Model Estimation & Numerical Diagnostics

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Abstractions about system identification, forecasting, numerical error, integration, fuzzy control, estimation, tracking, and certification of computational models.

15 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.

• Bode plot — A paired logarithmic-frequency display of a linear system’s frequency-response magnitude and phase.
• Computable real function — A real-valued function for which arbitrarily accurate output approximations can be generated effectively from arbitrarily accurate representations of its real inputs.
• Computational model — An executable formal representation used to simulate and analyze a system through encoded state, rules and parameters.
• Defuzzification — The mapping of an aggregated fuzzy output set or membership distribution to a single crisp value or discrete action.
• Error analysis (mathematics) — The study of how approximation, rounding, truncation, measurement, discretization, and conditioning create and propagate uncertainty in mathematical results.
• Forecast skill — A measure of predictive performance relative to observations and, in skill-score form, relative to a declared reference forecast.
• Fuzzy control system — A controller mapping imprecise linguistic input conditions to control actions through fuzzy sets, rules and defuzzification.
• Heronian mean — The symmetric mean of two nonnegative numbers equal to one third of their sum plus their geometric mean.
• Mean absolute scaled error — A scale-free forecast-accuracy measure dividing mean absolute forecast error by the in-sample mean absolute error of a specified naive benchmark.
• 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.
• Multi-time-step integration — A numerical time-integration strategy that advances different coupled components with different step sizes or integrators while synchronizing their interaction.
• Numerical certification — The production of a mathematically checkable guarantee that a numerically computed candidate corresponds to an actual solution of a stated problem.
• Pfafstetter Coding System — A hierarchical river-basin coding scheme that embeds tributary and downstream topology in numeric identifiers.
• System identification — Construction of a mathematical dynamical-system model from measured input-output behavior and declared structural assumptions.
• Tracking signal — A forecast-monitoring statistic comparing cumulative error with a scale estimate to flag sustained directional bias beyond ordinary variation.