Validation metrics summary¶

Definitions¶

Assume that we have a model $m$ and observations $o$ of the same size $N$.

Root mean square deviation (RMSD)

$$ \text{RMSD}(m, o) = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (m_i - o_i)^2} $$

Bias

$$ \text{Bias}(m, o) = \frac{1}{N} \sum_{i=1}^N (m_i - o_i) $$

Pearson correlation coefficient

$$ \text{Corr}(m, o) = \frac{\sum_{i=1}^N (m_i - \bar{m})(o_i - \bar{o})}{\sqrt{\sum_{i=1}^N (m_i - \bar{m})^2 \sum_{i=1}^N (o_i - \bar{o})^2}} $$

where $\bar{m}$ and $\bar{o}$ are the mean values of $m$ and $o$ respectively.

Software used¶

Models were matched up with observational data using the Python package nctoolkit. Plots were created using the Python package nctoolkit, and the R package ggplot2. Data analysis was performed using the Python packages pandas, nctoolkit, and statsmodels.