<p>Here is my solution to the problem. I am posting it here in case anyone else come up with the same idea but did not know how to formulate it in mathematical notation!</p>

<blockquote>
  <p>$$ \psi_i = \sum_{i=1}^9 S_i $$</p>
  
  <p>where $S_i$ is the score function and defined as:</p>
  
  <p>$$
S_i = \cases{
  0 &amp; \text{if $\theta(x_i) &lt; Q_1$ or $\theta(x_i) = $ benign/neutral} \\
  0.5 &amp; \text{if $Q_1 \leq \theta(x_i) &lt; Q_3$ or $\theta(x_i) = $ possibly damaging/uncertain} \\
  1 &amp; \text{if $\theta(x_i) \geq Q_3$ or $\theta(x_i) = $ damaging}
}
$$</p>
  
  <p>The $\theta(x_i)$ is the pathogenicity or conservation score for variant $x$ as defined by model $i$ and $Q$ denotes the quartile range for scores from M-CAP, CADD, GERP and Phylop models.</p>
</blockquote>

CC BY-SA 3.0
2017-08-18T09:47:56.360Z
If Q are quartiles, then the last line for damaging shouldn't be $>Q_3$?
llrs
CC BY-SA 3.0
2018-03-31T15:59:05.397Z
@Konrad and Reza : Can you look into this problem and provide some suggestions. https://math.stackexchange.com/questions/2716192/how-to-convert-a-detailed-mathematical-statistical-compuational-process-into-ma
everestial
CC BY-SA 3.0
2017-08-17T19:47:04.523Z
2017-08-18T17:39:08.600Z
2017-08-18T17:39:08.600Z
RJF
<p>This is a cross-post from <a href="https://math.stackexchange.com/q/2380215">Mathematics forum</a>. As no one has answered it yet, I fIgured post here as well.</p>

<p>I would like to describe a transform I used to rank my data points. I have recoded my variable columns from $10$ measurements with different range to $n$ (for each measurement) where $n \in \{0,0.5,1\}$.    </p>

<p>For columns where measurements were expressed as categorical values I simply recoded the categorical value to either $0$, $0.5$ or $1$ and for continuous variables I recoded the lower quartile as $0$, interquartile as $0.5$ and upper quartile as $1$ and finally I summed the recoded values to produce a single score $\sum n_{i1,..i10} $ for each row. </p>

<p>I am trying to write my method and I'd like to have it in mathematical notation. I was wondering if anyone could help me with this!  </p>

CC BY-SA 3.0
2017-08-02T22:09:59.793Z
Maybe try https://stats.stackexchange.com/
Alex Reynolds
CC BY-SA 3.0
2017-08-03T07:54:34.203Z
What do you mean by "have it in mathematical notation"? Can you give an example of something you consider "in mathematical notation"?
bli
CC BY-SA 3.0
2017-08-03T07:55:28.047Z
Also, it would be good to include the link to the cross-post
bli
CC BY-SA 3.0
2017-08-03T09:29:36.913Z
Hi bli, Thank you for your comment. By mathematical notation I mean mathematical representation of my transform. I am including the link as you suggested!
RJF
CC BY-SA 3.0
2017-08-04T09:45:14.693Z
Your question is not very clear to me. So can you please try to explain it with some example. Then we may able to help you.
Arijit Panda
CC BY-SA 3.0
2017-08-04T09:56:07.130Z
Have you looked at the dataframe I uploaded in Mathematics forum?
RJF
CC BY-SA 3.0
2017-08-04T10:27:43.863Z
Yes, I did. But still it not clear.
Arijit Panda
CC BY-SA 3.0
2017-08-09T21:10:13.680Z
I think the problem with your question is two-fold. 1) you don't provide any reproducible data so that we can grasp the details of how you calculate this "rank" score. [See this post for an example how you would make a reproducible example in R to get an idea of what we mean by "reproducible example"](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) 2) there is not likely to be a mathematical notation for what you have done, because there is no mathematical formula to convert strings ("I", "II", "III") into numbers. One way that you could potentially solv
Reilstein
CC BY-SA 3.0
2017-08-10T08:22:08.330Z
I think that "mathematical notation" does not necessary have to consist in "formulas". One could probably define a bijection between a set of strings and a set of numbers, in proper mathematical notation, and that would validly describe a conversion procedure.
bli
CC BY-SA 3.0
2017-08-10T14:56:35.360Z
Yeah you are probably right that there is some valid way of describing the rank score. I imagine in this case it would be something more akin to a key than notation/formula, but if you have an idea how to describe it why don't you add an answer?
Reilstein
CC BY-SA 3.0
2017-08-10T15:16:41.953Z
As you pointed out, it is difficult to grasp the details of what the OP wants. Besides, it's been a long time since I last wrote maths formally.
bli
<modelling>
Mathematical notation for formulating a rank score
# Mathematical notation for formulating a rank score

(Asked by: username_0 on 2017-08-02)

This is a cross-post from [Mathematics forum](https://math.stackexchange.com/q/2380215). As no one has answered it yet, I fIgured post here as well.

I would like to describe a transform I used to rank my data points. I have recoded my variable columns from $10$ measurements with different range to $n$ (for each measurement) where $n \in \{0,0.5,1\}$.

For columns where measurements were expressed as categorical values I simply recoded the categorical value to either $0$, $0.5$ or $1$ and for continuous variables I recoded the lower quartile as $0$, interquartile as $0.5$ and upper quartile as $1$ and finally I summed the recoded values to produce a single score $\sum n\_{i1,..i10} $ for each row.

I am trying to write my method and I'd like to have it in mathematical notation. I was wondering if anyone could help me with this!

**Tags:** modelling
> **Comments:**
> **username_1**: Maybe try https://stats.stackexchange.com/  
> **username_2**: What do you mean by "have it in mathematical notation"? Can you give an example of something you consider "in mathematical notation"?  
> **username_2**: Also, it would be good to include the link to the cross-post  
> **username_0**: Hi bli, Thank you for your comment. By mathematical notation I mean mathematical representation of my transform. I am including the link as you suggested!  
> **username_3**: Your question is not very clear to me. So can you please try to explain it with some example. Then we may able to help you.  
> **username_0**: Have you looked at the dataframe I uploaded in Mathematics forum?  
> **username_3**: Yes, I did. But still it not clear.  
> **username_4**: I think the problem with your question is two-fold. 1) you don't provide any reproducible data so that we can grasp the details of how you calculate this "rank" score. [See this post for an example how you would make a reproducible example in R to get an idea of what we mean by "reproducible example"](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) 2) there is not likely to be a mathematical notation for what you have done, because there is no mathematical formula to convert strings ("I", "II", "III") into numbers. One way that you could potentially solv  
> **username_2**: I think that "mathematical notation" does not necessary have to consist in "formulas". One could probably define a bijection between a set of strings and a set of numbers, in proper mathematical notation, and that would validly describe a conversion procedure.  
> **username_4**: Yeah you are probably right that there is some valid way of describing the rank score. I imagine in this case it would be something more akin to a key than notation/formula, but if you have an idea how to describe it why don't you add an answer?  
> **username_2**: As you pointed out, it is difficult to grasp the details of what the OP wants. Besides, it's been a long time since I last wrote maths formally.  

---

## 1 answers

### Answer by username_0 on 2017-08-17. Score: 1

Here is my solution to the problem. I am posting it here in case anyone else come up with the same idea but did not know how to formulate it in mathematical notation!

> $$ \psi\_i = \sum\_{i=1}^9 S\_i $$
>
> where $S\_i$ is the score function and defined as:
>
> $$
> S\_i = \cases{
> 0 & \text{if $\theta(x\_i) < Q\_1$ or $\theta(x\_i) = $ benign/neutral} \\
> 0.5 & \text{if $Q\_1 \leq \theta(x\_i) < Q\_3$ or $\theta(x\_i) = $ possibly damaging/uncertain} \\
> 1 & \text{if $\theta(x\_i) \geq Q\_3$ or $\theta(x\_i) = $ damaging}
> }
> $$
>
> The $\theta(x\_i)$ is the pathogenicity or conservation score for variant $x$ as defined by model $i$ and $Q$ denotes the quartile range for scores from M-CAP, CADD, GERP and Phylop models.

> **Comments:**
> **username_5**: If Q are quartiles, then the last line for damaging shouldn't be $>Q_3$?  
> **username_6**: @Konrad and Reza : Can you look into this problem and provide some suggestions. https://math.stackexchange.com/questions/2716192/how-to-convert-a-detailed-mathematical-statistical-compuational-process-into-ma  

---

