The definition for completeness is that if a statistic $s(x)$ is complete, we have that for every measurable $g$, $$E_\theta(g(s(x))) = 0\,, \ \forall\,\theta\ \Rightarrow\  g(s) = 0 \text{ a.s.}$$  I've heard that we can think of completeness as saying that if we wanted to estimate the zero function using a complete $s(x)$, among the class of all zero-unbiased functions of the statistic, the only one is one which takes value 0 almost surely. This seems like a bizarre notion--why would we want to estimate the zero function?  I've also heard that in estimating parameters of a probability model $P_\theta$, one does not need any more than a sufficient statistic. I heard that having any more than the sufficient statistic provides no additional information. How does this connect to the definition of completeness above (Basu's, maybe?) ?  Is there some better intuition for the (seemingly) bizarre condition above?
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.
Eevee - Light inside a bulb lamp not passing through glass Using Eevee, I'm trying to simulate a light bulb. I have a sphere with glass material and inside it, I have a Point light. But the light is not passing through the glass:  However, if I disable the sphere object, the light is working:   How to make the light inside a bulb lamp pass through glass (using Eevee)? Here my test project: Divergence as transpose of gradient? In his online lectures on Computational Science, Prof. Gilbert Strang often interprets divergence as the "transpose" of the gradient, for example  (at 32:30), however he does not explain the reason.  How is it that the divergence can be interpreted as the transpose of the gradient? When a ball is tossed straight up, does it experience momentary equilibrium at top of its path? This question has been asked many times all over the Internet and answers can be found on places such as yahoo and ask.com, but I'm not satisfied with those answers and I don't trust the validity of those places.  This seems like a more appropriate place to ask.  So, here's my train of thought and I would like to ask you if you think I'm right or wrong.  Even though most of the answers point to the fact that the ball does not achieve equilibrium because the force of gravity is constantly acting upon it, thus causing an acceleration, I still think there's a moment of equilibrium and here's why:  When the ball is traveling up, it's accelerating towards the ground and eventually reaches a point at which its speed reaches 0.  At this moment, isn't the reason the speed is 0 is due to the fact that net force is 0?  The force that made the ball travel in the upward direction was canceled out by the gravitational force.  So, the sum of forces at that brief moment is equal to 0, otherwise the ball would be moving.  I don't think gravity is the only force acting on the ball at that moment, since the throwing force was acting on it as well, until both canceled each other out for that brief moment.  Am I right or wrong? Wikipedia says that the name of concept comes from physics, but I cannot find any similarity between these two concepts. If $f$ is a concave function and $f(0) \geq 0$ then $f(a+b) \leq f(a) + f(b)$ for all $a,b >0$ Recently I'm working on a project aiming to convert the vibration of sound waves into electricity to charge batteries using a piezoelectric material (MFC type). I was trying to use the human voice as an input, but theoretically it was not enough, so do you have any ideas about some places that I can apply my project on it (that must be noisy or can give me vibrations)?  Moreover, has the MFC material been used before in this application? If I used many pieces of it in parallel would that help? Why use iterators instead of array indices? Take the following two lines of code:  for (int i = 0; i &lt; some_vector.size(); i++) {     //do stuff }   And this:  for (some_iterator = some_vector.begin(); some_iterator != some_vector.end();     some_iterator++) {     //do stuff }   I'm told that the second way is preferred. Why exactly is this? If $A$ is compact, is then $f(A)$ compact? I'm trying to find a simple way to create vertices where two objects intersect and delete the leftover internal planes + then join the meshes so that I have one hollow mesh to sculpt. The reason I need to know this is that on my first sculpt I just joined the meshes, but it didn't create vertices at the intersecting points so when I went to sculpt it just overlapped the meshes as you can see here in the neck.  Here is what I am working on now, it needs to be 1 hollow mesh How can I share files over a Windows network? I have a media computer which I recently reformatted to Ubuntu 10.04. I am probably just missing something obvious but I can't figure out how to share folders and files, so that I can browse to them on my Windows computers in order to copy files to/from the computer.  How do I do this? Is it really impossible to calculate in advance the result of throwing dice? I'm designing an I/O module by using optocouplers for the inputs and outputs which I want to control by a microcontroller.   Here are my questions:   In the datasheet of optocoupler's output current (per channel) is 50mA, and for the output port(figure 1) Relay nominal operating current is 16.7 mA. By knowing these can I calculate how much current will I need for the system. Which parameters do I know?   There are 12 relays, 20 optocouplers (5 module) in total. 3 Opto module for output, 2 for input ports     By directly connecting the GPIO pin and output of the optocoupler to the switches (as input), Can I control the inputs shown in the figures. For the input ports, I don't know how to make the connections. What should I connect to the collector pin? If I push or hit an object in space will it rotate or move along a straight line? What to do when you find a bad link in an answer? If a link has gone stale in an answer, what is the correct way to report this in the SO universe?  e.g. Jon's first link in    I have added a comment but not found the correct link yet. A long time ago, I remember hiding some really personal files on my computer. Something that nobody could ever find, so I buried them down pretty darn good.  Now to my problem, I don't remember where.   Do anyone know a way to scan a drive and list all hidden folders and/or files?   I know how to view hidden files in Windows, but as far as I know, there is no way to search for them? I've been looking for a program, but I couldn't find one - and now I'm here, asking the experts. ;)  I'd really appreciate any tips. Idempotent of closure and other properties Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$   Obviously $(2,1)$ and $(1,2)$ are two answers. But I was unable to manipulate the equation algebraically giving a useful form for finding all other possible answers! I also tried to view it as a quadratic equation in terms of $x$, but forming the Delta of that equation didn't help much other than if $y=1$ then certainly Delta would be a square and equation would have answer for $x$... mysql_fetch_array()/mysql_fetch_assoc()/mysql_fetch_row()/mysql_num_rows etc... expects parameter 1 to be resource Canonical vs. non-canonical terminal input I am studying for an exam and I am confused as to how canonical vs. non-canonical input/output works in Unix (e.g., curses).  I understand that there is a buffer to which "line disciplines" are applied for canonical input.  Does this mean that the buffer is bypassed for non-canonical input, or does it simply mean that no line disciplines are applied?  How does this process differ for input and output operations?  In the curses programs I have worked with that demonstrate canonical input, the input typed by a user is automatically entered either after a certain number of characters have been typed or a certain amount of time has passed.  Are either of these things considered "line disciplines" or is this something else entirely? I'm a committer for the .  It went to the private beta phase sometime in the last 12 hours, but yet to have been invited. When I visit  I get the standard "To log in, you must have commited to the Area 51 site proposal and received the invitation email." message.  However, when I navigate to the Pets site via the Android app, I'm able to view the site in it's entirety (questions, answers and comments). When I attempt to post, I get a message saying my user token isn't allowed to take action on this site.  Same behavior is observed when using the iOS app.