mb_r

HydroErr.HydroErr.mb_r(simulated_array, observed_array, replace_nan=None, replace_inf=None, remove_neg=False, remove_zero=False)

Compute Mielke-Berry R value (MB R).

../_images/MB_R.png

Range: 0 ≤ MB R < 1, does not indicate bias, larger is better.

Notes: Compares prediction to probability it arose by chance.

Parameters:
  • simulated_array (one dimensional ndarray) – An array of simulated data from the time series.
  • observed_array (one dimensional ndarray) – An array of observed data from the time series.
  • replace_nan (float, optional) – If given, indicates which value to replace NaN values with in the two arrays. If None, when a NaN value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.
  • replace_inf (float, optional) – If given, indicates which value to replace Inf values with in the two arrays. If None, when an inf value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.
  • remove_neg (boolean, optional) – If True, when a negative value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.
  • remove_zero (boolean, optional) – If true, when a zero value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.
Returns:

The Mielke-Berry R value.
Return type:

float

Notes

If a more optimized version is desired, the numba package can be implemented for a much more optimized performance when computing this metric. An example is given below.

>>> from numba import njit, prange

>>> @njit(parallel=True, fastmath=True)
>>> def mb_par_fastmath(pred, obs):  # uses LLVM compiler
>>>     assert pred.size == obs.size
>>>     n = pred.size
>>>     tot = 0.0
>>>     mae = 0.0
>>>     for i in range(n):
>>>         for j in prange(n):
>>>             tot += abs(pred[i] - obs[j])
>>>         mae += abs(pred[i] - obs[i])
>>>     mae = mae / n
>>>     mb = 1 - ((n ** 2) * mae / tot)
>>>
>>> return mb

Examples

>>> import HydroErr as he
>>> import numpy as np

>>> sim = np.array([5, 7, 9, 2, 4.5, 6.7])
>>> obs = np.array([4.7, 6, 10, 2.5, 4, 7])
>>> he.mb_r(sim, obs)
0.7726315789473684

References

  • Berry, K.J., Mielke, P.W., 1988. A Generalization of Cohen’s Kappa Agreement Measure to Interval Measurement and Multiple Raters. Educational and Psychological Measurement 48(4) 921-933.
  • Mielke, P.W., Berry, K.J., 2007. Permutation methods: a distance function approach. Springer Science & Business Media.