Lecture 4

Question 1

Model Comparison: Which model would you trust more?

Answer 1

Question 2

R², AIC, and Model Fitting

Answer 2

Question 3

Calibration in Models

Answer 3

Question 4

Why Calibration is Needed

Answer 4

Question 5

Parameter Sensitivity

Answer 5

Question 6

Calibration Techniques

Answer 6

Question 7

Measurement of Deviation

What are the key metrics used to measure deviation in model performance?

Answer 7

Question 8

Mean Absolute Error (MAE)

What does it represent?

Answer 8

• MAE takes the absolute value of errors, treating all errors equally.
• RMSE squares the errors, penalizing larger errors more heavily.

Interpretation:

• MAE gives the average size of the error in the same units as the data.
• RMSE emphasizes larger deviations, making it more sensitive to outliers.

Question 9

Mean Absolute Percent Error (MA%E)

What does it indicate?

Answer 9

Question 10

Root Mean Square Error (RMSE)

what does it emphasize?

Answer 10

Question 11

Answer 11

Question 12

Allometric Relationships

Answer 12

Power laws describe how one variable changes as a power of another. They are fundamental in understanding relationships across a wide range of natural and human systems, from metabolic rates to city sizes and wealth distributions.

Question 13

Automatic Calibration Algorithms

Answer 13

“minima” is desirable in this context because it represents the point at which the Residual Sum of Squares (RSS) is minimized.

• The global minimum is the point where RSS is minimized across the entire parameter space, resulting in the best possible model fit.
• A local minimum, however, might trap the optimization process if the algorithm converges there, leading to suboptimal parameter values and a less accurate model.

Question 14

Nash-Sutcliffe Efficiency

Answer 14

Question 15

Model Optimization

Answer 15

Question 16

Efficiency and Model Usefulness

Answer 16

Question 17

What is the purpose of calibration?

Answer 17

To adjust parameters to minimize the difference between model predictions and observed data.

Question 18

What steps are involved in calibration?

Answer 18

• Choose initial parameter values.
• Iteratively adjust parameters to minimize errors.
• Evaluate the fit using metrics like R-squared and RMSE.

Question 19

What is cross-validation?

Answer 19

A method that divides datasets into training and testing subsets for evaluation.

Question 20

What is k-fold cross-validation?

Answer 20

A repeated cross-validation process that reduces bias and improves reliability.