Technical Benchmark: BIDSim vs. Variational Inference

This technical benchmark evaluates the BIDSim (Chained Virtual Urns Simulator) against Varia- tional Inference (VI / ADVI), specically Mean-Field and Full-Rank Automatic Dierentiation Varia- tional Inference. While VI reformulates Bayesian integration into an optimization problem by minimizing the reverse Kullback-Leibler divergence DKL(q ∥ p), it suers from severe variance underestimation (under-dispersion), stochastic gradient noise, and softmax Jacobian boundary distortions. BID- Sim provides a 100% exact, glass-box, non-parametric alternative operating on discrete barycentric virtual urns (Popu = 1, 000).