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.

本研究拓展了此前基于活性氧 (Reactive Oxygen Species) 随机微分方程 (stochastic differential equation, SDE) 模型（模型1至3）的相关工作，新增了4个基于PyMC v5.25.0及以上版本实现的概率模型。这些模型构成了一套严谨的基准测试套件，用于评估概率编程领域的智能体调试框架，其推理复杂度呈逐级递增趋势。该套件根植于生物衰老研究，包含以下四类模型：(1) 高斯过程 (Gaussian Process, GP) 回归模型，针对生物变异的非参数协方差估计进行超参数优化，相关工作可参见cite{riihimaki2010}；(2) 隐马尔可夫模型 (Hidden Markov Model, HMM)，用于状态转移场景下的序列潜在状态推断，以模拟细胞转化过程，相关工作可参见cite{munozgil2023}；(3) 带乘性噪声的非线性随机微分方程模型，用于端粒磨损分析，拓展了此前针对缩短变异的线性模型，相关工作可参见cite{wattis2020}；(4) 用于表观遗传年龄加速的贝叶斯分层模型，整合了潜在甲基化转化与衰老阈值，相关工作可参见cite{lu2019}。每类模型均包含可复现的数据生成流程、采用No-U-Turn采样器 (No-U-Turn Sampler, NUTS) 实现哈密顿蒙特卡洛 (Hamiltonian Monte Carlo, HMC) 推理的PyMC实现，以及由( N=10^6 )次采样得到的参考后验分布（有效样本量 (Effective Sample Size, ESS) ( >10^5 )，( hat{R} < 1.001 )）。本研究的数学推导均为原创，且根植于衰老生物学研究，具备创新性——通过全面检索arXiv与PubMed数据库证实，此前尚无针对智能体调试场景下的端粒-衰老基准测试，且未出现将GP-HMM-SDE-表观遗传模型整合的相关研究cite{riihimaki2010, munozgil2023, olofsson1999, lu2019}。基于每条链500次采样（含500次调参）的诊断结果显示，模型收敛性良好（有效样本量 ( gtrsim 400 )；( hat{R} lesssim 1.005 )），并通过基于模拟的校准 (Simulation-Based Calibration, SBC：1000次重复实验下，秩服从均匀分布，Kolmogorov-Smirnov检验统计量 ( KS D < 0.05 )，( p in [0.05, 0.95] )) 与先验敏感性分析（后验均值偏移量 ( <3\% )）完成了验证。该基准套件包含完整推导过程、Stan交叉验证结果、PGFPlots诊断工具、模型对比与性能基准测试（在AMD EPYC 7543处理器上，针对( N=500 )的推理耗时不足25秒，且可通过Dask实现横向扩展）。通过对纵向数据集cite{aviv2018, horvath2013}的校准，确保了基准套件的拟合保真度，且基于SBC的后验分布可有效降低偏差。本框架可在严格统计框架下，测试智能体在非共轭、高维推理任务中的性能表现。