Hello, At the moment I am examining methods for estimating the mean and the variance of the mean of irregularly shaped blocks, in this case soil units and agricultural fields, based on an irregular soil sampling scheme.
The simplest solution is block kriging based on a fine mesh discretization of the block. However when the range of the variogram is less than the lengths of the block being estimated this is not recommended. In this situation conditional simulation is recommended, e.g the GSLIB manual and some papers by Goovaerts. This involves simulating values, conditional to the samples, onto a fine grid covering the block. Over many realizations, the mean and its variance of the region may be estimated from the simulated values on the fine grid. In particular, LU Decompsition has been mentioned. This issue has been raised on the list a few years ago but it was not clear which way was best. Other than getting a pdf, some reasons for preferring simulation include: (i) numerical instabilities when block kriging with large matrices (ii) the semivariogram is most accurate at short lags so to using modelled semivariance values beyond the range is unwise. I have used both methods (I used LU Decomposition for simualtion) and get very similar results which is probably as expected. It seems to me that problems with block kriging the regional mean equally apply to conditional simulation when using LU Decomposiiton. LU Decomposiiotn involves a larger matrix than kriging, and like kriging it uses the estimates of the semivariance at longer lags to fill out the covariance matrix between the condtioning data and non-conditioning locations. I could use other simulation algorithms such as Sequential Gaussian Simulation but it all seems an overkill when I just want an estimate of the mean and the variance. Especially if I want to extend my work to cokrige 4 variables simultaneously, each being equally important. I imagine this would take a long time with Sequential Gaussian Simulation let alone the time to code this! Finally, a good estimate of the variance is equally important as the mean in my work so finding the mean value based on dividing the blocks into smaller blocks is not appropriate as it does not give an estimate of the variance So given that I just want the mean and variance, and not the pdf, why should I use simulation, especially using LU Decompsition, when the results are the same? Would it be wise to state that if you only want the mean and variance = use block kriging, if you want a pdf = use condtional simulation? Thanks for your help in advance. Tom Thomas Bishop Biomathematics and Bioinformatics Division Rothamsted Research Harpenden Hertfordshire AL5 2JQ United Kingdom Tel: + 44 (0) 1582 763 133 ext 2574 Fax: + 44 (0) 1582 760 981
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