Difference between revisions of "Talk:Circular Error Probable"
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::: So when we measure <math>CEP</math> it is from <math>COI</math>. Thus due to sampling there are biases floating around as <math>COI^*</math> and <math>POI^*</math> and a bias between <math>COI</math> and <math>COI^*</math>.<br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 11:34, 3 June 2015 (EDT) | ::: So when we measure <math>CEP</math> it is from <math>COI</math>. Thus due to sampling there are biases floating around as <math>COI^*</math> and <math>POI^*</math> and a bias between <math>COI</math> and <math>COI^*</math>.<br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 11:34, 3 June 2015 (EDT) | ||
| − | ::: In the above suggested paragraph '''uncorrelated''' and '''equal variances''' are actually redundant, but I think it necessary to make both points clearly. In other words, I'm sure only about 1% of the readers would understand why the two are redundant. <br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 12:43, 3 June 2015 (EDT) | + | ::: In the above suggested paragraph '''uncorrelated''' and '''equal variances''' are actually probably the most redundant, but I think it necessary to make both points clearly. In other words, I'm sure only about 1% of the readers would understand why the two are redundant. Also "uncorrelated" and "independent" are two different concepts.<br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 12:43, 3 June 2015 (EDT) |
Revision as of 16:38, 3 June 2015
I think the section on "Systematic Accuracy Bias" misses the point.
Consider two experiments.
(1) Sight weapon then Shoot 10 groups
(2) (a)Sight weapon then shoot group (b) do (a) 10 times
Method (1) has accuracy bias but method (2) does not.
Herb (talk) 18:53, 1 June 2015 (EDT)
- Here's my take: "Systematic accuracy bias" on this page means that the true center of the shot distribution is different from the point of aim (POA). The CEP-radius can then be calculated around two possible centers - either a) around the known POA, or b) around the unknown true distribution mean.
- a) takes into account systematic accuracy bias because the further away the true center of the shot distribution is from the POA, the larger the CEP around the POA becomes, holding distribution spread constant. b) does not take into account systematic accuracy bias because CEP does not vary with increasing distance from true group center to POA, holding distribution spread constant.
- In a) only distribution spread (or the full covariance matrix) has to be estimated from observed data, in b) the true center also has to be estimated.
- Any help in getting this issue better across is highly appreciated.
RE: The CEP-radius can then be calculated around two possible centers - either a) around the known POA, or b) around the unknown true distribution mean. from above.
The wiki in general uses a third point, the \(\overline{POI_{sample}}\), from which the measurements are calculated. It is the only point for which an actual measurement can be obtained from the sample of shots.
All in all semantics, but the wiki ought to be consistent unless there is some reason to deviate. If a deviation is required, then it should be explicitly stated.
Herb (talk) 16:34, 2 June 2015 (EDT)
- True, we can sample the POI, but there exists a true POI. We can use the true POI in our models regardless of whether we can sample or estimate it in practice. That's true of many of the variables and measures discussed throughout the site: There is a true value we may (or may not) be able to estimate, and then there are sample values (which may be used to estimate the true value). David (talk) 16:39, 2 June 2015 (EDT)
- David, I fully agree. My explanation was concerned with the true CEP - which is unfortunately lacking its own distinct symbol. The true CEP has an estimator \(\widehat{CEP}\) which uses \(\overline{POI_{sample}}\) as an estimate for the true group center (when systematic accuracy bias is not taken into account).
- How about using * as a superscript to denote the value for the population? So \(CEP^*\) for the population \(CEP\) measure taken from the true \(COI^*\)? I had a mental fart using \(\overline{POI_{sample}}\). It is already well defined in the literature as \(COI\). So \(COI\) (sample of shots) as opposed to \(COI^*\) (the population of shots).
- I never doubted that the population values existed it is just that the typical frame of reference is the \(COI\) (from the shot sample), not \(COI^*\) (the population of shots). Since you hop around in a wiki, I think that the wiki has to be more diligent in using a consistent nomenclature than you might use in a book which is read more linearly.
- So I would change first paragraph to be:
- Rayleigh: When the true center of the shot distribution, \(COI^*\), coincides with the true point of aim, \(POA^*\), then radial error around the \(COI^*\) for a bivariate distribution with the horizontal and vertical measurements uncorrelated, independent, and normally distributed with equal variances, follows a Rayleigh distribution. This distribution is described in the Closed Form Precision section. In three dimensions (spherical error probable, SEP), the radial error follows a Maxwell-Boltzmann distribution which is the basis for the ideal gas laws in chemistry.
- In the above suggested paragraph uncorrelated and equal variances are actually probably the most redundant, but I think it necessary to make both points clearly. In other words, I'm sure only about 1% of the readers would understand why the two are redundant. Also "uncorrelated" and "independent" are two different concepts.
Herb (talk) 12:43, 3 June 2015 (EDT)
- In the above suggested paragraph uncorrelated and equal variances are actually probably the most redundant, but I think it necessary to make both points clearly. In other words, I'm sure only about 1% of the readers would understand why the two are redundant. Also "uncorrelated" and "independent" are two different concepts.
