v a l i d a t i o n   I need to write the word as vertically. I use overleaf.
For a book cover, I want to write the title vertically (like in Japanese, but using English text):           T T        I H        T I  I  M  L S  S  Y  E   How do I do this without jumping through a host of \vbox and \hboxes?
Is there any difference between Frequentist and Bayesian on the definition of Likelihood? Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me.  According to most sources I have seen, the likelihood of a distribution with parameter $\theta$, should be a product of probability mass functions given $n$ samples of $x_i$:  $$L(\theta) = L(x_1,x_2,...,x_n;\theta) = \prod_{i=1}^n p(x_i;\theta)$$  For example in Logistic Regression, we use an optimization algorithm to maximize the likelihood function (Maximum Likelihood Estimation) to obtain the optimal parameters and therefore the final LR model. Given the $n$ training samples, which we assume to be independent from each other, we want to maximize the product of probabilities (or the joint probability mass functions). This seems quite obvious to me.  According to , "likelihood is not a probability and it is not a conditional probability". It also mentioned, "likelihood is a conditional probability only in Bayesian understanding of likelihood, i.e., if you assume that $\theta$ is a random variable."  I read about the different perspectives of treating a learning problem between frequentist and Bayesian.   According to a source, for Bayesian inference, we have a priori $P(\theta)$, likelihood $P(X|\theta)$, and we want to obtain the posterior $P(\theta|X)$, using Bayesian theorem:  $$P(\theta|X)=\dfrac{P(X|\theta) \times P(\theta)}{P(X)}$$   I'm not familiar with Bayesian Inference. How come $P(X|\theta)$ which is the distribution of the observed data conditional on its parameters, is also termed the likelihood? In , it says sometimes it is written $L(\theta|X)=p(X|\theta)$. What does this mean?  is there a difference between Frequentist and Bayesian's definitions on likelihood??  Thanks.    EDIT:  There are different ways of interpreting Bayes' theorem - Bayesian interpretation and Frequentist interpretation (See: ). Tool to manage and/or make available a list of my publications on the web? I have a custom search page for use in Customer Portal.  VF Page:    &lt;form name="frmSearch"&gt;      &lt;input type="text" name="keyword" id="keyword" value="{!portalSearchModel.searchTerm}" onkeypress="return noenter(event);" style="width:25%; height:25px;margin:0; padding: 0px 6px 0px;" placeholder="What are you looking for?" /&gt;      &lt;input type="button" id="btnSearch" name="btnSearch" value="Search" onclick="searchTerm()" class="go-we3" /&gt;   &lt;/form&gt;   &lt;script type='text/javascript'&gt;       function searchTerm(){         var searchTerm = document.getElementById("keyword").value;          var url="/apex/PortalSearch?s="+searchTerm;          window.location = url;          return false;     }          &lt;/script&gt;   Is there a way to call this apex method in Controller on button click along with the JavaScript?      public void logSearchTerm(){         portalSearchModel.searches();         Search_Log__c sl = new Search_Log__c();          sl.search_term__c = portalSearchModel.searchTerm;         sl.user__c = UserInfo.getUserId();              insert sl;  } Flip x and y axes in Excel graph This should not be very difficult, but I cannot figure out how to do it.  I have a table similar to this     %low %high  0   0   12  1  13   26  ... 19  90   94 20  95  100   When I graph it, excel defaults to having the first column on the x axis and plotting the second and third column as y values. I want the first column to be on the y axis instead. I assume there is an easy way to do this, but I cannot figure it out. Most of the things I have found from searching have suggested the "Switch Row/Column" button, but that does something else.  Thanks for the help. How to fix "-5 No address associated with hostname error" while updating? What does the "yield" keyword do? "No such file or directory" when trying to remove a file, but the file exists? I am trying to remove a png image that was uploaded to my server via a PHP script. Whenever I try to delete it both through ftp and terminal, I get the error   No such file or directory   However, when I ls in the dir, the file is listed and it is also listed in my ftp client. I have tried creating a file with the same name and I end up getting two files with the same name.   I can open the file that supposedly does not exist, but I still can't remove it. I have also tried rebooting my server. Any ideas what may be the issue? I am running a 64 bit version of Ubuntu, but I don't think its a 32/64 bit issue. I should also note I have removed many other png files uploaded by the same PHP script.  Output for ls -l  total 224  -rw-r--r-- 1 www-data www-data 222838 May 13 04:14 qyxdshyikfr_fishing_timeout.png  -rw-r--r-- 1 root root 272 May 14 06:54 upload.php   Output when trying to rm  rm: cannot remove ‘qyxdshyikfr_fishing_timeout.png’: No such file or directory   upload.php: Someone gave me a bunch of envelopes of pizza crust yeast, "specially formulated for pizza crust". The packets also say that no rise time or proofing is needed, and that it's "NOT recommended for bread baking." The ingredients are yeast, enzymes, sorbitan monostearate, l-cysteine, and ascorbic acid. It does provide a recipe for pizza crust, with just mixing and a bit of kneading.   What has actually been done to this yeast to make it work like this? (What are those enzymes?) And is there any way I can use it for other things, or is it really only good for things like pizza crust? Getting user provided data out of a database and into R How do you show a hidden folder (whose name starts with .) in File Manager a.k.a. Nautilus on Ubuntu?  I am somewhat new to Ubuntu and can't seem to find the "view" menu. C# HttpWebRequest with XML Structured Data Can a PC be a lich? The heading says it all, can a PC be a lich? If so, how? The DMG hints that the Book of Vile Darkness contains the secrets of how; there is nothing official otherwise. I'm using MySQL's AUTO_INCREMENT field and InnoDB to support transactions. I noticed when I rollback the transaction, the AUTO_INCREMENT field is not rollbacked? I found out that it was designed this way but are there any workarounds to this? How can I find just the *.mp3 files with a recursive command like ls -R *.mp3 in a directory that contains several sub-directories and at the end copy these files in a directory that I choose.  Thanks for your support. math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$? I know there is something wrong with this but I don't know where. It's some kind of a math fallacy and it is driving me crazy. Here it is: $$-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1?$$ Why can "trans" be replaced with an x? I can't think of an example, so I may be wrong about this, but I think I've seen people replace the prefix "trans" as in transport with an x. "Cross" makes sense, as in "railroad crossing", and I guess "chris" is sort of a punny extension, the extension being like "chris cross" and the example being "xmas", but why trans? 1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation:  if $C = A+B$  or  $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = \frac{A}{B}$ $$\frac{\Delta C}{C} = \frac{\Delta A}{A}  + \frac{\Delta B}{B}$$ if $C = A^m$ $$\frac{\Delta C}{C} = |m|\frac{\Delta A}{A}$$   These formulas are derived from the expression for the differential of a function of multiple variables:  if $C = f(A,B)$ $$ dC = \frac{\partial C}{\partial A}dA + \frac{\partial C}{\partial B}dB \Rightarrow \Delta C = \frac{\partial C}{\partial A}\Delta A + \frac{\partial C}{\partial B}\Delta B$$  and I think that makes sense because the value C is just a function of two variables that happen to be measurements.  2) But this morning, I was told that this is wrong and I should actually use these instead:  if $C = A+B$  or  $C = A-B$ $$(\Delta C)^2 = (\Delta A)^2 + (\Delta B)^2$$ if $C = AB$ or $C = \frac{A}{B}$ $$\left(\frac{\Delta C}{C}\right)^2 = \left(\frac{\Delta A}{A}\right)^2  + \left(\frac{\Delta B}{B}\right)^2$$  which are apparently derived from a general formula:  $$(\Delta C)^2  = \left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...$$  or   $$\Delta C  = \sqrt{\left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...}$$  3) So:   Why is this formula better?  Where does it come from? What does it actually represent? (Do I recognize the shape of a norm in that last formula?)  What is wrong with the formula of the differential?   I'm asking a lot, but the propagation of uncertainty always confused the ship out of me. When can I be sure a questionable check has cleared? Write the digits of a number into an array Should the number "0" be pronounced "zero" or "oh"?