Is error-analysis not a physics topic?

Question

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.

Answer 1

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.

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$^*$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.

Answer 2

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?

Answer 3

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.

Answer 4

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).

Answer 5

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".