How are AUROC scores computed with just two vectors of actual and predicted values as input? In the R package ModelMetrics, the auc score as shown in the documentation takes only two inputs;  aucScore &lt;- auc(actual=actuallabels, predicted=predictedlabels)  where the inputs are pretty self explanatory. However, how is the AUC score even calculated here? From my understanding, do we not need the class "probabilities" (scores) produced from the model in order to graph the ROC curve in the first place? Each point on the ROC curve is the TPR vs. the FPR, at varying thresholds of class "probabilities" to trigger a "positive" prediction, if my understanding is correct. So how can we chart the ROC curve and find the area under said curve if we don't have the class probabilities to derive each point on the ROC curve itself? Based off labels alone, I would find that it would be impossible to find this unless there's some underlying estimation going on.  I've also noticed that many other packages also compute the area under the ROC curve by taking only two vectors of labels with seemingly no class probabilities.  Thanks.
How to calculate Area Under the Curve (AUC), or the c-statistic, by hand I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model.  For example, in the validation dataset, I have the true value for the dependent variable, retention (1 = retained; 0 = not retained), as well as a predicted retention status for each observation generated by my regression analysis using a model that was built using the training set (this will range from 0 to 1).  My initial thoughts were to identify the "correct" number of model classifications and simply divide the number of "correct" observations by the number of total observations to calculate the c-statistic. By "correct", if the true retention status of an observation = 1 and the predicted retention status is > 0.5 then that is a "correct" classification. Additionally, if the true retention status of an observation = 0 and the predicted retention status is &lt; 0.5 then that is also a "correct" classification. I assume a "tie" would occur when the predicted value = 0.5, but that phenomenon does not occur in my validation dataset. On the other hand, "incorrect" classifications would be if the true retention status of an observation = 1 and the predicted retention status is &lt; 0.5 or if the true retention status for an outcome = 0 and the predicted retention status is > 0.5. I am aware of TP, FP, FN, TN, but not aware of how to calculate the c-statistic given this information.
Should edits with only minor code improvements be accepted. As an example, I'm reviewing an edit that changes all double quotes to single quotes and renames a variable in some javascript. With the exception of the variable rename (which is not entirely necessary), the edit is frivolous. Should I accept on the merits of a debatable variable name change? I want to prove that $\lim_{(x,y)\to (0,0)} \frac{\sin(x+y)}{x+y} = 1$  Is it sufficient to say that if $u = x+y$ then as $(x,y) \rightarrow (0,0)$ then $u \rightarrow 0$ and then evaluate $\lim_{u\to 0} \frac{\sin u}{u}$ which is 1 by L'Hôpital's rule?  I feel that this is somehow "cheating" and I would really like to prove it in a more rigorous way, i.e., by using an $\epsilon$ - $\delta$ argument.  I have tried for a long time to use the one variable version and prove that if $0 \lt \sqrt{x^2 + y^2} \lt \delta$ then somehow $0 \lt |x+y| \lt \delta$ and it would follow from the one variable case that $| \frac{\sin(x+y)}{x+y} - 1| \lt \epsilon$. However, because $|x+y| = 0$ when $y = -x$ I am not getting anywhere with this.  Any input on this would be helpful :) Where has all the RAM gone? Starting with the episode "Crossroads Part II" the      final five Cylons begin to hear Bob Dylan's "All Along the Watchtower" in their heads.   Have the creators/writers ever stated why they picked that song in particular and what it might mean to the story? How do I create variable variables? what is the difference between kind, type and sort If $a$, $b$, and $c$ are sides of a triangle, then $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$. Let $a,b,c$ be the lengths of the sides of a triangle. Prove that $$\sum_{\text{cyc}}\frac{a}{b+c}=\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}&lt;2\,.$$  Attempt.  By clearing the denominators, the required inequality is equivalent to $$a^2(b+c)+b^2(c+a)+c^2(a+b)&gt;a^3+b^3+c^3\,.$$ Since $b+c&gt;a$, $c+a&gt;b$, and $a+b&gt;c$, the inequality above is true.  Is there a better, non-bruteforce way? Arrows linking table cells I'm currently trying to add arrows in my synthetic division example to show people clearly how synthetic division works. I'm working on Overleaf.   The code for my synthetic division right now is:  \begin{tabular}{c |r r r r r}     &amp;1&amp; 4 &amp; -1&amp;16&amp;-20\\   1&amp;&amp; 1 &amp; 5 &amp; 4&amp;20\\   \hline    &amp;1 &amp;5 &amp; 4 &amp; 20 &amp;\rule{3pt}{16pt}\;0\\   \end{tabular}   How would I add arrows to this? For instance, a down arrow going from the first 1 to 1, then an upwards arrow pointing right from 1 to 1, then an arrow pointing down from 1 to 5, etc. Basically I would like to add arrows that look like this: Print file content without the first and last lines Is there a simple way I can echo a file, skipping the first and last lines? I was looking at piping from head into tail, but for those it seems like I would have to know the total lines from the outset. I was also looking at split, but I don't see a way to do it with that either. Give an example about limits: $\lim\limits_{x\to0}f(x^{2})$ exists but $\lim\limits_{x\to0}f(x)$ does not. Problem with \pspicture in a simple plain TeX code Just writing the following very simple program I had some problems. I use to write in plain TeX and in this case I tried to make a picture with PSTricks and first of all sized it with \pspicture. The program is:  \input pstricks \pspicture (0,0)(5,5) \endpspicture \bye   but when I compiled with TeX, I encountered the following error:  Command Line:   tex.exe --src --interaction=errorstopmode "figura.tex" Startup Folder: C:\Users\MT\Documents\TeX  This is TeXk, Version 3.14159265 (TeX Live 2015/W32TeX) (preloaded format=tex)  Source specials enabled. (./figura.tex (c:/texlive/texmf-dist/tex/generic/pstricks/pstricks.tex we are running tex and have to define some LaTeX commands ... (c:/texlive/texmf-dist/tex/generic/xkeyval/pst-xkey.tex 2005/11/25 v1.6 PSTricks specialization of xkeyval (HA) (c:/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex (c:/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex (c:/texlive/texmf-dist/tex/generic/xkeyval/keyval.tex)) 2014/12/03 v2.7a key=value parser (HA) (c:/texlive/texmf-dist/tex/generic/xkeyval/xkvtxhdr.tex 2005/02/22 v1.1 xkeyval TeX header (HA)))) (c:/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex `pst-fp' v0.05, 2010/01/17 (hv)) (c:/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex (c:/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex)) (c:/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex (c:/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex)) (c:/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code .tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.te x) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics .code.tex))) (c:/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex) )) `PSTricks' v2.64b  &lt;2015/14/11&gt; (tvz) (c:/texlive/texmf-dist/tex/generic/pstricks/pstricks.con)) ! Undefined control sequence. \endpspicture ...z@ \box \pst@hbox \else \fboxsep                                                    =0pt \fbox {\rule [-\pst@s... l.5 \endpspicture  ? x No pages of output. Transcript written on figura.log.  _____________________________________________________________________   TeX Compilation Report (Pages: 0)   Errors: 1   Warnings: 0   Bad Boxes: 0 _____________________________________________________________________   What's the problem? How do I send a file with FileZilla from the command line? I have a batch file that builds an application, and then I want to upload it to an FTP server from the command line.   Considering I do the upload manually with , is there a command line for it to upload files?  I am limited to Windows. Does anyone know the (specific) reasons that it is recommended that old LTS server users wait until the point release to upgrade?  Is it just a matter of bug fixes and waiting for improved stability for production servers, or is there something more fundamental than that? In formal logic, how is it possible for an argument with a contradictory conclusion to be valid? I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point:  In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the premises to be true and at the same time the conclusion false."  The text then later prompts me to declare whether it's possible for an argument to be valid with a contradiction for a conclusion. The answer key then claims that yes, it is in fact possible, but offers no further explanation. I'm also supposed to create an example.  I just can't wrap my head around this one.  Here's the example I've worked up, is this a valid argument?   If grass is green then it is raining.  If water is wet then it is not raining.  Therefore: It is raining and not raining.   My head hurts. One of my Fellows asked me whether total induction is applicable to real numbers, too ( or at least all real numbers ≥ 0) . We only used that for natural numbers so far.  Of course you have to change some things in the inductive step, when you want to use it on real numbers.  I guess that using induction on real numbers isn't really possible, since $[r,r+\epsilon]$ with $\epsilon > 0$, $r \in \mathbb R$ is never empty.  Can you either give a good reason, why it isn't possible or provide an example where it is used? Is VGA port hot-pluggable? In meetings, I often see people detaching the VGA connector from one running laptop and connecting it to another, while the projector is still on. Is this 100% risk free, and OK by design of the VGA standard? If there's a risk involved in hot-plugging VGA, can it be removed by turning off or suspending either laptop, display, or both? I see this being done all the time without causing disaster, so clearly I'm not interested in answers stating &quot;we do it all the time, so it should be OK!&quot;. I want to know if there's a risk - real or in theory - that something breaks when doing this. EDIT: I did an internet search on the topic, and I never found a clear statement as to why it is safe or unsafe to hot swap VGA devices. The typical form is a forum question asking basically the same question as I did, and the following types of statements  Yes it's hot swappable! I do it all the time! It involves some kind of risk, so don't do it! You're some kind of moron if you think there's a risk, so just do it!  But no explanation as to why it safe or not... Joe Taylors answer below contains a link to a forum post and answers that basically give me the same statements as mentioned above. But again, no good explanation why. So I looked for an actual manual for a projector, and found . It states on page 3-1:  Connecting devices Computers and video devices can be connected to the projector at the same time. Check the user’s manual of the connecting device to confirm that it has the appropriate output connector. [image] Attention: As a safety precaution, disconnect all power to the projector and devices before making connections.  But again, no good explanation. I am running Wireshark on my linux machine and i have simple python web server running on localhost:8080  I am capturing only local port 8080. When i open browser on localhost:8080 wireshark captures huge amount of tcp communication (as page loads with all resources) but there`s no HTTP only TCP...   Why i cannot capture HTTP on custom port ? Run a command in a shell and keep running the command when you close the session I am using Putty to connect to a remote server. What I want to know is if there is any way to write my commands and allow them to keep running after I close the session with Putty. The reason for this is that I do not want to keep the computer ON all the time. Is there any way to do this?.  Update with the solution  For my question as it is presented the best solution is use one of the commands provided such as nohup, because you do not have to install any additional software. But if you are in the same problem use screen, install it and use it. It is amazing.  I have selected the answer of Norman Ramsey as favourite because propose several solutions using commands and screen. But please check the other answers specially the one of PEZ, then you get an insight of what screen is able todo. How do I select multiple elements and a class in JQuery How to place a float at the top of a floats-only page?