In Bayesian hypothesis testing, where one actually commits to estimates of the probabilities of each hypothesis, an analog of the Bonferroni correction is easy to justify. Namely, in the multiple comparison scenario, we might ask when Bayesian hypothesis testing: "what is the probability that at least one of these hypotheses is true, already knowing the probability of each individual hypothesis separately?". Then the  should give something analogous to Bonferroni.     Question: Is there an analog of Benjamini-Hochberg for Bayesian hypothesis testing?   More generally I am interested in the extent to which the theory for the multiple comparison problem is analogous between Bayesian and non-Bayesian hypothesis testing. But for the sake of specificity, and since that is the method I am most interested in right now, I refer to the Benjamini-Hochberg procedure. In particular, it is unclear to me whether the absence of p-values in the Bayesian setting makes procedures or considerations like Benjamini-Hochberg irrelevant.  Pointers to references will more than suffice for an answer. But of course if you want to share your unique insights into these issues, please do not hesitate.
Andrew Gelman wrote an extensive article on why Bayesian AB testing doesn't require multiple hypothesis correction: , 2012.  I don't quite understand: why don't Bayesian methods require multiple testing corrections?  A ~ Distribution1 + Common Distribution B ~ Distribution2 + Common Distribution C ~ Distribution3 + Common Distribution Common Distribution ~ Normal   My understanding is that the Bayesian approach shown above accounts for the shared underlying distribution by all the hypothesis (unlike in a frequentist Bonferroni correction). Is my reasoning correct?
$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $ $$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $$   (can this be duplicate? I think not) I tried it using many methods  $1.$ Solve this conventionally taking $1^\infty$ form in no luck  $2.$ Did this, expand $ {(1+x)^{\frac1x}}$ using binomial theorem got $\frac13$ then grouped coefficients of $x^0$ and it cancelled with $e$ then took coefficient of $x$ cancelled with $\frac{ex}{2}$ and so on   very messy right ? at last I got $\frac13$ but that's not the expected answer!  I must have went wrong somewhere can anyone help me with this. Can sudo be reinstalled after being removed? This seems to be a chicken-egg problem. The most common task using sudo is installing and removing software.  sudo apt-get purge &lt;appname&gt;   But sudo itself can be removed.  sudo apt-get purge sudo # Do not run this command on production computers!   This is where the fun comes  ubuntu@ubuntu:~$ sudo bash: /usr/bin/sudo: No such file or directory   Although it's obvious that no person in his right mind will purge sudo (other than me), someone can be fooled to run this command (not directly, in its hex mode, or whatever it's called) or a person could SSH in disguised as tech guru and do the mess.  So is there a way of reinstalling sudo? Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions How do I print all lines of a file with duplicate values in a certain column I'm trying to make airsoft chronograph/chronometer (a device that measures airsoft bullet speed). The idea is to measure time in which bullet is traveling from point A to point B, and then I can calculate bullet speed. Bullet is shot into plastic pipe with diameter of 32mm. I've tried to put on one side IR LED and on the other side phototransistor (BPW 40), both at the start and end of the tube. Something like this:  Blue circles are phototransistors, red circles are IR LEDs and white circles are airsoft bullets. When bullet passes through area where bullet 2  is drawn (just in between IR LED and phototransistor), everyting works perfectly. But when the bullet passes where bullets 1 and 3 are drawn, it isn't detected. That is expected, but unwanted behavior. So my question is: how can I detect bullets regardlessly of it's position ? I've thought about putting IR LEDs and phototransistors around the pipe (not only in one place), like this:  but this solution isn't cheapest: 5 IR LEDs + 5 BPW 40 = cca $12 times 2 (because I need it on both sides of the pipe) = $24. Is there any cheaper solution ? Is BPW 40 good choice for phototransistor ? I don't know which IR LEDs I'm using (and salesman in the store also doesn't know - he told me these are generic ones for remote controllers, like TV or DVD controller). Diameter of the pipe is 32mm and it will be long about 14cm (sensors will be 10cm apart). Diameter of airsoft bullet is 6mm. EDIT: I'll go for my second idea. I just have one more question: is it better to arrange IR emitters and photo transistors this way:  or this way:  Thanks !! geometric interpretation of $\vec v \cdot \operatorname{curl} \vec v = 0 $ There is a family of surfaces orthogonal to the vector field $\vec v \in \mathbb R^3$ iff $\vec v \cdot  \operatorname{curl} \vec v = 0 $. Now the necessity part is trivial, but the proof of sufficiency I have seen in physics textbooks, e.g. Kestin: Thermodynamics, is kind of mindless integration similar to the one usually offered to prove Poincare's lemma as in Flanders, or just asserted as in Born&amp;Wolf: Optics. Is there an intuitive and geometric interpretation of this condition that would make it obvious why its sufficiency must be true? How to handle calendar TimeZones using Java? I have a Timestamp value that comes from my application. The user can be in any given local TimeZone.  Since this date is used for a WebService that assumes the time given is always in GMT, I have a need to convert the user's parameter from say (EST) to (GMT). Here's the kicker: The user is oblivious to his TZ. He enters the creation date that he wants to send to the WS, so what I need is:  User enters: 5/1/2008 6:12 PM (EST)  The parameter to the WS needs to be: 5/1/2008 6:12 PM (GMT)  I know TimeStamps are always supposed to be in GMT by default, but when sending the parameter, even though I created my Calendar from the TS (which is supposed to be in GMT), the hours are always off unless the user is in GMT. What am I missing?  Timestamp issuedDate = (Timestamp) getACPValue(inputs_, "issuedDate"); Calendar issueDate = convertTimestampToJavaCalendar(issuedDate); ... private static java.util.Calendar convertTimestampToJavaCalendar(Timestamp ts_) {   java.util.Calendar cal = java.util.Calendar.getInstance(       GMT_TIMEZONE, EN_US_LOCALE);   cal.setTimeInMillis(ts_.getTime());   return cal; }   With the previous Code, this is what I get as a result (Short Format for easy reading):  [May 1, 2008 11:12 PM] Mid 2012 MBP shuts down claiming no power with charge at 30% or 40% or more When I'm editing a stack snippet, I often want to copy code from the original question into the snippet. But while the snippet editor is on display, there's no way to access the question, other than opening another tab/window. What I often do instead is copy all the code in the question to the clipboard, open the snippet editor, then paste it all in and revise it to what I want. But when the original code is poorly designed, that ends up being more work than just copying the bits and pieces that I want.  There could be a "View Question" button that pops up the question over the snippet editor and allows copying. Or maybe the Snippet Editor could be draggable and resizable, so you can reveal the question and copy from it; but this would require that it not be purely modal. New install - no network devices available - Realtek Device b822 I just purchased a Lenovo Yoga 730 15" laptop, and installed Ubuntu 16.04 in place of Windows 10. Install seemingly worked fine, but now I have no wifi device available.  Tried a reinstall just to be sure, and the same issue is happening. I don't believe it to be a hardware issue, as wifi was working without issue on Windows before I wiped it out.  When I run rfkill list I see:  0: ideapad_wlan: Wireless LAN Soft blocked: no Hard blocked: no   But when I run lspci I only see one item in the list claiming to be a network device:  3a:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device b822 (rev ff)   I have a USB wifi adapter and that gets me connected without issue, but obviously that is not the desired solution.  Does anyone have any insight on what might be causing the issue?  Output from modinfo -p rtl8822be:  fix_rate: (int) debug_level: (int) swenc:Set to 1 for software crypto (default 0) (bool) ips:Set to 0 to not use link power save (default 1) (bool) swlps:Set to 1 to use SW control power save (default 0) (bool) fwlps:Set to 1 to use FW control power save (default 1) (bool) msi:Set to 1 to use MSI interrupts mode (default 1) (bool) dma64:Set to 1 to use DMA 64 (default 0) (bool) aspm:Set to 1 to enable ASPM (default 1) (int) debug:Set debug level (0-5) (default 0) debug_mask:Set debug mask (default 0) (ullong) disable_watchdog:Set to 1 to disable the watchdog (default 0) (bool) Speed $v$ of a wave on a tightrope Quantum teleportation and no-communication theorem According to the Wikipedia article for the :     In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. This analogy is imprecise, because quantum entanglement suggests that perhaps a message could have been conveyed; the theorem replies 'no, this is not possible'.   According to the Jet Propulsion's recent article on quantum teleportation:   they can effect an entangled photon (B) with another photon (A) to change the state of the other entangled photon.  Doesn't this contradict what the no-communication theorem states ? problems with ellipse TikZ I'm working on a mac, I use the package TikZ and it works. But I have problems when I want use ellipse or diamond ex :  \documentclass{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[ellipse] {Ellipse}; \end{tikzpicture} \end{document}   If somebody could help me thank you ! What is the best way to explain how to choose between "its" and "it's"? Probably one of the most frequent grammar mistakes in the English language is:     The dog sat on it's mat.   Since spelling checkers don't catch it, and it is even logical, since you would correctly write:     The dog sat on Fluffy's mat.   What is the best way to explain to a learner of English how to choose between it's and its? Not only in ortho: top, front, back.  Please don't link this answer   I want a background image like this guy has -> Value of $x=\sum\limits_{n=1}^\infty {\frac{1}{10^n-1}} $ and location of second digit $1$ of $x$ What is the value of the series   $\sum\limits_{n=1}^\infty {\frac{1}{10^n-1}}$   and can one find closed forms for the sums   $\sum\limits_{n=1}^N {\frac{1}{10^n-1}}$?   I found that $\sum_{n=1}^N {\frac{1}{10^n-1}} $  =  $\sum_{n=1}^N (\lim_{m\to\infty  }{\frac{10^{-n}-10^{-nm}}{1-10^{-n}}})$  =  $0.111\ldots+0.0101\ldots+\ldots$ but I can't go farther.     The original question is: "Where does the second '1' appear?" Where is the pet store? I was playing sims freeplay on my iPod yesterday but could not find the pet store. Where is the pet store in the preteens are here update? C# difference between == and Equals() The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the same, but I don't think that's the case.   Can someone shed light on when the relationship is not symmetric, and how that relates to the Pearson correlation coefficient (which I always think of as summarizing the best fit line)? Wow, the iOS app feed sure showed me an interesting question! I want to read more. Uh, how do I get there? In the iOS app, pulling up a question from the feed gives the standard question view, which provides no means of navigating elsewhere on that site, either to browse or search. This should be changed for feed questions.  For example, I tapped on a highlighted Seasoned Advice question today, and found that I wanted to make a comment pointing to a related question on the site. The best way I could think of finding that post was to leave the app and use my browser. Then I came back with the link to copy-paste in.  Similarly, a question in the feed might be so intriguing that I want to look around for more cool stuff on the site. That requires two taps back and then a search via the "All Sites" menu item.  I'd suggest that questions selected from the feed should get a special header bar (or maybe stuck in between the questions and the answers) that provides a "More posts!" link at least to the site's top view; ideally there would also be a search field that could pop out of it.  Another possibility that would work pretty well, although it's a small tap target on a phone, would be to link the site name that appears under the question title to the site's top view.