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 riihimaki2010; (2) Hidden Markov Model (HMM) for sequential latent state inference in regime shifts, modeling cellular transitions munozgil2023; (3) non-linear SDE for telomere attrition with multiplicative noise, extending linear models for shortening variability wattis2020; and (4) Bayesian hierarchical model for epigenetic age acceleration, incorporating latent methylation transitions and senescence thresholds 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 ), ( 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 riihimaki2010, munozgil2023, olofsson1999, lu2019. Diagnostics from ( N=500 ) draws per chain (500 tuning) show convergence (ESS ( 400 ); ( R 1.005 )), validated by simulation-based calibration (SBC: uniform ranks, KS ( D < 0.05 ), ( p [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 aviv2018, horvath2013 ensures fidelity, SBC posteriors minimize biases. This framework tests agentic performance in non-conjugate, high-dimensional inference with statistical rigor.