Why do we only look at the sample from MCMC? (And ignore the sample points' posterior probabilities?)
When approximating a posterior using MCMC, why don't we save the posterior probabilities but use the parameter value frequencies afterwards?
How can you get the permalink for an answer to a question? I wanted to link to an answer to a Stack Overflow question, but couldn't find a way to do it. I couldn't get the ID of the answer in order to create the link.  How can you get the permalink for an answer to a question? At  I've read that being $\sin(x)=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)!}x^{2n+1}$ by using  we get $\sin'(x)=\sum_{n=0}^{\infty}(2n+1) \frac{(-1)^n}{(2n+1)!}x^{2n}=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n)!}x^{2n}=\cos(x)$ but the page  says that if $f(x)=\sum_{n=0}^{\infty}c_n(x-a)^n$ then inside the radius of convergence of the power series we have $f'(x)=\sum_{n=1}^{\infty}nc_n(x-a)^{n-1}$ so shouldn't it be $\sin'(x)=\sum_{n=1}^{\infty}(2n+1)\frac{(-1)^n}{(2n+1)!}x^{2n+1-1}=\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n)!}x^{2n}$?  Now I understand that this last result has a missing term due to the index of the series being $1$ and not $0$ but being the $1$ mandatory because of the above theorem and since trying to shift index doesn't help (we get $\sin'(x)=\sum_{n=0}^{\infty}\frac{(-1)^{n+1}}{(2n+2)!}x^{2n+2}$) how can the result that ProofWiki shows be rigorously justified?   (I mean, I think we can't just say "oh, there's a missing term!" after having applied the theorem and magically shift the index of the series to obtain the desired result) Two "if"s in a row What is the most CPU efficient way to ensure that NumLock is on? Situation: I have a script watching over NumLock status, well not really watching, but turning it On every 1 second. The script is running in the background.  Reasoning: I often accidentally turn off NumLock. And I have no indicator of NumLock status on the keyboard.  OS, DE, DM, WM, xmodmap:  :  $ lsb_release -a  No LSB modules are available. Distributor ID: LinuxMint Description:    Linux Mint 18 Sarah Release:    18 Codename:   sarah   :  echo $DESKTOP_SESSION  cinnamon   :  cat /etc/X11/default-display-manager  /usr/sbin/mdm   :  wmctrl -m | head -n 1  Name: Mutter (Muffin)   :  xmodmap -pm  xmodmap:  up to 4 keys per modifier, (keycodes in parentheses):  shift       Shift_L (0x32),  Shift_R (0x3e) lock        Caps_Lock (0x42) control     Control_L (0x25),  Control_R (0x69) mod1        Alt_L (0x40),  Alt_R (0x6c),  Meta_L (0xcd) mod2        Num_Lock (0x4d) mod3       mod4        Super_L (0x85),  Super_R (0x86),  Super_L (0xce),  Hyper_L (0xcf) mod5        ISO_Level3_Shift (0x5c),  Mode_switch (0xcb)   My original Bash script follows:  #!/bin/bash  while true do    numlockx on    sleep 1s  done   As you can see, the script does not care about current status of NumLock. It just keeps turning it on.  Goal: I would like to make the script at least somewhat CPU efficient.  Question: What is the most CPU efficient way to ensure that NumLock is On in Linux (Mint 18)? Error when using TikZ-Feynman package Today I downloaded and installed the new  package to draw Feynman diagrams. I included the packages   \usepackage{tikz}  \usepackage{tikz-feynman} \tikzfeynmanset{compat=1.0.0} \usetikzlibrary{shapes,arrows,positioning,automata,backgrounds,calc,er,patterns}   into my preamble (changed them already many times).  However, already a simple sample code like  \begin{tikzpicture} \begin{feynman} \vertex (a) {\(\mu^{-}\)}; \vertex [right=of a] (b); \vertex [above right=of b] (f1) {\(\nu_{\mu}\)}; \vertex [below right=of b] (c); \vertex [above right=of c] (f2) {\(\overline \nu_{e}\)}; \vertex [below right=of c] (f3) {\(e^{-}\)}; \diagram* { (a) -- [fermion] (b) -- [fermion] (f1), (b) -- [boson, edge label'=\(W^{-}\)] (c), (c) -- [anti fermion] (f2), (c) -- [fermion] (f3), }; \end{feynman} \end{tikzpicture}   directly gives the error:     Package pgfkeys Error: I do not know the key '/graph drawing/node distance'.   Can you please help me? Thanks in advance! Even when /tmp has no file called something, searching for it with find will return 0:    $ find /tmp -name something    $ echo $?   0   How can I get a non-zero exit status when find does not find anything? I have a dual monitor set-up. When I'm on YouTube, and I click the fullscreen icon, the fullscreen automatically goes to the second monitor. How do I get it to go fullscreen on my main monitor? A switch that is only ON if the reference voltage is matched -+ 0.1 volts Im a beginnerish will electronic and im looking for a switch that is only ON if the reference voltage is matched -+ 0.25 volts. So if i have a reference of 2.7v to match and i feed the switch a 2.75v the switch would be ON. But if i feed it  2.5v or 2.85v the switch would is OFF.   This might be a simple google search, but i am lacking the correct terminology. I have an existing windows application, for which I have decided to create a Mac version. The problem is that the current UI involves a lot of buttons, tabbed panels, multiple windows etc.  This UI had been rated as intuitive and easy to use and straightforward  by many customers and editors. But a beginner (very less experience) may find in confusing a little, but it has been complemented with tutorial.      When creating the Macintosh variant, should I focus on creating a simplified and minimalistic UI (this does not mean the current UI is complex, but I think Mac user's prefer a simple UI right?) or should I try to copy the exact same thing?  By reducing the UI some of the features may be missing. But it can be added later if needed. Should I focus on a fresh approach (this is easier rather than copying the complex UI pattern) or should I go with the old recognized setup? Bugged display in search using negation Problem: Evaluate $$ L=\displaystyle \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \left(  \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k}\right \rfloor \right).$$  Please help me with this one.  I tried using the sandwich theorem by first constructing the following  $$ 2 \geq \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k} \right\rfloor \geq -1 $$ and then summing over. But the limit of the two bounds are different so sandwich theorem doesn't help!. Is it possible to construct sharper bounds?  Also I observed that if we ignore question of continuity, etc. then we can write,  $L= \displaystyle \int ^{1}_{0}\left\lfloor \frac{2}{x} \right\rfloor -2\left\lfloor \frac{1}{x} \right\rfloor dx$  Now I am able to compute the above integral. But is the above process correct? If then how can make it rigorous? Or if any other approach is possible, please tell. indicates that the water pipes should bonded to the electrical ground even if a grounding rod is used. How would one normally tell if that is the case? Is that bonding required to be accessible, or can it be hidden behind walls or buried? Where in the water system would it normally be bonded (e.g., before the main water shutoff, after, at the hot water tank)?  I recently had my electrical panel relocated and replaced, and don't recall seeing anything running from the panel to a water pipe - in the old panel or new. The electrician put in an intersystem bonding bridge, so the new ground rod, ground from the panel, and ground from the cable service are connected to it. I suppose that's where the bond from the water pipe would go? Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the material, but I don't know why a difference in the number of oscillations would impede the wave- I don't even know why things slow down in general. Why some electromagnetic wave would slow down just because it's entering other electromagnetic fields... It would seem to me that the only factor would be time taken to physically move some electron or something in the direction of the fields... But that seems to simple of an explanation to me. Question:      Let $p$ be any prime and $n \geq 3$. Show that there exists a non-abelian group of order $p^n$.    Attempt:   Take $n = 3$. Writing $\mathbb Z_p \times \mathbb Z_p = \{e, \alpha_1, \ldots, \alpha_{p^2 - 1}\}$ and considering $$\begin{align}\tau_{jk} : \mathbb Z_p \times \mathbb Z_p&amp;\to \mathrm {Aut} (\mathbb Z_p)\,\\e &amp;\mapsto id\\\alpha_j &amp;\mapsto id \\\alpha_i &amp;\mapsto \rho_k  \end{align}$$  $\forall i \neq j$ where $\rho_k : \mathbb Z_p \to \mathbb Z_p$ is such that $\rho_k (1) = k$, with $k \in \{2, \ldots, p-1\}$. Then we take the group $(\mathbb Z_p \times \mathbb Z_p) \ltimes_{\tau_{jk}} \mathbb Z_p$.   Then $$(\alpha_i , 2) \ltimes_{\tau_{jk}} (\alpha_i, 1) = (2\alpha_i, 1  + \tau_{jk} (\alpha_i)(2)) = (2\alpha_i , 1  +2 k)$$  and $$(\alpha_i , 1) \ltimes_{\tau_{jk}} (\alpha_i, 2) = (2\alpha_i, 1  + \tau_{jk} (\alpha_i)(2)) = (2\alpha_i , 1  +k)$$  taking $k = 1$ for example we have that the group $(\mathbb Z_p \times \mathbb Z_p) \ltimes_{\tau_{jk}} \mathbb Z_p$ is not abelian.    I was wondering if this is a good aproach. If not, is there an easier way to reach the result?  If this is the "best" way then would the higher cases ($n &gt; 3$) be more of a notation play game? After mis-reading this question:  I found myself wondering if there are other non-weapon items such as tools that utilize lightsaber technology.  Example: the lightsaber bread knife When app is moved to SD card, where is the app data stored on SD card? Shortest distance between $2$ lines with direction vectors Let L1 be the line passing through the point $P_1=(−11, 10, −1)$ with direction vector $\vec d_1=\begin{bmatrix}−2\\ 3\\ −1\end{bmatrix}t$, and let $L_2$ be the line passing through the point $P_2=(−8, 9, 10)$ with direction vector $\vec d_2=\begin{bmatrix}−1\\ 3\\1\end{bmatrix}t$. Find the shortest distance, $d$, between these two lines, and find a point $Q_1$ on $L_1$ and a point $Q_2$ on $L_2$ so that $d(Q_1,Q_2) = d$.   I dont really understand how to properly approach this question, how do i start? How to use measured step response to tune control system How does one use a measured step response to tune either a PID or convolution control scheme? Inspired by , I'm interested a more detailed explanation of how to implement a control system based on the measured step response.  I would not try to guess all the effects.  There are probably some non-obvious things going on, and you can't know all the parameters. I would measure the step response.  Find two pump settings that both result in the ball being within the measurable range within the tube.  Then have the controller suddenly switch from one setting to the other open loop.  Meanwhile measure what the ball does over time.  That is the step response.  You can take the derivative of that and get the impulse response.  From the impulse response you can predict the motion of the ball for any history of pump settings, assuming this is a linear system.  It is probably linear enough over the small range of settings to keep the ball within its normal range. You can use this as a simulation base to find the parameters for old fashioned PID control.  Or you can use the impulse response directly to do a convolution control.  You have to low pass filter the control input enough so that convolution kernel doesn't go negative unless your pump is actually reversible and can suck the ball back down.  How exactly does this work? ; I assume &quot;convolution control&quot; is the use of the pole-zero or transfer function, but don't see exactly how to get the parameters. RELATED:  * How many levels are there for Steam Trading Card badges? With the new Steam Trading Cards, I decided to craft the badge for CS:GO. I got this:    I then noticed that this is only a level 1 badge, and there was a level 2 badge to get. So I crafted it too:    Now it says there's a level 3 badge to get next. How many levels are there in total? Is there a criterion to differentiate "thriller" from "horror"?