mb_r¶
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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).
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: 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.