Parametertilpasning

Parametertilpasning is the process of estimating the parameters of a mathematical model so that its outputs align with observed data. It is used across disciplines, including statistics, engineering, natural sciences, and economics, and is closely related to model calibration, regression, and inverse problems. The goal is to identify parameter values that make the model’s predictions most consistent with measurements, while accounting for uncertainties in data and model structure.

Common approaches include least squares estimation, maximum likelihood estimation, and Bayesian inference. Nonlinear models often require iterative optimisation, using gradient-based or global search methods. Regularisation techniques such as L1 or L2 penalties help prevent overfitting and address ill-posedness. The estimation can be frequentist (point estimates with uncertainty via confidence intervals) or Bayesian (posterior distributions).

A typical workflow involves specifying a mathematical or computational model, selecting an objective function to quantify the mismatch between predictions and data, collecting and pre-processing data, running the optimisation to obtain parameter values, and validating the fitted model on independent data. Sensitivity analysis and uncertainty quantification are commonly performed to assess robustness.

Challenges include identifiability (where different parameter values yield similar predictions), data quality issues, measurement error, missing data, model misspecification, and computational demands. Parametertilpasning is widely supported by software tools in R, Python, MATLAB, and Julia, with specialised libraries for optimisation, regression, and Bayesian inference.