Search Results for « Probabilistic Models »

This paper presents an extension to the foundational Reactive Oxygen Species (ROS) stochastic differential equation (SDE) model through four probabilistic models implemented in PyMC v5.25.0+. These models provide a robust empirical framework for evaluating agentic debugging methods in probabilistic programming. The models increase in inferential complexity based on stochastic processes relevant to biological aging: a Gaussian Process (GP) regression with hyperparameter optimization for non-parametric covariance estimation, accounting for biological variability \cite{riihimaki2010}; a Hidden Markov Model (HMM) for sequential latent state inference under regime shifts, representative of cellular transitions \cite{munoz2023}; a non-linear SDE for telomere attrition incorporating regime-switching multiplicative noise to capture stochastic shortening variability, improving on prior linear models \cite{wattis2020}; and a Bayesian hierarchical model for epigenetic age acceleration, modeling senescence thresholds through latent methylation transitions \cite{lu2019}.Each model includes reproducible data generation procedures, PyMC implementations using the No-U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo (HMC) inference, and protocols for obtaining high-fidelity reference posteriors via extensive sampling (\( N=10^6 \) draws, effective sample sizes ESS \( >10^5 \), Gelman-Rubin \( \hat{R} < 1.001 \)). The derivations are original and grounded in aging biology to ensure independence from AI training data contamination, confirming novelty—no prior combinations of GP-HMM-SDE-epigenetic models for telomere-senescence benchmarking in agentic settings exist, as verified by an exhaustive arXiv search \cite{riihimaki2010, munoz2023, olofsson1999, lu2019}. Diagnostics from \( N=500 \) draws per chain (after 500 tuning steps) show strong convergence (ESS \( \gtrsim 400 \); \( \hat{R} \lesssim 1.005 \)), supported by simulation-based calibration (SBC) rank histograms uniform over 1000 replications (\( p \)-values \( \in [0.05, 0.95] \)) and prior sensitivity analyses with \( <3\% \) shifts in posterior means.The suite includes detailed mathematical derivations, Stan implementations for validation, diagnostic plots using PGFPlots, model comparisons, and computational profiles (e.g., inference times \( <25 \) s on AMD EPYC 7543 for \( N=500 \), scalable to \( N=10^6 \) with Dask). This benchmark evaluates agentic performance in non-conjugate, high-dimensional inference. Calibration against longitudinal telomere and epigenetic datasets \cite{aviv2018, horvath2013} ensures biological relevance, while SBC-validated posteriors minimize inferential biases, making the framework robust to methodological scrutiny.