ErrorMetrics.jl

A Julia package providing error / performance metrics for comparing model outputs with observations.

Features

• Loss & skill metrics: MSE, NSE/NNSE (and inverse forms for minimization)
• Correlation metrics: Pearson and Spearman (and squared / normalized variants)
• Optional uncertainty weighting: variants that accept observational uncertainty yσ
• Simple, extensible API: dispatch on metric types via metric(m, ŷ, y[, yσ])

Installation

using Pkg
Pkg.add("ErrorMetrics")

Quick Start

using ErrorMetrics
using Random

y  = randn(100)           # observations
ŷ  = y .+ 0.1randn(100)   # model output

mse  = metric(MSE(),  ŷ, y)
nse  = metric(NSE(),  ŷ, y)
pcor = metric(Pcor(), ŷ, y)

# with observational uncertainty
yσ = 0.2 .* ones(100)
nseσ = metric(NSEσ(), ŷ, y, yσ)

Available Metrics

• MSE: Mean Squared Error: Measures the average squared difference between predicted and observed values
• NAME1R: Normalized Absolute Mean Error with 1/R scaling: Measures the absolute difference between means normalized by the range of observations
• NMAE1R: Normalized Mean Absolute Error with 1/R scaling: Measures the average absolute error normalized by the range of observations
• NSE: Nash-Sutcliffe Efficiency: Measures model performance relative to the mean of observations
• NSEInv: Inverse Nash-Sutcliffe Efficiency: Inverse of NSE for minimization problems
• NSEσ: Nash-Sutcliffe Efficiency with uncertainty: Incorporates observation uncertainty in the performance measure
• NSEσInv: Inverse Nash-Sutcliffe Efficiency with uncertainty: Inverse of NSEσ for minimization problems
• NNSE: Normalized Nash-Sutcliffe Efficiency: Measures model performance relative to the mean of observations, normalized to [0,1] range
• NNSEInv: Inverse Normalized Nash-Sutcliffe Efficiency: Inverse of NNSE for minimization problems, normalized to [0,1] range
• NNSEσ: Normalized Nash-Sutcliffe Efficiency with uncertainty: Incorporates observation uncertainty in the normalized performance measure
• NNSEσInv: Inverse Normalized Nash-Sutcliffe Efficiency with uncertainty: Inverse of NNSEσ for minimization problems
• Pcor: Pearson Correlation: Measures linear correlation between predictions and observations
• PcorInv: Inverse Pearson Correlation: Inverse of Pcor for minimization problems
• Pcor2: Squared Pearson Correlation: Measures the strength of linear relationship between predictions and observations
• Pcor2Inv: Inverse Squared Pearson Correlation: Inverse of Pcor2 for minimization problems
• Scor: Spearman Correlation: Measures monotonic relationship between predictions and observations
• ScorInv: Inverse Spearman Correlation: Inverse of Scor for minimization problems
• Scor2: Squared Spearman Correlation: Measures the strength of monotonic relationship between predictions and observations
• Scor2Inv: Inverse Squared Spearman Correlation: Inverse of Scor2 for minimization problems
• NPcor: Normalized Pearson Correlation: Measures linear correlation between predictions and observations, normalized to [0,1] range
• NPcorInv: Inverse Normalized Pearson Correlation: Inverse of NPcor for minimization problems
• NScor: Normalized Spearman Correlation: Measures monotonic relationship between predictions and observations, normalized to [0,1] range
• NScorInv: Inverse Normalized Spearman Correlation: Inverse of NScor for minimization problems

Documentation

For detailed documentation, see the ErrorMetrics.jl documentation.

License

This package is licensed under the EUPL-1.2 (European Union Public Licence v. 1.2). See the LICENSE file for details.

Contributing

Contributions are welcome! Please open an issue or pull request in this repository.