Hi Colin, What I'm talking about in my example is comparing two descriptive statistics for this population which consists of 27 data points. No estimation here is involved, so the thing about confidence interval of the mean or variance is not of concern here. And it doesn't matter which model I used in the generator or what parameters I used, since I re-calculated the population sill and variance after the data are generated.
Let me state this clear: (Capitalization indicates highlighting, not speaking tone :p) 1. I generated a POPULATION which is, believe it or not, a series of 27 data. 2. The POPULATION variance, in my example, doesn't match the POPULATION sill calculated in the POPULATION variogram. 3. So how are we going to estimate the POPULATION variance by the sill in a SAMPLE, when the sill and the variance in the POPULATION just doesn't match? And just a personal opinion, I would like to think geostatistic theories apply to population of any size, as small as 27, or as large as 1,000,000. If I'm making an example that geostatistics doesn't apply, then there's something to concern about in this approach. Meng On Wed, 8 Dec 2004, Colin Daly wrote: > > Hi Meng-Ying > > 27 points - you can't really calculate a variogram. With a range of 3 - > you have about 9 correlation lenghts in the field. So as a crude > approximation, even the standard deviation on the estimate of the mean > would be of the order of s.d/sqrt(9) (I vaguely remember trying to get a > more accurate version of this in the case of a Gaussian RF as an > exercise in one of Matheron's classes...) > > so with s.d = 2.8 (or 2.4 ---similar answers), then standard error is > 2.8/3=0.9 (approx) > > so your confidence interval for the mean would be [m-1.8, m+1.8] > > - this is the same order for both the estimate of the sill and for the > direct estimate of the variance... both are bad > > That is for the comparitively easy case of the mean - The situation > for the variance is even worse - so there is no way that you can > complain about the quality of the estimate. > > I'm not sure if you are suggesting that you should get different > answers - or that there is some bias involved but to convince yourself > that there is not repeat your experiment but use a length of 1,000,000 > instead of 27....then at least we would get rid of most of the > statistical fluctuations - and the estimates should be similar. How are > you generating the random sequence - is it an AR process or something > where the variance is known theoretically? > > Colin > > -----Original Message----- > From: Meng-Ying Li [mailto:[EMAIL PROTECTED] > Sent: Wed 12/8/2004 6:36 PM > To: Digby Millikan > Cc: ai-geostats > Subject: Re: [ai-geostats] Re: Sill versus least-squares classical > variance estimate > Hi Digby and All, > > I did a little experiment on the idea that Digby mentioned: The sill will > estimate the population variance, but found it not true in my experiment: > > 1. I generated a set of one-dimentional data with 27 points on regular > unit spacings, which I'd like to take it as the true, or population > value. On purpose, I generate the data so it has an influence range of > three length units. > 2. I calculated the experimental variogram. Notice that the variogram is > the population variogram. The sill value is around 2.8. > 3. But the population variance is 2.39, lower than the sill value. > > This confirms my doubt about using sill value as the estimate of > population variance, since I calculate the variogram and variance based on > all data points. Please tell me what you think. The data I generated are > as follows: > > 0.056970748 > 0.14520424 > 0.849710204 > 1.650514605 > 1.101666385 > 1.015177986 > 2.150259206 > 2.830780659 > 0.223495817 > -2.47615958 > -3.372697392 > -0.530685611 > 0.786582177 > 0.970673 > 0.674755256 > 0.338461632 > 1.020874834 > 0.410936991 > 1.702892405 > 2.649748012 > 4.290179731 > 3.442015668 > 1.488818953 > 0.862788738 > 0.728709892 > 2.398182914 > 1.522546427 > > > > > > > > DISCLAIMER: > This message contains information that may be privileged or confidential and > is the property of the Roxar Group. It is intended only for the person to > whom it is addressed. If you are not the intended recipient, you are not > authorised to read, print, retain, copy, disseminate, distribute, or use this > message or any part thereof. If you receive this message in error, please > notify the sender immediately and delete all copies of this message.
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