Model estimation by maximum likelihood

John M. Drake

Model calibration

Model calibration requires tuning the parameters to “best” represent reality

Evaluation of this representation is by

  • goodness-of-fit
  • generalizability

Least squares estimation

Model calibration is performed by adjusting the parameters to minimize some objective function (aka loss function)

For instance, least squares estimation minimizes the sum of squared errors

\[ SSE = \sum_{i=1}^n (y_i - f(x_i))^2 \]

where \( y_i \) is the \( i^{th} \) observation, \( x_i \) are the inputs to the model, and \( f() \) is the model.

Least squares estimation

The “adjustment” of parameters is typically performed by numerical optimization