Mehrparametriger

Mehrparametriger is an adjective used in German to describe something that involves or depends on multiple parameters. In practice, the term is commonly applied to statistical, mathematical, and scientific models that require more than a single parameter to describe data, relationships, or processes. A mehrparametriges Modell typically contrasts with einparametrige or einparametrische approaches, which rely on only one parameter.

In statistics and data analysis, mehrparametrige (multivariate) methods encompass models and analyses with several parameters or coordinates. Examples include multiple regression, multivariate analysis of variance, time-series models with several coefficients, and pharmacokinetic–pharmacodynamic models with multiple rate constants. Such models can capture complex relationships and interactions that single-parameter models cannot, but they also introduce additional challenges.

Key considerations for mehrparametrige models include parameter identifiability, estimation complexity, and the risk of overfitting as the number of parameters grows. Common approaches to address these issues are likelihood-based estimation (such as maximum likelihood), Bayesian inference with prior information, regularization and shrinkage methods, model selection criteria, cross-validation, and sensitivity analyses.

Applications of mehrparametrige modeling span many fields, including biology, economics, engineering, and environmental science. The term emphasizes the need to estimate and interpret several parameters simultaneously, reflecting the multifaceted nature of real-world phenomena. In English, the concept is often described as multivariate or multi-parameter modeling.