# Difference between revisions of "Talk:Precision Models"

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Herb 4/19/2015:

1. I'd rename this page "Models for Precision". Done David (talk) 16:37, 22 April 2015 (EDT)
2. "We have four options for measuring and analyzing precision:" Wrong. There are zillions of options. Good point. Corrected David (talk) 16:37, 22 April 2015 (EDT)
3. "General Bivariate Normal" is not "The normal, a.k.a. Gaussian, distribution." Is it a two dimensional distribution which is somewhat analogous to the one dimensional distribution.
• Symmetrical meaning SD(V) = SD(H) vs Unsymmetrical meaning SD(V) <> SD(H)
• Correlated meaning ρ <> 0, vs Uncorrelated meaning ρ = 0.
So there are 4 cases. (Symmetrical Uncorrelated Bivariate Normal is a special case known as Rayleigh Distribution.)
4. "Statistical Analysis of Dispersion #1. The Closed Form Precision model requires that we assume the shot group is, or can be normalized to be, a fairly symmetric bivariate Gaussian process, but allows for the most convenient estimators and analysis. Therefore, whenever σx≈σy we prefer this approach." This is just wrong. "Closed form" means that integrals of the PDF exists so that a CDF can be calculated. The Radial Standard Deviation is a closed form model, Extreme Spread (aka group size) is not.
I don't understand the complaint. The Closed Form Precision model is closed form. Extreme Spread is treated separately. David (talk) 16:37, 22 April 2015 (EDT)
5. "Statistical Analysis of Dispersion #2. Circular Error Probable disregards any ellipticity in the actual shot process in order to characterize precision using a single parameter." Not really true. Circular Error Probable assumes no ellipticity. If you apply model incorrectly and get burned then that is your problem, not a fault of the model.
We are describing the distinguishing characteristics of the model, so I don't see the problem here. David (talk) 16:37, 22 April 2015 (EDT)
Maybe we can carry over parts of the more detailed discussion on the Circular Error Probable page. Specifically, the most common (Rayleigh) estimator indeed assumes no ellipticity in the shot distribution and only gives unbiased estimates if this assumption (among others) is met. But there are CEP estimators with different, less restrictive, assumptions that allow for elliptic shot distributions. These differences notwithstanding, CEP always characterizes precision using a single parameter, and this parameter can be statistically meaningful even for elliptic shot distributions. With some assumptions, the question "how large do I have to make a circle such that it is expected to cover half of the shots" can be answered without bias for some elliptic distributions as well. Calling this property "disregarding any ellipticity" because the interest is in the radius of a circle seems accurate to me (caveat: non-native speaker). armadillo
6. "Statistical Analysis of Dispersion #4. Extreme Spread and the other Range Statistics, which increase with group size n, do not have any useful functional forms." First group size is used incorrectly again here to mean the Number of shots per group. Second there are not any "Closed Forms" for the distributions. So functions must be evaluated via Monte-Carlo sampling rather than integrated. "Functional forms" is an undefined concept.
Fixed the first problem. Functional forms are the opposite of empirical forms like Monte-Carlo methods. Is there a better way to phrase that? David (talk) 16:37, 22 April 2015 (EDT)
7. Overall I'd remove "Statistical Analysis of Dispersion" and "Tools" section from page if renamed to "Models For precision."
8. If page was renamed to be for models, then I add section for Error Propagation and move that discussion from "What is Precision?" page here.

Herb 5/9/2015

The overall point is that there are two levels to the "models." The lower level is the assumptions which we make about how shots are dispersed. For instance, is the horizontal and vertical dispersion the same?

The higher level is the mathematical model used to analyze the pattern of shots. For example the Rayleigh distribution and the extreme spread use the same assumptions about how shots are dispersed, but are different analysis models. You flip between analysis models without stating the assumptions upon which each analysis model depends.

Agreed, we should use more careful language to delineate the two "models." The word is appropriately applied to the mathematical models. Should we refer to the assumptions and conditions as just "assumptions"? David (talk) 13:25, 15 May 2015 (EDT)
Sounds good to me. A specific statistical model allows for correct inference under the condition that its assumptions of the data-generating process are met. armadillo

Worse Closed Form Precision isn't an analysis model per se. It denotes a mathematical characteristic of an analysis model.

Right, I just thought it was worth highlighting the one closed-form model we have because that's what I was looking for initially. We should probably change that because it's possible there are other closed-form models for more liberal assumptions. (Any graduate students out there looking for a good thesis topic? ;) David (talk) 13:25, 15 May 2015 (EDT)
Don't need a grad student to know which distributions are closed forms. That is well documented in the literature. The aspect that would be good for a thesis topic would be some statistical tables for various distributions like "group size." Consider that I have a 5 shot group with one wide shot. What would the statistic be for comparing (5-shot size)/(4-shot size)? Pretty straight forward with Monte Carlo method. The real research topic is how would you then convert the 4-shot size to an estimate of a 5-shot size?

At this point I think this page should be refactored. Make it Modeling Dispersion.

Then put this page after "Introduction" page.

I dummied up a page on my talk page. Sections:

1 Modeling Dispersion
1.1 Simplifications into cases
1.2 Error Propagation
1.3 Stringing
2 Four Special Cases for Dispersion
2.1 Case 1, Equal variances and uncorrelated
2.2 Case 2, Equal variances and correlated
2.3 Case 3, Unequal variances and uncorrelated
2.4 Case 4, Unequal variances and correlated

Herb (talk) 21:05, 23 May 2015 (EDT)