I have a sample with data and I would like to compare the result I get from Monte Carlo integration and by analytically computing the marginal likelihood. Now I know that in many cases this is a challenging computation, but in this case apparently it is possible. I have the code for doing it, but I don't understand how it is done, and the code doesn't make me wiser.  So, let  $Y \sim N(\theta,1)$ and the prior on $\theta \sim N(0,1)$.  How would I analytically compute the  marginal likelihood $p(y)$  $$p(y) = \int p(y|\theta)\,p(\theta)\, d\theta$$
Given that $a$~$\mathcal{N}(\mu, \Sigma)$ and $\mu$~$\mathcal{N}(0, \sigma^2 I)$, Is $p(a|\Sigma, \sigma)=\int p(a|\mu, \Sigma)p(\mu|\sigma)d\mu$ again a Normal distribution? And how to estimate the mean and variance respectively? Thanks a lot!
GNU screen: Running commands in different window when screen is started Creating a row for each value in a comma-separated string I'm currently trying to create a View from a Table that does the following:  Table A ╔═════════════╦═══════════════╗  ║ PART NUMBER ║   FILE NAME   ║ ╠═════════════╬═══════════════╣ ║  PN0001-01  ║      FOO      ║ ║  PN0002-01  ║      BAR      ║ ║  PN0003-01  ║    FOO,BAR    ║ ║  PN0004-01  ║  BAR,FOO,FOB  ║ ╚═════════════╩═══════════════╝   To create  View B ╔═════════════╦═══════════════╗  ║ PART NUMBER ║   FILE NAME   ║ ╠═════════════╬═══════════════╣ ║  PN0001-01  ║      FOO      ║ ║  PN0002-01  ║      BAR      ║ ║  PN0003-01  ║      FOO      ║ ║  PN0003-01  ║      BAR      ║ ║  PN0004-01  ║      BAR      ║ ║  PN0004-01  ║      FOO      ║ ║  PN0004-01  ║      FOB      ║ ╚═════════════╩═══════════════╝   So, essentially, I need to take records from Table A and insert them into View B, where if the record from A has a LIKE '[,]' property, then that field is split into multiple records in B, depending on the number of times the ',' is present, with the text between each ',' being given its own record in View B. Solve $\sin x = 1 - x$ How would you be solve sin x = 1 - x, without drawing the graph and manually measuring the point of intersection? Short Story About Contact With An Alien Race That Extruded An Elixir Note: This is an attempt to create a canonical question that covers all instances of &quot;low-graphics mode&quot; error that occurs to a user, including but not limited to installation of wrong drivers, incorrect or invalid lightdm greeters, low disk space, incorrect installation of graphics card like ATI and Nvidia, incorrect configuration of xorg.conf file while setting up multiple monitors among others. If you are experiencing the &quot;low-graphics mode&quot; error when trying to login but none of the following answers work for you, please do ask a new question and then update the answers of this canonical question as and when your new question gets answered.   When I try to boot into my computer, I am getting this error:  The system is running in low-graphics mode Your screen, graphics cards, and input device settings could not be detected correctly. You will need to configure these yourself.   How do I fix the failsafe X mode and login into my computer?  Answer index: Let $\mathbb{R^{ n×n}}$ be the space of n × n real matrices. Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$ is the sum of the determinants of $n$ matrices, in which the $i$th matrix is $A(t)$ except that the $i$th row is differentiated. Use this result to prove that the directional derivative of the determinant function at the matrix $A \in \mathbb{R ^{n×n}}$ along the direction $B \in \mathbb{R^{ n×n}}$ is given by $$(det)^{'} (A; B) = tr(Adj(A)B) = \langle Adj(A)^{T} , B \rangle $$ where $Adj(A)$ is the adjoint of $A$, and where the inner product on $\mathbb{R^{n×n}}$ is the trace inner product given by $\langle X, Y \rangle = tr(X^{T} Y )$ Conclude that $$D(det)(A) = Adj(A) ^T $$. This question was prompted by questions about ls' -1 option and the recurring tendency of people to ask question and answers that includes processing the output of ls.   This reuse of the output ls seems understandable, e.g.: if you know how to sort a list of files with ls you might want to use the output in that way as input for something else.  If those Q&amp;A don't include a reference to the file name list produced consisting of nicely behaving file names (no special characters like spaces and newlines), they are often commented upon by someone pointing out the danger of the command sequence not working when there are files with newlines, spaces etc.  find, sort and other utilities solve the problem of communicating "difficult" file names to e.g. xargs by using an option to separate the file names with the NUL character/byte which is not a valid character in file name (the only one in addition to /?) on Unix/Linux filesystems.  I looked to the man page for ls and the output for ls --help (which has more options listed) and could not find that ls (from coreutils) has an option to specify NUL separated output. It does have a -1 option which can be interpreted as "output file names separated by newline")  Q: Is there are technical or philosophical reason why ls does not have a --zero or -0 option that would "output file names separated by NUL"?  If you do something that only outputs the file names (and not use e.g. -l) that could make sense:  ls -rt -0 | xargs -r0 …   I could be missing something why this would not work, or is there an alternative for this example that I overlooked and that is not much more complicated and/or obscure.    Addendum:  Doing ls -lrt -0 probably does not make much sense, but in the same way that find . -ls -print0 does not, so that is not a reason to not provide a -0/-z/--zero option. How can you smooth the edge between two materials? C# - how can I get owner's name for a Mutex I have a shared mutex between 2 applications. I want to create an administration console that shows the current owner's name of the mutex.  How can I get the application name that currently owns the Mutex? Why do function pointers all have the same value? Why is foo.hasOwnProperty('__proto__') equal to false? Do the SSH or FTP protocols tell the server to which domain I am trying to connect? When using the ssh or ftp commands from the Bash shell, does the server that I am connecting to learn of the domain name used? I understand that the domain name is locally translated into an IP address via DNS. In HTTP, after that happens, the server is told the original domain name as well in order to serve the correct page, or to present the correct TLS cert (SNI).  host serverfault.com GET /   Does a similar phenomenon happen when connecting to ssh or ftp?  I ask because I am  trying to ssh into a server (GoDaddy webhosting) which expects a domain name, but is not letting me in when I try to connect via user@IPaddress as the DNS is not yet moved to the GoDaddy IP address. Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$ This an interesting problem my friend has been working on for a while now (I just saw it an hour ago, but could not come up with anything substantial besides some PMI attempts).  Here's the full problem:  Let $x_{1}, x_{2}, x_{3}, \cdots x_{y}$ be all the primes that are less than a given $n&gt;1,n \in \mathbb{N}$.   Prove that $$x_{1}x_{2}x_{3}\cdots x_{y} &lt; 4^n$$  Any ideas very much appreciated! Drupal site moved from development to live - IE won't load stylesheets anymore Before you ask ... I have looked everywhere for a solution, even drupal.org but nothing so far seems to work.  I developed a Drupal site (custom child theme for Zen) and on the development server everything looks fine in all browsers.  I did a test migration to another server before the launch. This move went well and everything looks fine in all browsers.  Then I moved the site to its live server where everything looks fine in all browsers except Internet Explorer which is not loading the stylesheets.  I know Drupal is known for generating many stylesheets and Internet Explorer will not load them if there are more than 31 (I believe) of them, but I did set the "Aggregate and compress CSS files" feature and clear the cache. This did not seem to help.  Could the answer be in one of the two following things?   The development site and backup site are both with one hosting provider. The live site is with a different hosting provider. The development site and backup site are in subfolders of two different portfolio sites ... ie www.portfoliosite.com/Newsite. The live site is a subdomain of the parent site ... ie www.newsite.parentsite.com.   I have run out of ideas so if anyone has a possible solution or direction to look, please let me know. Thanks Image upload from photo gallery So this is pretty obvious. Image upload?    How about allowing to attach images in questions from the photo gallery, by perhaps sending the image for off-site storage like done from the full-web version? What causes these inconsistent dark bands in some of my photos from an indoor event? Yesterday I took photos of an event at school.  The lighting was poor so I increased the iso to 3200, shutter speed was between 80 and 250 and the aperture between 2.8 and 4.0.  Canon EOS500  about 10% of the photos got this weird horizontal black area. The position of the black area is not the same,  Sometimes it is in the middle, sometimes it is in the upper or lower part of the frame  Is this an artifact from the lighting frequency? or can it be a shutter problem? How to force Mac window to foreground? Java Command line arguments Escape velocity from long ladder How to split algorithm2e over two pages