mcmc_freundlichNLM {adsoRptionMCMC} | R Documentation |
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
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:
- 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)