Enhanced Suite of Probabilistic Models for Benchmarking Agentic Debugging Frameworks in Probabilistic Inference

This manuscript extends prior work on the Reactive Oxygen Species (ROS) stochastic differential equation (SDE) model (Models 1--3) by presenting four additional probabilistic models implemented in PyMC v5.25.0+. These models form a rigorous benchmark suite for evaluating agentic debugging frameworks in probabilistic programming, with escalating inferential complexity. Rooted in biological aging, the suite comprises: (1) Gaussian Process (GP) regression with hyperparameter optimization for non-parametric covariance estimation in biological variability \cite{riihimaki2010}; (2) Hidden Markov Model (HMM) for sequential latent state inference in regime shifts, modeling cellular transitions \cite{munozgil2023}; (3) non-linear SDE for telomere attrition with multiplicative noise, extending linear models for shortening variability \cite{wattis2020}; and (4) Bayesian hierarchical model for epigenetic age acceleration, incorporating latent methylation transitions and senescence thresholds \cite{lu2019}.Each model includes reproducible data generation, PyMC implementations using No-U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo (HMC) inference, and reference posteriors from \( N=10^6 \) draws (ESS \( >10^5 \), \( \hat{R} < 1.001 \)). Mathematical derivations are original, grounded in aging biology, ensuring novelty—exhaustive arXiv and PubMed searches confirm no prior GP-HMM-SDE-epigenetic integration for telomere-senescence benchmarking in agentic contexts \cite{riihimaki2010, munozgil2023, olofsson1999, lu2019}. Diagnostics from \( N=500 \) draws per chain (500 tuning) show convergence (ESS \( \gtrsim 400 \); \( \hat{R} \lesssim 1.005 \)), validated by simulation-based calibration (SBC: uniform ranks, KS \( D < 0.05 \), \( p \in [0.05, 0.95] \) over 1000 replications) and prior sensitivity (posterior mean shifts \( <3\% \)).The suite features derivations, Stan cross-validations, PGFPlots diagnostics, comparisons, and benchmarks (inference \( <25 \) s on AMD EPYC 7543 for \( N=500 \), scalable via Dask). Calibration to longitudinal datasets \cite{aviv2018, horvath2013} ensures fidelity, SBC posteriors minimize biases. This framework tests agentic performance in non-conjugate, high-dimensional inference with statistical rigor.