Some bad grades but many (good) publications; applying for a PhD
How do you get a bad transcript past Ph.D. admissions?
Under which assumptions a regression can be interpreted causally? First, don't panic. Yes, there are many similar question on this site. But I believe none gives a conclusive answer to the question below. Please bear with me.  Consider a data generation process $\text{D}_X(x_1, ... , x_n|\theta)$, where $\text{D}_X(\cdot)$ is a joint density function, with $n$ variables and parameter set $\theta$. It is well known that a regression of the form $x_n = f(x_1, ... , x_{n-1}|\theta)$ is estimating a conditional mean of the joint distribution, namely, $\text{E}(x_n|x_1,...,x_{n-1})$. In the specific case of a linear regression, we have something like $$ x_n = \theta_0 + \theta_1 x_1 + ... + \theta_{n-1}x_{n-1} + \epsilon $$ The question is: under which assumptions of the DGP $\text{D}_X(\cdot)$ can we infer the regression (linear or not) represents a causal relationship? It is well known that experimental data does allow for such interpretation. For what I can read elsewhere, it seems the condition required on the DGP is exogeneity: $$ \text{E}(x_1, ... x_{n-1}|\epsilon) = 0$$ The nature of randomisation involved in experimental data ensures the above is the case. The story goes then to argue why observational data normally fails in achieving such condition, reasons including omitted variable bias, reverse causality, self-selection, measurement errors, and so on. I am however uncertain about this condition. It seems too weak to encompass all potential arguments against regression implying causality. Hence my question above. UPDATE: I am not assuming any causal structure within my DGP. I am assuming that the DGP is complete, in the sense that there must be some causality (an ontological position it could well be debated), and all relevant variables are included. The key is to identify the set of assumptions which ensure me causality goes from certain variables to the other, without assuming from the outset such direction of causality.  Many similar posts on the site spend time mentioning why correlation does not imply causation, without providing hard arguments about when it does. That is the case, for instance, of  very popular post. Additionally, in the  on the site about the topic, the accepted answer gives the very vague answer:  Expose all hidden variables and you have causation.  I do not know how to translate that to my question above. Neither is the second most upvoted answer. And so on. That is why I believe this post does not have an answer elsewhere. How to delete a file in Windows with a too long filename? My wife has several files and folders that somehow ended up having filenames that have caused them to be undeleteable (can't be deleted) by normal means or via the command line. I believe the filenames are too long due to the depth of the folder structures. Does anyone know of a good utility for cleaning up files like this? Shouldn't this table span the whole page width? I have this table definition as part of a invoice  \begin{tabularx}{\textwidth}[ht]{lXrr}%   It worked fine for years until I have a very short word in the X column for the first time. Now my table is very small in width and centered horizontally on the page.  In my expectation the X column should fill up all space until the width of the table reaches the width of the page except the margins.  I have read about workarounds specifying something like 1.2\textwidth, but I don't like that, because the table is a template included via \include, so it would affect all my invoices.  I also tried \linewidth, \hsize and \columnwidth, but everything results in the same layout.  Is there a way to make the only X column expand so that it uses all available space?    Complete included table definition (Rechnungstabelle.tex):  \newcommand{\Rechnungstabelle}[4]{% vielen Dank für Ihren Auftrag. \noindent \begin{tabularx}{\textwidth}[ht]{lXrr}% \toprule% \bf{Anzahl} &amp; \bf{Bezeichnung} &amp; \bf{Einzelpreis} &amp; \bf{Gesamtpreis} \\% \midrule% #1% \bottomrule% &amp; \bf{Rechnungsbetrag}  &amp; &amp; \bf{\EUR{#2}} \\% \ifthenelse{\equal{#3}{}}{}{&amp; Enthaltene MwSt. 19\% &amp; &amp; \EUR{#3} \\}% \ifthenelse{\equal{#4}{}}{}{&amp; * Enthaltene MwSt. 7\% &amp; &amp; \EUR{#4} \\}% \end{tabularx}% }   Changing the table header row to  \bf{Anzahl} &amp; \bf{Bezeichnung} \hspace{\textwidth} &amp; \bf{Einzelpreis} &amp; \bf{Gesamtpreis} \\%   is a workaround, but I don't think that would be good TeX style.  Minimum example for reproducing:  \documentclass[ fontsize=12pt,                  paper=a4,                 foldmarks=TBMPL,                 fromalign=center,                 ngerman                 ]{scrlttr2} \usepackage{babel} \usepackage[utf8]{inputenx} \usepackage[right]{eurosym} \usepackage{tabularx} \usepackage{ltablex} \usepackage{booktabs} \usepackage{ifthen}  \input{Rechnungstabelle} \begin{document} \begin{letter}  \Rechnungstabelle{     1,0 h &amp; Do something &amp; \EUR{99,00} &amp; \EUR{99,00} \\      }     {99,00}     {}{} \end{letter} \end{document} How would you do a "not in" query with LINQ? I have two collections which have property Email in both collections. I need to get a list of the items in the first list where Email does not exist in the second list. With SQL I would just use "not in", but I do not know the equivalent in LINQ. How is that done?  So far I have a join, like...  var matches = from item1 in list1 join item2 in list2 on item1.Email equals item2.Email select new { Email = list1.Email };   But I cannot join since I need the difference and the join would fail. I need some way of using Contains or Exists I believe. I just have not found an example to do that yet. How do you display the archives of a Custom Post Type by Year &amp; Month? How do I enumerate the properties of a JavaScript object? How to calculate a heading on the earths surface? Given an initial position and a subsequent position, each given by latitude and longitude in the WGS-84 system.  How do you determine the heading in degrees clockwise from true north of movement? I'm trying to create a signature and date line in a document.  I need the date line to always be in the same spot on the page no matter what name is under the signature line, such as:  ----------------------   ---------------------- Representative           Date  ----------------------   ---------------------- Program Manager          Date   Here is the code I currently have:  \makebox[2.5in]{\hrulefill} \hspace {1.0in}\makebox[2.5in]{\hrulefill} \\ User Representative \makebox[2.5in][r]{Date} \\  \vspace{.2in} \makebox[2.5in]{\hrulefill} \hspace {1.0in}\makebox[2.5in]{\hrulefill} \\ Program Manager \makebox[2.5in][r]{Date} \   I want to be able to change the names, such as change Program Manager to Joe Foo and have the word 'Date' stay in the exact place.  Any help would be greatly appreciated.  I'm still a newbie at TeX so please forgive my ignorance. What is the origin of "man on the spot"? What is the origin of "man on the spot" ?   defines on the spot and uses as an example man on the spot.     on the spot -  at the place in question; there; "they were on the spot when it happened"; "it had to be decided by the man on the   spot" (Emphasis added)   Some evidence suggests that the origin of the phrase refers to decisions made by officials of the past British empire and actions taken by them. What is the probability that a person is the second person to roll a 6 for the first time? Suppose $A$, $B$, and $C$ roll a die in turns. What is the probability that $A$ is the second person to roll a $6$ for the first time? CUDA writing to constant memory wrong value Cruise ship in the Schengen area: Do the days spent at sea count toward the limit for short visits? I am planning on spending 90 days in Schengen zone countries.  I will be taking a cruise between Lisbon and Barcelona.  Do the days at sea count against the 90 days allowed for staying in the Schengen zone? notation of distribution I have a question:      Does  $$N(0, x)$$ mean a normal distribution with mean $0$ and variance $x$? Or standard deviation $x$?   The notation seems ambiguous sometimes. Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ Question 1: For $n \in \mathbb{N}$ explain why $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$   We must show that it is normal and separable.   $\mathbb{Q}(\zeta_n)/\mathbb{Q}$ is normal since it is a splitting field for $X^n-1 \in\mathbb{Q}[X]$ (I think... Is this correct?).  It is separable because it is of characteristic $0$  Question 2: $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$  Is this because the primitive nth root of unity $\zeta_n$ acts as a generator for a cyclic group? I am unable to fill out a decent proof on this.   Thanks for your help I have a shop created with drupal commerece modules,I enabled 2 currency in my shop , but only show one of them, I want to show price in 2 currency       something like this price :  10$  / 20 IRR I use multi currency module to achieve this job, but  I my problem is in payment  phase, I use multi currency module to achieve this job,in multicurrency  module's setting I don't want  use  synchronize method, if you want have two field in my product , one form $ and another for IRR, I did this job by this method     first enable IRR currency in  admin/commerce/config/currency  then in  admin/commerce/config/currency/handling under Enable dedicated price fields for Product check Iranian Rial  by doing this  another field added you my product ( ** Price for IRR** ), this is good , after this I enable  *currency selector * block ,in checking out process by switching the currency I don't see any change in current currency of billing and cart. :( why changing currency not changing cart currency? Why use gradient descent for linear regression, when a closed-form math solution is available? I am taking the Machine Learning courses online and learnt about Gradient Descent for calculating the optimal values in the hypothesis.  h(x) = B0 + B1X   why we need to use Gradient Descent if we can easily find the values with the below formula? This looks straight forward and easy too. but GD needs multiple iterations to get the value.  B1 = Correlation * (Std. Dev. of y/ Std. Dev. of x)  B0 = Mean(Y) – B1 * Mean(X)   NOTE: Taken as in   I did checked on the below questions and for me it was not clear to understand.      The above answers compares GD vs. using derivatives. Why don't wizards always use multiple wands? Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric Drawing different tikz shapes parameterized by data from a file I have a file with three columns of data, x, y, r.  # x y r 1 1 0.1 2 2 0.5 3 3 1.2   and so on. I'd like to loop over the rows, and draw a circle at x,y with radius r for each row.  I first thought I'd use pgfplots with customized marks, but I couldn't figure out how to pass the radius parameter into the pgfplot mark handler. Then I thought I'd use tikz and pgf directly, but I couldn't figure out how to reference the values for r inside a draw command sequence.   Any thoughts ? I'd be very grateful for some help. Prove that f is one-to-one on D