Validating a resource estimate: cross-validation, swath plots and grade-tonnage checks
Validating a resource estimate means testing it against data it was not fitted to, comparing it with the samples in space and statistics, and checking that the tonnes and grade respond sensibly to the cut-off.
No single check proves an estimate is right. Cross-validation tests the model’s ability to predict held-out samples and is the right tool for choosing range and kernel. Swath plots compare the estimate with the samples along an axis and expose drift and bias. Statistics and grade-tonnage curves check that the estimated population is believable. Used together, they show where an estimate can be trusted and where it cannot.
Cross-validation: predicting what you hide
Cross-validation removes samples, predicts them from the rest and compares prediction with truth. It is the most direct test of whether a model of continuity is useful, and it is how parameters should be chosen, instead of by eye.
In GEOREKA, cross-validation follows the model you will actually use. For support vector regression it tunes the range and the smoothing (epsilon) with the same exponential kernel, and under LVA it uses the non-stationary kernel, so the test matches the real run. For kriging it tunes range and nugget, and for RBFs range and a smoothing term, using fast leave-one-out formulas.
For LVA specifically, cross-validation answers the question that matters: does the local anisotropy field measurably improve prediction compared with a single global ellipsoid? If it does not, the field is decoration.
Comparing estimators on the same samples
Because IDW, RBF, SVR and dual ordinary kriging in GEOREKA run on the same samples and domains, you can compare them directly. The estimators use all points, so there is no search neighbourhood to tune. They assume continuity within a domain, so a well-defined domain matters more than a clever neighbourhood. See the shared mathematics of the methods.
Statistics: is the estimated population believable?
Compare the histogram and summary statistics of the estimate with those of the (declustered) samples in each domain. Estimates are smoother than the samples, so the variance of the estimate should be lower, but the mean should agree. A mean that is far from the declustered sample mean is a flag for bias, a bad domain or an outlier problem.
Swath plots: drift and local bias
A swath plot slices the domain into bands along an axis, usually easting, northing or elevation, and plots the mean of the samples and of the estimate in each band. The two curves should track each other. Systematic offsets suggest a bias such as over-smoothing in sparse areas, an extrapolation problem or the wrong domain boundary. Bands with few samples are noisy, so read them with the sample counts.
Grade-tonnage curves: does the estimate behave?
A grade-tonnage curve shows tonnes and average grade above a range of cut-offs for each domain. It is both a result and a check. Smoothing makes tonnage at high cut-offs look lower than selective mining might achieve, so the curve should be read with the support (block size) in mind, and compared across estimators and parameters to see how sensitive the result is.
Look at it
Slice the model through the drillholes in 3D and compare grade in the blocks with the colours of the nearby samples. Many errors, such as a domain boundary placed on the wrong side of a hole, are obvious to the eye and invisible in a table.
Validate in layers: cross-validate to choose parameters, compare statistics and swath plots to find bias, check grade-tonnage for sensitivity, and finish with the visual check. Each layer catches what the others cannot.
Keep reading
Validation of the kernel and range feeds classification, see resource classification methods, and the covariance function is explained in part 4 of the introduction.
Apply it
Validate on the same model
Cross-validation, statistics and charts, swath plots and grade-tonnage results are part of Premium. Resource estimation in GEOREKA →
Common questions
Validating a resource estimate FAQ
What is cross-validation in resource estimation?
Cross-validation removes samples, predicts them from the remaining data and compares the predictions with the real values. It tests how well the model of continuity predicts, and it is used to choose parameters such as the range.
What is a swath plot?
A swath plot compares the mean grade of the samples and of the estimate in bands along an axis. Systematic differences between the two curves point to bias or drift in the estimate.
Should the estimate have the same variance as the samples?
No. Estimation smooths, so the estimate should have lower variance than the samples, but its mean in a domain should agree with the declustered sample mean.
Does a good cross-validation mean the estimate is right?
It means the model predicts held-out samples well. It does not test the domain boundaries, the geology or extrapolation, so combine it with the other checks.