Talk:Parametric model

More?

I suggest this needs more content that is not just statistics-related. Melcombe (talk) 09:20, 21 May 2008 (UTC)

As far as I know the term "parametric model" is only used in statistics and has a very precise meaning (see the definition I just added). Flavio Guitian (talk) 20:27, 12 November 2008 (UTC)

Clarity

I would very much like to see less jargon. All of the symbols are indecipherable to me. Is it feasible that we could include a plain-English, linked explanation? That way, it may be possible for myself, and others who wish to understand the topic better, to eventually understand the content of this article through articles in Wikipedia. ZendarPC (talk) 23:02, 23 July 2009 (UTC)

Definition

I made a change to the definition, with edit summary "revise to simplify and avoid circularity with definition of parameter space". The article definition then said this:

A statistical model is a collection of probability distributions on some sample space. We assume that the collection, 𝒫, is indexed by some set Θ. The set Θ is called the parameter space.

Bender235 reverted my edit, with edit summary "unnecessary confusion created; the parameter space is a space, so why call it a set and pretend "space" is just a label?". The article then said this:

A statistical model is a collection of probability distributions on some sample space. We assume that the collection, 𝒫, is indexed by some parameter space Θ.

To explain my edit summary more....

Firstly, a set is a concept that will be understood by many more readers than a space. When people read the definition preferred by Bender235, many will wonder what a parameter space is. Ergo, my edit simplified the definition.

Secondly, the article parameter space essentially says that a parameter space is the space of parameters of a model. That introduces some circularity into the definitions of the two terms, parametric model and parameter space. Ergo, my edit removed some quasi-circularity in the definitions.

My edit is only 7 words longer, and will be better for many readers who are unfamiliar with the topic.

BetterMath (talk) 18:37, 6 October 2019 (UTC)

I do not agree. Sure, "parameter space" will be a new term for most readers, but that's why it is wikified and pointing to the article parameter space for further explanation. Calling $\Theta$ first a set and then a space is more confusing, in particular since the current wording suggests that "space" is merely a label here ("$\Theta$ is ... a set called space."). --bender235 (talk) 19:56, 6 October 2019 (UTC)

@Bender235: I appreciate that you agree "parameter space" will be a new term for most readers. Readers should not have to click on a link to read this article—that is much less nice for them. An article should be as easy-to-read, by itself, as practicable.

Your reply does not address the issue of quasi-circularity in definitions.

Your reply says that “Calling Θ first a set and then a space is more confusing”. For me, that is not true, especially because every set is a space. Possibly, though, there are some readers for whom that would be true. I have a suggestion to address this issue.

The primary reference for statistical models is doi:10.1214/aos/1035844977 by Peter McCullagh. That reference refers to Θ as a “parameter set”. Ergo, the issue could be addressed by replacing the sentence “The set Θ is called the parameter space” with this sentence: “The set Θ is called the parameter set or, more commonly, the parameter space”.

BetterMath (talk) 20:06, 7 October 2019 (UTC)

"...especially because every set is a space."

That's not correct. Every space is a set, but the inverse is not generally true. As an example, the set of all four-legged mammals is not a space. A set becomes a space by adding some structure. Take that structure away, and you no longer have a space (but still a set).

Anyhow, I don't think that clicking on parameter space for further explanation what the term means is a discomfort to our readers.--bender235 (talk) 20:19, 7 October 2019 (UTC)

A set is a space with some additional structure, but the structure can be null; so a set is a space. For a general statistical model, there is no structure required on Θ; maybe that is why McCullagh uses the term "parameter set".

Your reply does not address the issue of quasi-circularity in definitions.

Readers would surely prefer to not have to click on a wikilink, if a few extra words would have made the meaning clear.

BetterMath (talk) 22:25, 8 October 2019 (UTC)