formalstatistical

Formalstatistical is an interdisciplinary field that seeks to integrate formal methods from logic, computer science, and mathematics with statistical modeling and inference. Proponents define it as the practice of specifying statistical models with formal semantics, reasoning about assumptions using rigorous logic, and deriving conclusions that are verifiable beyond empirical results. The approach emphasizes explicit specification of hypotheses, data-generating mechanisms, and decision criteria, aiming to provide correctness guarantees for statistical conclusions and to improve reproducibility.

Core techniques include the use of formal specification languages, theorem provers, and proof assistants to encode statistical assumptions; probabilistic programming languages with formal semantics; model checking for stochastic systems; and Bayesian reasoning augmented with formal verification to assert properties of algorithms. Formal analysis may yield bounds on error rates, convergence, and calibration under stated conditions.

Applications span safety-critical domains such as aerospace, automotive, and healthcare, as well as finance and AI reliability, where decisions depend on guarantees about uncertainty. Challenges include computational complexity, limited tooling maturity, reconciling empirical data practice with formal reasoning, and developing education and standards that bridge statisticians and formal-methods communities. The field remains relatively young and evolving, with ongoing work aimed at making formal guarantees more practical and broadly applicable in real-world statistical practice.