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[ai-geostats] Adding kriging variances.

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  • Digby Millikan
    Dear list, If you had a set of blocks is it possible to add their kriging variances together, to get a standard error for the mine head grade, is this
    Message 1 of 4 , Nov 6, 2005
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      Dear list,

       

       If you had a set of blocks is it possible to add their kriging variances together,

      to get a standard error for the mine head grade, is this something that is done

      in practice or has been done in the past to estimate possible deviations from a

      kriged head grade?

       

      Digby

    • Digby Millikan
      Sorry, I should have been more specific, I meant the kriged estimates error distribution is normally distributed, with a variance of the kriging variance for
      Message 2 of 4 , Nov 7, 2005
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        Sorry, I should have been more specific, I meant the kriged estimates’ error distribution

        is normally distributed, with a variance of the kriging variance for input sample data with

        a normal distribution.

         

        Regards Digby

      • Pierre Goovaerts
        Hi Digby, The variance of a sum of random variables is not equal to the sum of their variances, except if they are independent.. Consequently, the kriging
        Message 3 of 4 , Nov 7, 2005
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          Hi Digby,

          The variance of a sum of random variables is not equal to the sum of their variances, except if they are independent.. Consequently, the kriging variances cannot be simply combined to compute the variance of the global estimator, see Mining Geostatistics, Page 323 (Journel and Huijbregts, 1978).
          The most flexible approach is to use stochastic simulation to generate a set of realizations of the block values, aggregate them, and use the empirical distribution of aggregated block values as a model of uncertainty.
          You can find an example in my publication http://home.comcast.net/~goovaerts/karen.pdf and there is a whole
          book devoted to the use of stochastic simulation in mining.
          Journel and Kyriakidis. 2004. Evaluation of Mineral reserves. A simulation approach. Oxford University Press.

          Cheers,

          Pierre

          -----Original Message-----
          From: Digby Millikan [mailto:digbym@...]
          Sent: Mon 11/7/2005 1:09 AM
          To: AI Geostats mailing list
          Cc:
          Subject: [ai-geostats] Adding kriging variances.
          Dear list,



          If you had a set of blocks is it possible to add their kriging variances
          together,

          to get a standard error for the mine head grade, is this something that is
          done

          in practice or has been done in the past to estimate possible deviations
          from a

          kriged head grade?



          Digby
        • Isobel Clark
          Dear Digby! If your samples are Normal, your variance is chi-squared!!! You can combine (not add together) kriging variances for separate blocks but, unless
          Message 4 of 4 , Nov 7, 2005
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            Dear Digby!
             
            If your samples are Normal, your variance is chi-squared!!!
             
            You can combine (not add together) kriging variances for separate blocks but, unless they are widely separated or big enough to be considered independent this is a non-trivial task. Basically you need to store how much weight is given to each sample for each block, geometry of all blocks and compute a humungeous estimation variance.
             
            Generally for head grade purposes, stopes or blocks are widely separated enough to combine the variances. Weight by size and shape of block (or tonnage) as a proportion of the total -- squared.
            Isobel
             

            Digby Millikan <digbym@...> wrote:

            Dear list,

             

             If you had a set of blocks is it possible to add their kriging variances together,

            to get a standard error for the mine head grade, is this something that is done

            in practice or has been done in the past to estimate possible deviations from a

            kriged head grade?

             

            Digby

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