Surrogate-Assisted Delayed-Acceptance MCMC for Efficient Parameter Estimation of the Extended Burr Type XII Distribution under Progressive Type-II Censoring

We present a unified estimation framework for the Extended Burr Type XII (EBXII) distribution under progressive Type-II censoring that combines classical and modern approaches: (i) EM-based initialization tailored for censoring, (ii) maximum likelihood estimation with Fisher and bootstrap intervals, and (iii) surrogate-assisted delayed-acceptance MCMC (DA-MCMC) to accelerate Bayesian inference. The surrogate is a KD-tree k-nearest-neighbor model operating in a whitened logarithmic parameter space; it screens proposals cheaply in Stage 1 while Stage 2 performs unbiased corrections using exact or pseudo-marginal likelihood evaluations. On simulated EBXII datasets with (α,β,γ)=(2.5,1.5,3.0) and progressive censoring, our primary experiment shows DA-MCMC reproduces reference posteriors (comparable means and 95% credible intervals) while requiring only 7,854 exact likelihood evaluations compared to 12,000 in the reference run — a reduction of approximately 34.5%. Coverage analysis, bootstrap validations, and ESS diagnostics are reported. An appendix provides concise symbolic derivations for the likelihood, score and observed information, and the EM MC-step formulations. The pipeline is implemented in Python and made reproducible.