Conditional Bias in Kriging – Let’s Keep It

Marek Nowak, Oy Leuangthong
Friday, September 30, 2016
First presented: 
International Geostatistical Congress
Published paper

Mineral resource estimation has long been plagued with the inherent challenge of conditional bias. Estimation requires the specification of a number of parameters such as block model block size, minimum and maximum number of data used to estimate a block, and search ellipsoid radii. The choice of estimation parameters is not an objective procedure that can be followed from one deposit to the next. Several measures have been proposed to assist in the choice of kriging estimation parameters to lower the conditional bias. These include the slope of regression and kriging efficiency.

The objective of this paper is to demonstrate that both slope of regression and kriging efficiency should be viewed with caution. Lowering conditional bias may be an improper approach to estimating metal grades, especially in deposits for which high cut-off grades are required for mining. A review of slope of regression and kriging efficiency as tools for optimization of estimation parameters is presented and followed by a case study of these metrics applied to an epithermal gold deposit. The case study compares block estimated grades with uncertainty distributions of global tonnes and grade at specified cut-offs. The estimated grades are designed for different block sizes, different data sets and different estimation parameters, i.e., those geared towards lowering the conditional bias and those designed for higher block grade variability with high conditional biases.

Feature Author

Marek Nowak

Marek Nowak has over 25 years of experience in the mining industry. He specializes in natural resource evaluation and risk assessment using a selection of linear and non-linear geostatistical techniques.

  • Resource estimation is typically conducted using classical geostatistical techniques such as ordinary or indicator kriging
  • Risk assessments may be based on a variety of simulation techniques such as sequential Gaussian, sequential indicator or probability field
  • All the techniques used are custom modified or blended according to the practical requirements of the problem


Principal Geostatistician
SRK Vancouver
Dr. Oy Leuangthong

Dr. Leuangthong has over 15 years of experience in geostatistics for resource characterization and uncertainty assessment.  Prior to joining SRK, she was an Assistant Professor in Mining Engineering at the University of Alberta in Edmonton, Alberta.  She has taught geostatistics in various industry courses to engineers and geologists from national and multinational companies in North and South America.  She has also consulted on a range of projects in both the mining and petroleum industry.  Further, she has authored and co-authored 2 books, 16 journal papers and over 30 conference articles.  Her areas of expertise are resource estimation, conditional simulation and uncertainty assessment using geostatistics.

Principal Geostatistician
Ph.D. Mining Engineering, Geostatistics
SRK Toronto
SRK North America