plans.stochastic.metrics#

Association and agreement metrics between two samples.

Formulas use \(o_i\) for observed values and \(p_i\) for predicted values.

Functions

bias(observed, predicted)

Compute the Bias (%), positive when predicted overestimates observed.

get_metrics(observed, predicted)

Get all fit metrics between observed and predicted sample.

mae(observed, predicted)

Compute the Mean Absolute Error (MAE).

pearson(x, y)

Compute the Pearson correlation coefficient (r), a measure of linear association.

rmse(observed, predicted)

Compute the Root Mean Squared Error (RMSE).

rsq(observed, predicted)

Compute the coefficient of determination (R2), as the fraction of observed variance explained: 1 - SS_res / SS_tot.

spearman(x, y)

Compute the Spearman rank correlation coefficient (rho), a measure of monotonic association.
plans.stochastic.metrics.get_metrics(observed, predicted)[source]#

Get all fit metrics between observed and predicted sample.

Parameters:

  • observed (numpy.ndarray) – vector of observed values

  • predicted (numpy.ndarray) – vector of predicted values

Returns:

dictionary of metrics (r, rho, R2, RMSE, MAE, Bias)

Return type:

dict

plans.stochastic.metrics.pearson(x, y)[source]#

Compute the Pearson correlation coefficient (r), a measure of linear association. Symmetric: swapping x and y gives the same value.

\[r = \frac{\sum_i (x_i - \bar{x})(y_i - \bar{y})} {\sqrt{\sum_i (x_i - \bar{x})^2} \sqrt{\sum_i (y_i - \bar{y})^2}}\]
Parameters:

  • x (numpy.ndarray) – vector of x values

  • y (numpy.ndarray) – vector of y values

Returns:

r value, from -1 to 1

Return type:

float

plans.stochastic.metrics.spearman(x, y)[source]#

Compute the Spearman rank correlation coefficient (rho), a measure of monotonic association. It is the Pearson r of the ranks (ties averaged). Symmetric: swapping x and y gives the same value.

\[\rho = r\left( \mathrm{rank}(x), \mathrm{rank}(y) \right)\]
Parameters:

  • x (numpy.ndarray) – vector of x values

  • y (numpy.ndarray) – vector of y values

Returns:

rho value, from -1 to 1

Return type:

float

plans.stochastic.metrics.rsq(observed, predicted)[source]#

Compute the coefficient of determination (R2), as the fraction of observed variance explained: 1 - SS_res / SS_tot.

Note

Equals r squared only for least-squares linear models with intercept. For other models it can differ, and is negative when the model is worse than the observed mean.

\[R^2 = 1 - \frac{\sum_i (p_i - o_i)^2}{\sum_i (o_i - \bar{o})^2}\]
Parameters:

  • observed (numpy.ndarray) – vector of observed values

  • predicted (numpy.ndarray) – vector of predicted values

Returns:

R2 value

Return type:

float

plans.stochastic.metrics.rmse(observed, predicted)[source]#

Compute the Root Mean Squared Error (RMSE).

\[\mathrm{RMSE} = \sqrt{\frac{1}{n} \sum_i (p_i - o_i)^2}\]
Parameters:

  • observed (numpy.ndarray) – vector of observed values

  • predicted (numpy.ndarray) – vector of predicted values

Returns:

RMSE value

Return type:

float

plans.stochastic.metrics.mae(observed, predicted)[source]#

Compute the Mean Absolute Error (MAE).

\[\mathrm{MAE} = \frac{1}{n} \sum_i \lvert p_i - o_i \rvert\]
Parameters:

  • observed (numpy.ndarray) – vector of observed values

  • predicted (numpy.ndarray) – vector of predicted values

Returns:

MAE value

Return type:

float

plans.stochastic.metrics.bias(observed, predicted)[source]#

Compute the Bias (%), positive when predicted overestimates observed.

\[\mathrm{Bias} = 100 \, \frac{\sum_i (p_i - o_i)}{\sum_i o_i}\]
Parameters:

  • observed (numpy.ndarray) – vector of observed values

  • predicted (numpy.ndarray) – vector of predicted values

Returns:

Bias value

Return type:

float