Bayesian Parameter Estimation and MCMC Calibration for Non-Markovian K-Kernel Cosmological Models

The validation of alternative cosmological models relies on their ability to be constrained by observational data. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm (Metropolis-Hastings) to perform Bayesian parameter estimation for the non-Markovian K-Kernel cosmological framework. Using a simulated dataset with Gaussian noise representing observational redshift data, we estimate the memory decay parameter (\lambda). The simulation demonstrates that the MCMC chain converges rapidly and the posterior probability distribution accurately recovers the true parameter value (\lambda = 0.5). The trace plot and posterior histogram confirm the statistical robustness and numerical stability of the K-Kernel model. This framework provides a standardized statistical pipeline for future comparisons with real datasets from Planck, DES, or JWST.