# 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