Structural Cosmology v3.8: Statistical Inference Framework From Multi-Survey Integration to Full Bayesian Inference, Model Selection, and Precision Structural Cosmology

Structural Cosmology v3.8 introduces a statistical inference and model selection framework for integrating multi-survey cosmological observations within a unified Bayesian pipeline. Building upon the multi-survey integration framework developed in v3.7, this release incorporates Markov Chain Monte Carlo (MCMC), Nested Sampling, Bayesian evidence evaluation, hierarchical Bayesian inference, cross-probe covariance modeling, forecast emulation, and model selection diagnostics. The framework is designed to connect nonlinear structure formation, higher-order statistics, Euclid DR1 integration, and multi-survey likelihood analysis into a reproducible statistical workflow. Illustrative demonstrations include posterior inference, Bayesian evidence comparison, emulator performance evaluation, hierarchical modeling, and extended falsifiability assessment through the C73–C80 survival network. This release contains 69 figures covering the complete Structural Cosmology v3.5–v3.8 series and establishes the statistical foundation for the planned v3.9 Precision Structural Cosmology program. All quantitative examples presented in this work are illustrative framework demonstrations and should not be interpreted as observational constraints. Future observational analyses will determine the empirical validity of the proposed framework.