I was wondering if any of the members of this community would like to share his/her intuition about completeness in statistics. For the sake of &quot;completeness&quot;, here's the definition, taken from :  Consider a random variable $X$ whose probability distribution belongs to a parametric family of probability distributions $P_\theta$ parametrized by $\theta$. The statistic $T$ is said to be complete for the distribution of $X$ if for every measurable function $g$ (which must be independent of $\theta$) the following implication holds: $$E(g(T(X))) = 0 \mbox{ for all }\theta \mbox{ implies that }P_\theta(g(T(X)) = 0) = 1\mbox{ for all }\theta.$$  Now, to give you an idea of what kind of answer I am looking for, here's how I think about (minimal) sufficiency: I think of a statistic as a partition of the sample space. In that context, a statistic is sufficient for $\theta$ if this partition does not result in a loss of &quot;information&quot; about $\theta$; it is minimal sufficient if it is the coarsest partition which does not result in a loss of information (superlatives carry a uniqueness connotation, which I am ignoring here). Note: I am aware that a  has been asked before, but I'm looking for a different answer.
In classical statistics, there is a definition that a statistic $T$ of a set of data $y_1, \ldots, y_n$ is defined to be complete for a parameter $\theta$ it is impossible to form an unbiased estimator of $0$ from it nontrivially. That is, the only way to have $E h(T (y )) = 0$ for all $\theta$ is to have $h$ be $0$ almost surely.   Is there a intuition behind this? Is seems like a rather mechanical way of defining this, I am aware this has been asked before, but was wondering if there was a very easy to understand intuition that would make introductory students have an easier time digesting the material.
For my MAC laptop, I only have 250GB and out of this 250GB MAC is taking up 129GB in the other section. I looked everywhere to the best of my knowledge. Please note my home directories is only 45GB. Can you somehow please help me? Divisibility and the Fibonacci sequence Should postdocs work only on the projects they are hired for, or can they work with other people in the same research group on other projects? Would the latter be an issue with the funding body, when the project proposal and budget only covers the expenses for hiring one postdoc? Note: it is the supervisors who got the grants, not the postdocs themselves. Prove that $\left (\frac{1}{a}+1 \right)\left (\frac{1}{b}+1 \right)\left (\frac{1}{c}+1 \right) \geq 64.$ Let $a,b,$ and $c$ be positive numbers with $a+b+c = 1$. Prove that $$\left (\dfrac{1}{a}+1 \right)\left (\dfrac{1}{b}+1 \right)\left (\dfrac{1}{c}+1 \right) \geq 64.$$   Attempt  Expanding the LHS we obtain $\left (\dfrac{1+a}{a} \right)\left (\dfrac{1+b}{b} \right)\left (\dfrac{1+c}{c} \right)$. We are given that $a+b+c = 1$, so substituting that in we get $\left (\dfrac{b+c+2a}{a} \right)\left (\dfrac{a+c+2b}{b} \right)\left (\dfrac{a+b+2c}{c} \right)$. Then do I say $\left (\dfrac{b+c+2a}{a} \right)\left (\dfrac{a+c+2b}{b} \right)\left (\dfrac{a+b+2c}{c} \right) \geq 64$ and see if I can get a true statement from this? What animal is a “weefil”? What animal is depicted in this image labelled “weefil”? Need a MP3 ID3 tagger, and cover fetcher I need to tag my MP3 library, and have tried kid3 (which was manual tagging), when I used Kubuntu 9.10 (I now use Ubuntu Meerkat) Here are the features I am hoping for:   A good and clean UI. Tagging should be automatic, like Winamp's autotag feature, which rocks, btw! It should also embed the cover-art in the mp3, not copy a jpeg file in the folder, because now-a-days all players support displaying cover art. But acceptable if not possible. Rename the files as per some regular expression like %TrackNo - %Artist - %Title.  Should be accurate, and more importantly smart. I want to start tagging at night, and hopefully my collection should be done by the morning, w/o it being stuck at a user prompt at 1%.   If one app cant do all, I am willing to use 3, wouldn't mind exposure to a few more apps ;)  I have used picard or someting, and I didnt like it quite a lot. But wouldn't mind using it, if there is no other alternative.   Thanks for your time! My understanding is that a question is historically locked because the information in it is too valuable for the question to be deleted.   But if the "valuable information" becomes obsolete, what happens then?  We cannot modify the question content, or the answers for a historically locked question, right? Huge close votes review queue on Stack Overflow Enumerations on PHP I know that PHP doesn't yet have native Enumerations. But I have become accustomed to them from the Java world. I would love to use enums as a way to give predefined values which IDEs' auto-completion features could understand. Constants do the trick, but there's the namespace collision problem and (or actually because) they're global. Arrays don't have the namespace problem, but they're too vague, they can be overwritten at runtime and IDEs rarely know how to autofill their keys without additional static analysis annotations or attributes. Are there any solutions/workarounds you commonly use? Does anyone recall whether the PHP guys have had any thoughts or decisions around enumerations? Why is looping over find's output bad practice? This question is inspired by    I see these constructs  for file in `find . -type f -name ...`; do smth with ${file}; done   and  for dir in $(find . -type d -name ...); do smth with ${dir}; done   being used here almost on a daily basis even if some people take the time to comment on those posts explaining why this kind of stuff should be avoided... Seeing the number of such posts (and the fact that sometimes those comments are simply ignored) I thought I might as well ask a question:  Why is looping over find's output bad practice and what's the proper way to run one or more commands for each file name/path returned by find ? Regular Expression to match valid dates If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$   I was practicing quadratic equation questions online but I am stuck on this question.  I found the values of roots $a= 1$, $b= 1/2$ How to fix Footnote position at the bottom of the page \footnote[1]{\nameref*{8.1.16} is an अधिकार सूत्र it goes upto \nameref*{8.3.55}} \&amp; अङ्गाधिकार (अङ्गस्य)\footnote[2]{\nameref*{6.4.1} is an अधिकार सूत्र it goes upto \nameref*{7.4.97}}  I am using footnote as shown above. However the footnote appears to be floating and when I don't have much in the page it appears in the middle of the page. I got by so far with \vspace{} but I think there must be a way to position this at the bottom of the page despite whats in the page. Thanks for your help Usually, when we see two letters put together it is to define the pronunciation or to differentiate synonyms or just its foreign origins. But some words don't seem to have any reason to double up.     Why does vacuum have two of the letter U?  Why does aardvark have two of the letter A?  Why does llama have two of the letter L? Where can I find good literature for beginners? I am trying to find some database tutorials,books and similar, since I have started this course in college, and received some material, but it is really hard to manage through all the info on the net. I searched through the questions on the site but didn't find any. Thankfull for all your input. Proxying fake domain to a localhost port I'd like to do much the same thing described at  for web app development purposes, but with the twist that I'd like requests to fakedomain.com:80 to be routed to localhost:8080, say, so that I don't have to actually use my development machine's port 80.  I'd welcome answers that take the form of:   Small changes to configuration files like /etc/hosts, and/or An easy-to-configure proxy server I could run   Note:  takes the approach of setting a firewall rule to forward all incoming traffic on port 80 to port 20559. That may be an acceptable solution, but ideally, I'd like to forward only a specific domain + port combination. Convert timestamps with offset to datetime obj using strptime Tikz shortandoff-on newcommand problem Usually I have no problem with babel and !:, and I don't use shortandoff-on switch. But since I made a command using !#1 parameter, the problem comes up again.  The same synthax used outside the command work fine, but in the command I get the error message :  ! Package tikz Error: + or - expected.  How to solve the problem without using the shortandoff-on switch ?  \documentclass[french,a4paper]{article} \RequirePackage{etex} \RequirePackage[utf8]{inputenc} \RequirePackage[T1]{fontenc} \RequirePackage{fourier}  \RequirePackage{tikz} \usetikzlibrary{calc,intersections}  %%%%%%%%%%%%%%%%%%%%%% %%%% Francisation %%%% %%%%%%%%%%%%%%%%%%%%%%  \RequirePackage{babel}  %%%%%%%%%%%%%%%%%%% ---------------------------------------- %%%% Géométrie %%%% %%%%%%%%%%%%%%%%%%%-----------------------------------------      % #1 option du path     % #2 premier point     % #3 second point     % #4 longueur dans un sens     % #5 longueur dans l'autre     % défini Mil#1#2 \newcommand{\Med}[5][]{%     \path[#1,name path=Med#2#3] ($(#2)!.5!(#3)$) node (Mil#2#3) {}      ($(Mil#2#3)!#4!90:(#3)$) -- ($(Mil#2#3)!#5!270:(#3)$) ; }  \tikzset{small dot/.style={fill=black,circle,scale=0.3}}  \begin{document}  %\shorthandoff{:!} \begin{tikzpicture}  \coordinate[label=below left:$A$] (A) at (0,0) ; \coordinate[label=below right:$B$] (B) at (4,0) ;  \draw (A)--(B) ;  %\Med[draw]{A}{B}{1}{1} ;  \draw($(A)!.5!(B)$) node (MilAB) {}      ($(MilAB)!1!90:(B)$) -- ($(MilAB)!1!270:(B)$) ;   \end{tikzpicture} %\shorthandon{:!}  \end{document} How to control Windows 7 snap feature with two monitors? There is an  feature in Windows 7. However, it seems to not work when dragging a window to the edge that is adjoined to the second monitor. How to make it work properly? Maybe some regedit modification or something? Fixing geometry validity errors in QGIS 2?