mb_r

HydroErr.HydroErr.mb_r(simulated_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], observed_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], replace_nan: float | None = None, replace_inf: float | None = None, remove_neg: bool = False, remove_zero: bool = False) → floating[Any]

Compute Mielke-Berry R value (MB R).

\[\Re=1-\frac{MAE}{n^{-2}\sum_{j=1}^{n}\sum_{i=1}^{n}|S_j-O_i|}\]

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

Notes: Compares prediction to probability it arose by chance.

Parameters:

  • simulated_array – An array of simulated data from the time series.

  • observed_array – An array of observed data from the time series.

  • replace_nan – 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 – 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 – 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 – 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.

Return type:

The Mielke-Berry R value.

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.