:	3
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-05-28 14:36:32 UTC; PTRI
Repository:	CRAN
Date/Publication:	2025-05-30 09:30:12 UTC

MCMC Analysis for Freundlich Isotherm Linear Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) to estimate the parameters of the Freundlich isotherm based on its linearized form: log(Qe) = log(Kf) + (1/n)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

Value

A list containing:

mcmc_results

An object of class mcmc.list containing posterior samples from all MCMC chains. Each chain includes samples of the intercept and slope.

Kf_mean

Posterior mean estimate of the Freundlich constant (Kf).

n_mean

Posterior mean estimate of the Freundlich exponent (n).

logKf_mean

Posterior mean of (log(Kf)) from the first MCMC chain.

inv_n_mean

Posterior mean of (1/n) (the slope) from the first MCMC chain.

logKf_sd

Posterior standard deviation of (log(Kf)), quantifying uncertainty in the intercept estimate.

inv_n_sd

Posterior standard deviation of (1/n), quantifying uncertainty in the slope estimate.

logKf_ci

95% credible interval for (log(Kf)) from the first MCMC chain, representing the posterior uncertainty in the intercept.

inv_n_ci

95% credible interval for (1/n) from the first MCMC chain, representing the posterior uncertainty in the slope.

gelman_diag

Gelman-Rubin diagnostic output from coda::gelman.diag(), used to assess convergence of the multiple MCMC chains. A potential scale reduction factor (PSRF) close to 1 indicates good convergence.

mcmc_summary

Summary statistics of the first MCMC chain, including means, standard deviations, quantiles, and sample sizes 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_freundlichLM(Ce, Qe, burnin = 1000, mcmc = 5000, thin = 10,
                  verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

MCMC Analysis for Freundlich Isotherm Non-linear Model

Description

Performs Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) for the non-linear Freundlich isotherm model: Qe = Kf * Ce^(1/n) This approach is applied to obtain a probabilistic distribution of the model parameters, capturing uncertainties and potential correlations between them.

Arguments

Value

A list containing:

Kf_mean

Posterior mean estimate of Freundlich constant (Kf).

n_mean

Posterior mean estimate of Freundlich exponent (n).

logKf_mean

Posterior mean of (log(K_f)).

inv_n_mean

Posterior mean of (1/n).

logKf_sd

Posterior standard deviation for (log(Kf)).

inv_n_sd

Posterior standard deviation for (1/n).

logKf_ci

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

inv_n_ci

95% credible interval for (1/n).

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

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

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)

MCMC Analysis for Langmuir Isotherm Linear (Form 2) Model

Description

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

Value

A list containing:

mcmc_results

An object of class mcmc.list with posterior samples from all chains.

Qmax_mean

Posterior mean estimate of (Qmax).

b_mean

Posterior mean estimate of (b).

slope_mean

Posterior mean of slope (1 / (Qmax * b)).

intercept_mean

Posterior mean of intercept ((1/Qmax)).

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_langmuirLM2(Ce, Qe, burnin = 1000, mcmc = 5000, thin = 10,
                 verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

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

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)

MCMC Analysis for Langmuir Isotherm Linear (Form 4) Model

Description

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

Value

A list with:

mcmc_results

Combined posterior samples (mcmc.list).

Qmax_mean

Posterior mean of Qmax.

b_mean

Posterior mean of b.

intercept_mean

Posterior mean of intercept (b * Qmax).

intercept_sd

Posterior standard deviation of intercept.

intercept_ci

95% credible interval for intercept.

slope_mean

Posterior mean of slope (-b).

slope_sd

Posterior standard deviation of slope.

slope_ci

95% credible interval for slope.

gelman_diag

Gelman-Rubin convergence diagnostics.

mcmc_summary

Summary 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_langmuirLM4(Ce, Qe, burnin = 1000, mcmc = 10000, thin = 10,
                 verbose = 100, plot = TRUE, n_chains = 2, seed = 123)

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

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)

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

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)

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

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)