Statistical Estimation & System Inference

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Abstractions about estimating unknown states or distributions under uncertainty, including Bayesian and likelihood-based inference such as Jeffreys prior, hidden Markov models and recursive Bayesian estimation, robust and consensus fitting methods like least absolute deviations and random sample consensus, and dynamical-system state representations such as state variables and moving horizon estimation.

13 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Blahut–Arimoto algorithm — A family of alternating iterative optimization algorithms for channel capacity and rate-distortion problems that updates distributions until the information-theoretic objective converges.
• Generalised likelihood uncertainty estimation — A hydrological uncertainty framework that weights an ensemble of behaviorally acceptable model realizations using chosen likelihood-like measures and thresholds.
• Hidden Markov model — Model an observed sequence as emissions from an unobserved Markov state process, separating state transition dynamics from state-conditioned observation distributions.
• Jeffreys prior — A Bayesian prior measure proportional to the square root of the Fisher-information determinant, constructed to remain invariant under smooth reparameterization.
• Least absolute deviations — Fit a model by minimizing the sum of absolute residuals, yielding median-centered robustness to large response outliers while retaining leverage and identifiability boundaries.
• Linear dynamical system — A dynamical system whose state evolution and output laws are linear, enabling superposition and analysis through matrices, spectra, and modes.
• Maximum entropy thermodynamics — An inference-centered formulation of equilibrium thermodynamics that selects the probability distribution of greatest entropy subject to known macroscopic constraints.
• Moving horizon estimation — A constrained state-estimation method that repeatedly optimizes model fit over a finite recent measurement window and summarizes earlier data in an arrival cost.
• Random sample consensus — Estimate a model under substantial outlier contamination by repeatedly fitting random minimal subsets, scoring each hypothesis by thresholded consensus support, and refining the best supported model.
• Recursive Bayesian estimation — Sequential estimation of a changing hidden state by alternating model-based prediction with Bayesian updating from each new observation.
• Set estimation — Estimate every parameter or state consistent with bounded prior and measurement uncertainty, producing an inner or outer feasible set instead of a single point or fully specified probability distribution.
• State variable — One coordinate in a minimal sufficient state description whose current values, together with inputs and a model, determine the system's admissible future evolution and observable outputs.
• Ziv–Zakai bound — A Bayesian lower bound on estimation error that integrates binary hypothesis-testing difficulty across parameter separations.