Talk:Elementary event

Discussion 2003

This is one of those subjects where we really need, in addition to "See also:", a standard way of indicating "Pre-requisites" and "Post-requisites". Defined loosely, in terms used by universities and such ("instructional capital" etc.), the "Pre-requisites" are those things that you really must understand in order to understand the article, and the "Post-requisites" are things that let you make use of what's in the article, or which are required to inform you of the limits of usefulness of what's in the article, or the dangers of using it.

For instance the main use of probability is to support statistics, and the main use of statistics is to justify decisions taken with respect to risk. Thus one could say that risk is a Pre-requisite, since you won't apply probability correctly without understanding uniform time horizons and threats versus risks. One could also say that statistics is a Post-requisite, since (beyond one-time military-type risk calculations as in game theory) it is important for anyone using probability theory to understand how their tests or other numerical conclusions will be integrated with real world decision making over many many instances. That may make them more cautious about such stupid statements as the above, and at least would discourage nonsense writing that's misleading to people without math degrees.

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There's also a problem with certain overloaded terms being stolen by ideologies associated with science, e.g. elementary event, fundamental forces, the Standard Model and Theory of Everything come to mind as cases where the physics community (aided and abetted by the probability theorists) have simply stolen language to assert that it knows what is "elementary", "fundamental", "standard", and most galling of all, "Everything". This is just nonsense, and those entries should be qualified as "Standard Model (physics)", etc., if only to distinguish them from the "standard model" of the latest Mercedes SUV. The capitalization problem, increasingly galling especially at the wikipedia, makes this worse.

Does there have to be a project to remove this physics and probability bias in the wikipedia? It smacks of scientism and mathematics fetishism at the best, and a conspiracy of dunces at the worst.

Most people on this planet do not believe that probability and physics define what is real. They either believe in a more social reality or religion as the source of such truth. You may not like this, but it is certainly true.

"For instance the main use of probability is to support statistics..."

That statement will startle many probabilists and physicists!! Michael Hardy 17:50 Jan 13, 2003 (UTC)

That's correct, it will. To most probabilists, the main use of probability is to get tenure. To most physicists, the main use of probability is to lord it over those who claim (like Einstein) that "God does not play dice" and etc. But probabilists and physicists are a very tiny minority on this planet, and the abstract and theoretical and small-beyond-human-perception events that they study is not of any great interest to the vast majority. I suppose the world could get very interested in a hurry if something like a Gravity Bomb showed up, but it hasn't, so the primary impact of probability theory and physics on humanity via non-statistics so far has been nuclear fission, and the A- and H-bomb. Admittedly this is huge, but mostly in terms of resisting the impact.

Take it any way you want: the main use of probability is to support statistics, both in terms of the number of applications and the frequency of their use in the real world.

Lots of probabilists apply probability to real-world phenomena without ever thinking about statistical inference. Not only physical phenomena, but also economic and biological phenomena (e.g., branching processes in biology).

sadly, often this work leads into misapplications on a large scale precisely because the probabilists did not consider the implications of applying their models on a large scale, where measurements are less disciplined and the circumstances of measurement (not to mention time horizons) tend to vary. In combination, such variations will completely invalidate statistical argument.

That said, I agree it CAN be done by brilliant minds without reference to these social factors, and the use of 'environmental pathway analysis' is an example of a branching process that can be applied prior to statistical use. But there's a feedback loop - the success of the analysis and controls based on them will be used, statistically, to fund the improvement of branching process models. Hmm this belongs in philosophy of science not here.

There are also physicists who apply probability to physics other than quantum physics; e.g., astronomical phenomena, physics of porous media, and statistical mechanics. Perhaps it is true that the main use of probability is to support statistics, but very many books and courses on probability seem to be the work of people who don't suspect that. Michael Hardy 19:45 Jan 13, 2003 (UTC)

BTW, I fully agree that physicists should be severely beaten if they utter the words "theory of everything". That phrase is a fatuous imbecility. Michael Hardy 19:48 Jan 13, 2003 (UTC)

An anonymous poster, above, wrote: "There's also a problem with certain overloaded terms being stolen by ideologies associated with science, e.g. elementary event, fundamental forces, the Standard Model and Theory of Everything come to mind as cases where the physics community". Although I agree with the claims about physicists being idiotic in this regard, this poster is wrong to cite "elementary event", in the sense in which that phrase is used in this article, as an example. The way in which that locution is used here makes it clear that it is to be understood only within a very narrow context. Moreover, it is hardly a frequently used expression. Michael Hardy 19:29 Jan 14, 2003 (UTC)

Bad definition?

I thought, elementary event is an element of a sample space, not its subset with one element. See de-wiki for example. Any sources for the current definition? Olaf (talk) 05:26, 24 January 2009 (UTC)[reply]

As an event is a set of outcomes, an elementary event has to be a set of outcomes rather than an outcome if it is to be an event. The use of "elementary event" as a set of outcomes can be found in

Grinstead, Snell: Introduction to Probability

although the term "elementary event" is only used there, not explicitly defined. --Dan Polansky (talk) 11:09, 25 November 2009 (UTC)[reply]

Just an event?

There seems to be another definition of elementary event. Suppose, there is an event E. If, for any event A from the sample space, ether A or "not A" must happen when E happens, then E is an elementary event. If this definition is correct then the article in its present form describes the concept of just an event rather than the elementary event.

The difference is actually quite important. Existence of elementary events is not guaranteed. For example, the Wigner function in quantum mechanics is the quasi-probability distribution over phase space points which, by themselves, are not elementary events (one can't measure coordinate and momentum simultaneously). —Preceding unsigned comment added by 67.184.128.248 (talk) 07:30, 8 June 2009 (UTC)[reply]

You gave an example of a compound event for an elementary event, didn't you?

"{HH}, {HT}, {TH} and {TT} if a coin is tossed twice. S = {HH, HT, TH, TT}. H stands for heads and T for tails."

All of {HH}, {HT}, {TH} and {TT} describe compound events. An elementary event is, all over the web in disparate sources, defined as an event containing one element only. Please correct me if I'm wrong. — Preceding unsigned comment added by Scholarly (talk • contribs) 13:15, 30 December 2010 (UTC)[reply]

You are wrong...

The example with heads and tails of a fair coin is the only example of elementary events which Kolmogorov himself gives in his "Foundations of the Theory of Probability". It appears that for him the concept of "elementary event" is basic and self-evident, comparable in spirit to the concept of a point in Euclidian geometry. The major purpose of elementary events in Kolmogorov's formulation of probability axioms is to introduce a set of objects on which one can postulate an integrable measure. However, it does appear that elementary events have some properties which are tacitly assumed: a) they are disjoint and b) an occurrence of a particular elementary event determines whether any other random event has occured.

Kolmogorov spends quite some time discussing the internal consistency and completeness of his system of axioms. Ironically, he does not discuss the realm of their applicability in the real world, although it is clear that there are phenomena (e.g., measurements of non-commuting variables in quantum mechanics) for which a space of "elementary events" can not be constructed. —Preceding unsigned comment added by 129.118.29.133 (talk) 21:05, 25 January 2011 (UTC)[reply]

I'm tagging this article as low importance, stub quality. -Bryanrutherford0 (talk) 20:49, 18 July 2013 (UTC)[reply]

Must an elementary event be an element of the sample space?

I would have thought in a probability space $(\Omega ,{\mathcal {F}},P)$ , you had ${\mathcal {F}}$ as the σ-algebra of events, so an element of the sample space $\omega \in \Omega$ does not have to be an event. You do not have $\omega \in {\mathcal {F}}$ and do not need to have $\{\omega \}\in {\mathcal {F}}$ and, if not, then it would not be an elementary event. Instead I would have thought an elementary event here would be a non-empty element of ${\mathcal {F}}$ which did not have a non-empty proper subset. 2A00:23C6:148A:9B01:A549:DCEF:21E2:BF5C (talk) 02:46, 17 February 2024 (UTC)[reply]