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I have a question about my Physics Stack Exchange post: How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

I am dealing with a rather hard question, and hoped to get some help on stack-exchange. Being a computational physicist allows me to work at the interface between theory and experiment. This makes what I do, and what I ask sometimes look weird to either the theoretician, the experimentalist, the computer scientist or the statistician (the last part due to ML).

The question posted is one of error-analysis, specifically error propagation (typical experimental physics exercises for anyone who ever had physics labs). Alternately, the statistical component makes it also a statistics question, as also that the statistics community deals with this topic.

Posting the question on statistics site gets it locked because it may not entirely be in the lingo default by statisticians (which I do not claim to be, hence I was asking the question) and as far as I can tell looks a lot like a default question statisticians deal with, but is uniquely different. Maybe this makes it hard to understand.

Posting it on a physics forum (error-analysis as I remember it actually seems closer related to the question I have) gets it locked because it is not "physics" related. Indeed it is a "model"...but point me towards a physicist not using models. And if error-bars are not an import concept in physics, or as a physicist you never encountered them during your training, please tell me.

I do understand that the question may look strange. And any suggestion or question is welcome. The underlying work is rather complex (and long winded), so if you ask a question, and tell me why you need to know, I can give a more understandable and focused answer.

At this point, I feel I am being dismissed out of hand.

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    $\begingroup$ Please note that it has been only an hour since you edited the post to include your physical motivation for the question. Our site does not work in real-time, that the question has not been reopened an hour after your edit is not an indication that it is still considered off-topic. You can follow the reopen review results here $\endgroup$ – ACuriousMind Apr 2 at 9:51
  • $\begingroup$ Thank you for the link. $\endgroup$ – DannyVanpoucke Apr 2 at 10:21
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    $\begingroup$ Just in case you question doesn't finally get accepted on this network, don't forget that there are sites with other formats than Question&Answer: forums. In particular, Google does give some useful links on "physics forums" query. $\endgroup$ – Ruslan Apr 2 at 19:47
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    $\begingroup$ SE.DataScience might also work. SE.Statistics probably should've allowed this too. $\endgroup$ – Nat Apr 2 at 22:16
  • $\begingroup$ Thank you very much for the hint Nat. I'll look into placing it there as well (since I do believe physicists have the kind of answer I am looking for from experimental experience) $\endgroup$ – DannyVanpoucke Apr 3 at 9:36
  • $\begingroup$ btw SE.Statistics is the location of the original posting... $\endgroup$ – DannyVanpoucke Apr 3 at 15:53
  • $\begingroup$ @DannyVanpoucke : For the record ; the fact that the stat people wanted a detailed paper on how you got where you got suggests (to me, at least), that you are at the very least on the right track. Your comment (that I have re-posted) probably captures very accurately the issue with your question on this forum (I should add. I know next to nothing about the contents of your question). The question you ask occupies a niche. Also, there are always ways to make your question more accessible to non-specialists (defining your terminology in easy to understand ways may be a place to start) $\endgroup$ – insomniac Apr 3 at 22:08
  • $\begingroup$ A lot of people on stack exchange are mostly interested in categorizing posts and following protocol. It's a feature of this community that is useful as far as tracking and finding data, but also frustrating when one just wants to address an important but hard to categorize issue. I've found it's worthwhile to refine a post as needed for it to be taken seriously, as long as it's something you sincerely need advice about. $\endgroup$ – j0equ1nn Apr 13 at 5:54
  • $\begingroup$ @J0equ1nn a bit like: "The bureaucracy is expanding to meet the needs of the expanding bureaucracy."(Oscar Wilde) There seem to be a lot of people only interested in categorization (also in real life)...and when you don't fit a box, you end up in trouble. However: the question is open, time to actually answer it (as there was a halfway answer (by Sammy gerbil IIRC), but that was erased because it was not posted as answer. $\endgroup$ – DannyVanpoucke Apr 13 at 11:00
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    $\begingroup$ Yeah, like that. I'm my case I can't answer because I don't know whether or not error analysis is a physics topic. I'm not even a physicist. I've posted many things leading to similar problems so just wanted to be encouraging and hopefully positive. $\endgroup$ – j0equ1nn Apr 14 at 5:08
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This is a borderline case, so I'm not entirely convinced of my position, but I think the closure reason was valid.

Closure of your question doesn't mean error analysis is not important in physics. It just means that your question is not about any physics principles. As a contrived example, let's say I posted a question that said

How do I solve this equation for $t$? $$y=v_0t+\frac12at^2$$

Ignoring the other problems with a post like this, it would be closed for being just an algebra problem and not asking about any physics.

If I then edited the question to be

I am trying to solve a projectile motion problem, which is relevant in physics. I know the equations that describe projectile motion, but how do I solve this equation for $t$? $$y=v_0t+\frac12at^2$$

then the post would still not belong on PSE because it is still an algebra question.$^*$

Is algebra important for physics? Of course it is. Is projectile motion a physics topic? Of course it is. But at the heart of it, my question is a math question, not a physics question.

I am not saying your question is as simple and clear-cut as the example I give. I think your question is more likely to belong on this site than my example is for sure, and I wouldn't be upset or confused if your question were to be reopened. The main point I'm trying to make here is that just because your question comes from physics and asks about techniques used by physicists doesn't mean the heart of the question is a physics question. Error analysis is used in many disciplines, so a question about it doesn't automatically make it on topic.


$^*$I could see this example being better though

I am trying to solve this projectile motion problem. I end up with an equation that looks like $$y=v_0t+\frac12at^2$$ and I need to solve for the variable $t$. The issue is that I get two possible solutions for $t$, as this is a second order polynomial for $t$. What does it physically mean for this equation to have two solutions, and how do I pick the correct one?

Of course, this question still lacks some things, like more context as to what the specific system is, but it is a step in the right direction. It is a question about how the mathematics relates to the physical system.

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    $\begingroup$ I agree with the basic idea behind your argument. The question is "how pure" does it need to be? And who gets to decide? In itself these questions can be discussed and I think reasonable rules can be set up.(But there will always be exceptions.) These are also the discussions where much interdisciplinary research dies: not pure enough, too pure, not interdisc. enough. At this point,I feel like I am not fighting my problem but rather the right to ask for help with my problem...because it is not pure enough. Neither in Physics nor in Statistics. (and thanks for not being confused if reopened:-)) $\endgroup$ – DannyVanpoucke Apr 2 at 13:31
  • $\begingroup$ @DannyVanpoucke I agree. I'm in biophysics, so I understand the importance of interdisciplinary work. Like I said (or tried to say), closure of your question doesn't mean it isn't important to physics, just that it doesn't fit this specific site. The closure isn't an attempt to stifle interdisciplinary work. $\endgroup$ – BioPhysicist Apr 2 at 13:41
  • $\begingroup$ No, don't worry. I do not think its an attempt to stifle interdisciplinary work. :-) $\endgroup$ – DannyVanpoucke Apr 2 at 16:01
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    $\begingroup$ @DannyVanpoucke I feel your pain here -- setting aside interdisciplinary aspects, it's pretty hard to pin down what "physics" should mean exactly. Like, what's the line between engineering and experimental-physics... if I want to design something for fun, maybe it's off topic, but if it's a design for a physical experiment, maybe it's on topic. Or where do math questions fit in... I laid out an argument to a different question on Meta, but the gist is -- it's hard to pin down "physics" because the questions "physicists" need help on are really about the tools, not the physics. $\endgroup$ – tpg2114 Apr 2 at 16:51
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    $\begingroup$ Taking the "if physicists use it, it should be on topic here" argument to my favorite extreme example -- physicists need to eat meals also, but questions about baking pies don't belong :) Like Aaron, I think I wouldn't be opposed to this being reopened, but I also see why it was closed. To answer your "who gets to decide" question -- we all do. We decide by making policies on Meta, and by voting to close or voting to reopen questions. If there isn't a clear policy, we tend to follow recent precedence, so closing/reopening questions is a way to establish the bounds before making policies. $\endgroup$ – tpg2114 Apr 2 at 16:55
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    $\begingroup$ @tpg2114 I concure. Physicists tend to play in a lot of areas, and in general, my most difficult questions are generally rather on methods/tools than the underlying physics. And apparently we tend to ask 'the different" questions. Since starting in AI, I've had already quite a few times that the response to a (to me obvious) question was: "Why would you want to know/do/check that?" I truly hope the question can be opened up again, as I am really interested in the answer. (Even if it's: You idiot, don't you know that for this trivial reason you don't need to do it.) $\endgroup$ – DannyVanpoucke Apr 2 at 17:44
  • $\begingroup$ @DannyVanpoucke Have you tried asking statistics users who closed your question how you could make your question better for their site? What was their close reason, specifically? $\endgroup$ – BioPhysicist Apr 2 at 17:46
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    $\begingroup$ Yes, their answer was (1) don't understand (2) please write a full paper on your methodology. we want all details of how you got there. And since then no more reaction. Here it seems it was also voted to remain closed...(Buzz, Jon Custer, and yourself voted to keep it closed). Which is nice and dandy but doesn't resolve my problem. Instead I have now wasted two days on trying to ask a question which in retrospect I could have used to try and find the answer elsewhere. Is this the purpose of Stack: earning the right to ask questions? $\endgroup$ – DannyVanpoucke Apr 2 at 17:54
  • $\begingroup$ @DannyVanpoucke Is this the purpose of Stack: earning the right to ask questions? I don't think that is a fair assessment. I have told you my reasoning in this post. Did I say anywhere that the question was closed because I think you don't deserve / don't have the right to ask questions? I am sorry if my post has given you that impression. $\endgroup$ – BioPhysicist Apr 2 at 17:57
  • $\begingroup$ @Aaron Stevens: No you did not, neither did I say you said this. This is how the actions are perceived. $\endgroup$ – DannyVanpoucke Apr 2 at 17:59
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    $\begingroup$ @Aaron Stevens Could you please read your last statement again? "I don't know enough about what you are asking about in order to make suggestions." But you can suggest it to remain closed? And hope that someone else will fix it...can you see how such comments can be frustrating for the other side of the discussion? $\endgroup$ – DannyVanpoucke Apr 2 at 18:13
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    $\begingroup$ @AaronStevens Comment on the answer: while I think I agree with you, your second example is a really fuzzy case. Our help center says that mathematics in the context of physics is on topic, and saying that you're trying to solve a projectile motion problem is certainly a step toward putting the mathematical problem in a physical context. I think with a very slight step further in the same direction, that would become an on-topic question. (Granted, not a good one, but I think it would meet the bar for topicality.) $\endgroup$ – David Z Apr 2 at 20:18
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    $\begingroup$ It's up to you. I actually think it might be most useful to add a third example with more physical context which would be on topic, just to clarify where the line is. $\endgroup$ – David Z Apr 2 at 20:47
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    $\begingroup$ @DavidZ Got it. I included both :) $\endgroup$ – BioPhysicist Apr 3 at 4:51
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    $\begingroup$ @DannyVanpoucke As an engineer who does a lot of work involving correlation of models and experiments, I'm inclined to agree with the response you say you have from the Stats guys. My reaction is "OK, so you seem to have invented a strange non-standard way to get some parameters and now you want to analyse your method." But why do it like that anyway, unless you have shown that standard methods don't work for you? There isn't any evidence in your post that they don't work, or why this idea might be better. $\endgroup$ – alephzero Apr 4 at 0:10
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Maybe this could be asked if framed as a traditional physics experiment?

For example, say some students are using the Arrhenius equation, $$ k ~=~ A \, \exp{\left(\frac{-E_{\text{activation}}}{RT}\right)} \,,$$ to find the Arrhenius constant, $A ,$ and the activation energy, $E_{\text{activation}} ,$ from lab-observed values of $k$ and $T .$

Then, students can take the natural-log of the Arrhenius equation, $$ \ln{\left(k\right)} ~=~ \frac{-E_{\text{activation}}}{RT} + \ln{\left(A\right)} \,,$$ then plot it as a linear correlation of the form $y=mx+b,$ $$ \underbrace{\ln{\left(k\right)}}_{y} ~=~ \underbrace{\frac{-E_{\text{activation}}}{R}}_{m} \underbrace{{T}^{-1}}_{x} + \underbrace{\ln{\left(A\right)}}_{b} \,,$$ then use linear regression to find the $E_{\text{activation}}$ and $A$ from their data for $k$ and $T .$

But surely it'd be naive for the students to assume that their values for $E_{\text{activation}}$ and $A$ are precise, real-number values. So:

  1. How can we quantitatively describe the values of $E_{\text{activation}}$ and $A$ to include uncertainty?

  2. If the Arrhenius equation is then used to predict more values of the reaction-rate constant $k$ at different temperatures $T ,$ then how do the errors in $E_{\text{activation}}$ and $A$ carry through to these predictions?

  3. What would change if the linear regression were based on multiple independent values?

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  • $\begingroup$ Why does it need to be "an experiment"? (except for the fact that error analysis is mainly an aspect in experimental physics ;-) ) $\endgroup$ – DannyVanpoucke Apr 6 at 20:28
  • $\begingroup$ @DannyVanpoucke: As you stated in the question here: "The question posted is one of error-analysis, specifically error propagation (typical experimental physics exercises for anyone who ever had physics labs).". Providing such a concrete grounding may make it feel more on-topic, I guess? Plus it'd be nice to have a concrete grounding to demonstrate how the subject matter connects to real-life stuff. $\endgroup$ – Nat Apr 6 at 20:35
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In your 1st sentence you say the context is the stickiness of glue compounds. However, that statement on its own does nothing to make your question answerable by physicists. If that sentence is removed your question could apply in any discipline. No physics insight is required to answer it. So I agree with those who voted to close it.

Just because we have tags for error analysis, linear algebra and statistics does not mean that all questions on such topics are on topic here.

You say that physicists have the right kind of answer you are looking for. That might be the case if you explain your experiment from a physics viewpoint. But you have not done so. When you were asked for such information in Cross Validated SE you refused to provide it.

I don't agree with Aaron that it is a borderline case.

Your question was closed on Cross Validated SE because it was judged to be unanswerable without further information. That included a user with a rep of 233k. You were unwilling to provide the information asked for. (You were not asked to write a full paper on your methodology.) Whether that information is irrelevant is not something which I am able to decide. The users on that site are probably more expert in the subject than anyone here. If they are unable to answer the question then it is even less likely that someone here will be able to do so. (This comment was also made by Semoi.)

The fact that someone here might be able to provide an answer is not sufficient to make it on topic here. There are many users here who can answer simple questions about mathematics and statistics, and to a lesser extent chemistry. We have tags for those also, but such questions are not automatically on topic here.

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    $\begingroup$ May I read your highlighted sentence as a statement that physicists who do not work in a lab performing experiments, but who do simulations or theoretical work are not acceptable here? I hope not. May I ask you if you would consider I have the knowledge to asses if certain information is relevant? Or is this just depending on the reputation one has here? (btw the information was added but that was ignored) PS: I'm working with atoms quite a lot...am I a chemist? $\endgroup$ – DannyVanpoucke Apr 4 at 18:55
  • $\begingroup$ @DannyVanpoucke No one has said anything about your reputation points. People keep explaining why the question itself is considered to be off topic. Why do you keep equating that to how much reputation you have, or to what is actually considered to be physics? Just because something doesn't belong on PSE does not mean it isn't considered to be physics. $\endgroup$ – BioPhysicist Apr 4 at 19:17
  • $\begingroup$ @Aaron: "That included a user with a rep of 233k."[By sammy gerbil] (Is the argument I get thrown in my face) "Just because something doesn't belong on PSE does not mean it isn't considered to be physics" ...am I allowed to say WTF to that? $\endgroup$ – DannyVanpoucke Apr 4 at 19:20
  • $\begingroup$ @DannyVanpoucke sammy is referring to that user's reputation to indicate they know about the site and what does / doesn't belong on that site, what could be done to improve the post for that site, etc. Sammy did not say anything about your reputation, nor did they say anything to suggest that your question was closed due to your low reputation. $\endgroup$ – BioPhysicist Apr 4 at 19:21
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    $\begingroup$ @DannyVanpoucke My meaning is that, except for the 1st sentence, your question is entirely statistical. If you want an answer from an experimental physicist you ought to describe your difficulty within the context of an experiment. Background information helps others understand what you are trying to do. It is relevent to them. You might think it is irrelevant, but you already have that information. It can also help others to suggest an alternative solution. (See What is the XY problem?) $\endgroup$ – sammy gerbil Apr 4 at 19:23
  • $\begingroup$ Hmm...I could try to reformulate it in terms of a fictitious experiment...(but then how to avoid another entire set of discussions on the "experiment itself")? $\endgroup$ – DannyVanpoucke Apr 4 at 19:29
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I share your pain. Physicists take pride in their field being an experimental science, but the art of statistics - i.e., knowing to analyze the experimental data - has been largely lost among the mainstream practitioners (theorists and to large extent even experimentalists). This finds its reflection in the fact that many physics programs do not even include a course in basic statistics, and many physics PhDs do not know what is likelihood, statistical test, confidence interval, etc.

Why?
Lest the physicists get upset about this, let me note that there are some legitimate reasons for such a state of affairs:

  • Physics measurements nowadays are so precise that analyzing errors does not really affect much the experimental conclusions, so most theorists and even experimentalists may safely ignore this noise.
  • When statistics is an issue, physicists do get proper background and/or employ professional statisticians - experimental particle is a notable example. The statistical reviews written by particle physicists are well-known even beyond the physics community.

Where
If you are looking for analyzing some raw real-world data, it may be a good idea to look beyond physics, for less mature fields, such as biology (I mean the computational biology rather than biophysics) and data science (which has shortage of people who, besides knowing programming and algorithms, are also capable of analyzing and understanding data).

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    $\begingroup$ Your response implies that the reason the question was closed was because physicists do not know how to deal with errors/statistics. While I'm not questioning your opinion, this is not why the question was closed. $\endgroup$ – BioPhysicist Apr 8 at 13:27
  • $\begingroup$ @AaronStevens It was closed as off-topic, which suggests that the people who voted to close it do not think that statistical analysis is a part of physics. $\endgroup$ – Vadim Apr 8 at 13:32
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    $\begingroup$ No, it means that the question is not on topic for this specific site. No one is arguing that error analysis is not a part of physics. Off topic does not mean "not relevant to physics" (Not being about physics is a sufficient but not necessary condition for something to be off topic here). For a better explanation, see either my answer or sammygerbil's answer. $\endgroup$ – BioPhysicist Apr 8 at 14:20
  • $\begingroup$ @AaronStevens I think it is very subjective: e.g., in my opinion many questions in physics forum are really about math rather than about physics. However, many members of the forum feel strongly about math, and I think they should be allowed to discuss it there, because these mathematical questions are best understood and discussed within physics context. I think one could say the same about the statistics question that we debate here. (I myself am a theorist, passionate about applying math to the real-world problems.) $\endgroup$ – Vadim Apr 8 at 14:32
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    $\begingroup$ First, this isn't a forum. Second, there are set policies as to what is / is not on topic. "Relevant to physics" is not enough to make a question on topic here. The closure of this question is not a statement of how relevant this is for physics, nor is it a statement about how great of a discussion a question like this could produce. If you want to make a change to how the site works, you should make a separate post on meta proposing / discussing that change. But don't mislead others by talking about how you think things should be as if that is how they actually are. $\endgroup$ – BioPhysicist Apr 8 at 14:36
  • $\begingroup$ @AaronStevens I am not suggesting any changes or criticizing how the site works. I pointed out that math and statistics are both relevant to physics, while both being not physics, yet one is allowed and the other is not, because it is decided by a popular vote. I am providing a phenomenological description of what is happening. $\endgroup$ – Vadim Apr 8 at 14:45
  • $\begingroup$ Pure math questions are usually migrated to MathSE. This question wasn't closed because it has statistics in it, and questions that have math in them don't remain open just because math is involved. $\endgroup$ – BioPhysicist Apr 8 at 14:48
  • $\begingroup$ @AaronStevens Again, who decides what is pure math? Is QFT pure math? $\endgroup$ – Vadim Apr 8 at 14:59
  • $\begingroup$ The users of the site get to decide, which is why voting to close and voting to reopen is a thing. e.g see tpg2114's comment on this same meta question. If a question motivated by QFT required no physics knowledge to solve, then I would vote to migrate to mathematics. If others agree, then that would happen. If not, then it would stay here. If a question motivated by QFT asked about the physics of QFT, then I would not vote to do that. $\endgroup$ – BioPhysicist Apr 8 at 15:02
  • $\begingroup$ But that all of that is irrelevant to this discussion. The bottom line is that the closure reason in this case was not because the question asked about statistics. This is the reason I originally commented on your answer here, since it suggested that the closure reason was because the question involved statistics. $\endgroup$ – BioPhysicist Apr 8 at 15:03
  • $\begingroup$ @AaronStevens You are right, my answer was not really specific to this question, but rather lamenting the general state of affairs in physics and physics education. I did my best to remain polite, stick to the facts, and remain objective... yet I understand why many people may not like it. $\endgroup$ – Vadim Apr 8 at 15:08
  • $\begingroup$ @Vadim indeed. It is often hard to see that there exists physics outside the parade examples. If you talk about physics, many people easily think of space telescopes, superconducting collider machines or fusion reactors...the unfortunate truth is that most practical physics is materials science, which is a lot less sexy (unless it is a new hip material without practical use, since to expensive to produce ;-) In addition, sample errors in MS are significant despite the accuracy of the measurement device, as you stated). $\endgroup$ – DannyVanpoucke Apr 8 at 15:16
  • $\begingroup$ This doesn't seem like the appropriate place to vent this frustration... I don't see how this is really relevant to the question OP asked, besides that it's also about statistics in physics. It also seems to make some weird assumptions about why this isn't allowed; but I feel Aaron covered that. $\endgroup$ – JMac Apr 8 at 17:29
  • $\begingroup$ @JMac if it breaks the rules, flag it accordingly. If it doesn't, than it is completely appropriate. $\endgroup$ – Vadim Apr 8 at 17:53
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Issues:

  1. Notions like $X^T X $ wasn't obvious for physists even though it's undergraduate regression. People simply spoke differently in different "fields".

  2. In physics, people cared about a. uncertainty in experimental observation b. bias in simulations c. deviation in theoretical calculations. Thus, complicated estimations of PI or CI in some model was not quite common for quite a while.

  3. "Error" was a very dangerous word. i kind of get idea these days, that the "physists culture" wasn't a fan of the words "error". This you really want to show that you know what you are talking about when you mentioned the words "error".

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