The Epistemology of Discretized Bayesian Induction: From Frequentist Dogma to Glass-Box Decision-Making under Uncertainty (Part 7/7)

Statistical inference across empirical science, biostatistics, opinion polling, and operational decision-support systems stands at a critical epistemological crossroads. For nearly a century, statistical practice has been dominated by two computational paradigms: frequentist Null Hypothesis Significance Testing (NHST) reliant on Fisherian p-values, and continuous Bayesian modeling reliant on subjective conjugate priors or computationally opaque Markov Chain Monte Carlo (MCMC) samplers. Frequentist p-values collapse rich empirical evidence into arbitrary binary verdicts ("significant" vs. "non-significant"), confusing P(Data | H0) with P(H0 | Data) and triggering a global reproducibility crisis. Conversely, continuous Bayesian models introduce artificial bias through continuous prior densities (such as Beta or Dirichlet laws) and encounter an MCMC computational wall characterized by heavy latency, sample autocorrelation, burn-in losses, and non-deterministic opacity. This paper establishes the foundational epistemological framework of Discretized Bayesian Induction (BID). Originating from high-dimensional industrial knowledge compilation systems developed at Renault (SICG/C2G), BID reconciles Jaynesian Bayesian logic with real-time operational execution. We conduct a rigorous critique of the "continuous dogma" (le procès du continu), proving that continuous integration is an abstraction error that implicitly assumes an infinite population (Popu -> infinity). We demonstrate the phenomenological rehabilitation of discretization: evaluating exact discrete summations over representative virtual urns of cardinal Popu = 1,000 (0.1% measurement step size) delivers zero-error physical precision, creating a visually smooth, continuous bell curve—the Retina Effect—executing in 1.59 milliseconds on standard CPUs for binomial induction. Furthermore, BID eliminates researcher subjectivity by assigning objective Maximum Entropy (Maxent) priors via the PEMPI algorithm. Finally, we establish the necessity of a deterministic BID Induction Layer to manage epistemic uncertainty, eliminate hallucinations in sparse demographic hypercubes, and provide certified decision support in Generative AI and Foundation Models.