Discretized Bayesian Induction: Overview of the BID Framework (Part 1/7)

Empirical science, biostatistics, opinion polling, and industrial decision-support systems face a double crisis: a global reproducibility crisis driven by the misuse of frequentist p-values, and an explicability crisis caused by computationally heavy, opaque statistical black boxes (Markov Chain Monte Carlo / MCMC samplers). This paper provides the foundational synthesis of the Discretized Bayesian Induction (BID) framework (Bayesian Induction for Dummies). Originating from high-dimensional industrial knowledge compilation systems developed at Renault (SICG/C2G, 2000), BID reconciles Jaynesian Bayesian rigor with real-time operational execution. Grounded in E.T. Jaynes's probability theory as extended logic, BID replaces continuous calculus with exact arithmetic operations over finite, representative virtual urns of adjustable cardinal (typically Popu = 1,000, establishing a 0.1% measurement step size). Prior distributions are assigned objectively without researcher subjectivity using E.T. Jaynes's Principle of Maximum Entropy via the PEMPI (Probabilisation en Entropie Maximale par Propagation Itérée) algorithm. We detail the complete architecture across its modular hierarchy: BID2 for binary 1D induction in linear O(Popu) time; BID3 for exact trinomial joint induction over the 2D barycentric simplex (501,501 hypotheses at Popu = 1,000); BIDn for linear 1-vs-Rest multinomial candidate tracking; BIDnC for contextual inference over a set of causal variables (VaCs), using geometric Focalisation and Fusion algebra inherited from the SICP structure; BIDSim for ultra-fast chained urn scenario sample generation (149.4x speedup over MCMC with zero autocorrelation); and EvalCout for coupling probability vectors with monetary utility matrices to compute Expected Net Gain (EBBilan), Value at Risk (VaR), and Pivot Prices in 1.59 milliseconds. Finally, we outline the deployment of BID across permanent adaptive clinical trials, causal web panel rebalancing, and real-time interactive decision support via the C2GP probabilistic configurator.