<p>I'm a statistics student, currently working on "quantum inference", which is the statistical problem of inference in the quantum model:</p>

<p><span class="math-container">$y_i = \alpha + \beta x_i + \epsilon_i$</span></p>

<p>which is similar to a simple linear model, except instead of <span class="math-container">$x_i$</span> being a known constant, it is instead a random integer. The prototypical example is von Mises's analysis of atomic weights in 1918, trying to assess the significance of the observation that they tended to be integer multiples of the mass of hydrogen. For more information on the subject see <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/0471667196.ess2129.pub2" rel="nofollow noreferrer">DG Kendall's overview</a>.</p>

<p>I am not sure if I should continue working on this problem because the applications are so few, mostly in archaeology, where weights or lengths are often integer multiples of an ancient unit of measure. However, it occurred to me that there may be applications in astronomy.</p>

<p>For example, perhaps the brightness of a spot has been measured, and the spot could represent any number of objects which are not distinguishable at the present resolution. This could be a problem of quantum inference... but only if if were for some reason known <em>a priori</em> that all objects had to have the same brightness.</p>

<p>So, while that specific scenario might be implausible, is there some problem in astronomy data analysis that involves quantum inference in this sense? In other words, are there ever cases where a histogram of the data shows multiple, <em>equally spaced</em> modes?</p>

CC BY-SA 4.0
2019-01-21T02:15:17.310Z
I'm not sure if [orbital resonance](https://en.wikipedia.org/wiki/Orbital_resonance) suits your question: "when orbiting bodies exert a regular, periodic gravitational influence on each other, usually because their orbital periods are related by a **ratio of small integers**" (my emphasis).
Chappo Hasn't Forgotten
CC BY-SA 4.0
2019-01-21T03:30:31.533Z
I assume that $\alpha$ & $\beta$ are (real) parameters to be determined, and that $\epsilon_i$ is an error term, but you should mention that in the question.
PM 2Ring
CC BY-SA 4.0
2020-02-28T11:50:56.057Z
Zeeman splitting is observed in the interstellar medium
usernumber
<data-analysis>
Do integer multiples occur in astronomy data?
user54038
# Do integer multiples occur in astronomy data?

(Asked by: username_0 on 2019-01-21)

I'm a statistics student, currently working on "quantum inference", which is the statistical problem of inference in the quantum model:

$y\_i = \alpha + \beta x\_i + \epsilon\_i$

which is similar to a simple linear model, except instead of $x\_i$ being a known constant, it is instead a random integer. The prototypical example is von Mises's analysis of atomic weights in 1918, trying to assess the significance of the observation that they tended to be integer multiples of the mass of hydrogen. For more information on the subject see [DG Kendall's overview](https://onlinelibrary.wiley.com/doi/abs/10.1002/0471667196.ess2129.pub2).

I am not sure if I should continue working on this problem because the applications are so few, mostly in archaeology, where weights or lengths are often integer multiples of an ancient unit of measure. However, it occurred to me that there may be applications in astronomy.

For example, perhaps the brightness of a spot has been measured, and the spot could represent any number of objects which are not distinguishable at the present resolution. This could be a problem of quantum inference... but only if if were for some reason known *a priori* that all objects had to have the same brightness.

So, while that specific scenario might be implausible, is there some problem in astronomy data analysis that involves quantum inference in this sense? In other words, are there ever cases where a histogram of the data shows multiple, *equally spaced* modes?

**Tags:** data-analysis
> **Comments:**
> **username_1**: I'm not sure if [orbital resonance](https://en.wikipedia.org/wiki/Orbital_resonance) suits your question: "when orbiting bodies exert a regular, periodic gravitational influence on each other, usually because their orbital periods are related by a **ratio of small integers**" (my emphasis).  
> **username_2**: I assume that $\alpha$ & $\beta$ are (real) parameters to be determined, and that $\epsilon_i$ is an error term, but you should mention that in the question.  
> **username_3**: Zeeman splitting is observed in the interstellar medium  

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## 0 answers

