Hi Abani
Actually, the idea of calculating the regression slope (for each block) from the kriging variance etc. was put forth by Vann etc. in a paper called Quantitative Kriging Neighbourhood Analysis for the Mining Geologist - A Description of the Method With Worked Case Examples. The idea proposed by the paper is that a regression slope of 1.0 indicates conditionally unbiased estimates. However, this idea is based on theory with rigorous assumptions and doesn't work very well in practice. You can test it by cross validation and see for yourself. Vanns' paper goes further and argues that one should design a kriging search neighborhood by trial and error with the objective of obtaining a regression slope of 1.0 to insure the estimates of any or all kriged models are conditionally unbiased. However, this advice is misleading or to put it bluntly, wrong. In order for the grade-tonnage curves of a long term mine planning model or ore resource model to predict unbiased recoveries, the kriged estimates themselves must necessarily be conditionally biased! See "THE KRIGING OXYMORON: A CONDITIONALLY UNBIASED AND ACCURATE PREDICTOR " for proof. The only exception is the case where the kriged estimates will actually be used for selection at the time of mining, e.g. grade control. To summarize - if the kriged estimates are going to be used for selection at the time of mining (grade control), then conditionally unbiased estimates are desirable. For all other models such as mine planning block models or resource models - forget about conditional bias. It is irrelevant. Both of these papers can be downloaded from <http://www.isaaks.com/> www.isaaks.com by clicking on "Geo Docs". Hope this helps, ed _____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Abani R Samal Sent: Sunday, November 11, 2007 9:57 PM To: [email protected] Subject: AI-GEOSTATS: Kriging variance, lagrangian multiplier My First question: I am using a mining software to get a krigged block model. The tool also saves a parameter called "Slope of Regression". The "Slope of Regression" is defined as (Block Variance - Kriging Variance +Lagrange_multiplier)/(Block_variance-KrigingVariance+2*abs(Lagrange_Multipl ier)) provided the denominator is not zero. Unfortunately, there is NO literature available (Including no help file). I have hard time to understand what this "Slope of Regression"means and how this slope is usable. I'll highly appreciate your thought on this. My second question: If s is the sample, v is the block and V is the whole panel of blocks or the whole deposit, the Krige's additive relation can be written as: σ 2 (s,V) = σ2(s,v) + σ2(v,V) But how is: σ2(s,V) related to σ2ok? (σ2okKriging variance), under what condition? Abani R Samal Lakewood, CO __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
