Parametrisesti

Parametrisesti is a Finnish adverb meaning “in a parametrized way” or “using parameters.” It is used to describe representations, models or methods that are defined by one or more parameters rather than fixed constants. In mathematics, engineering and related fields, parameterization (parametrointi) expresses a set, curve, surface or function through one or more parameters, typically denoted t, u or v.

In mathematics and geometry, a parameterization describes objects by functions of parameters. For example, a line can be given parametrically as x(t) = x0 + a t, y(t) = y0 + b t. A circle can be described by x(t) = r cos t, y(t) = r sin t. A parametric surface uses two parameters, such as x(u,v), y(u,v), z(u,v). Different parameterizations can describe the same geometric object, and choosing a parameterization can affect properties like simplicity or computational efficiency.

In statistics and data science, the term is used to distinguish parametric models from non-parameteric approaches. A parametric model assumes the data come from a family of distributions characterized by a finite-dimensional parameter vector. Estimation focuses on determining these parameters, often leading to compact representations and tractable inference, while risking model misspecification if the chosen family does not fit the data well.

Parametrisesti is also common in computer-aided design and computer graphics, where shapes and motions are controlled by adjustable parameters, enabling flexible, reusable designs.