I was following along with the MIT Opencourseware "Statistics for Applications" and their analysis of GLMs only covers discussion of GLMs whose dependent variable $y$ is distributed according to a distribution in the canonical exponential family (i.e. of the form below): $$ P(y\ |\ \theta) = h(y)\exp(\theta^Ty - A(\theta)) $$ If this is the case, then one can easily determine that $\mu = \mathbb{E}[Y] = A'(\theta)$, and since $\mu$ is related to the linear predictor via the link function $g$, we have $$ X^T\beta = g(A'(\theta)),\qquad \theta = (g\circ A')^{-1}(X^T\beta) $$  However, I'm curious about the more general case where the distribution belongs to the overdispersed exponential family: $$ P(\mathbf y\ |\ \theta,\tau) = h(y,\tau)\exp\left(\frac{\mathbf b(\mathbf \theta)^T\mathbf{T}(\mathbf y) - A(\theta)}{d(\tau)}\right) $$  Using the identity $\mathbb{E}[\nabla_\theta\ell] = 0$ where $\ell$ is the log-likelihood function I was able to arrive at $$ [D_\theta \mathbf b]^T\mathbb{E}[\mathbf T(\mathbf y)] = \nabla_\theta A $$ but there are two problems with this. For one, the dimension of $\mathbf b$ might not equal the dimension of $\theta$, and even if it did this would not guarantee the matrix $D_\theta\mathbf b$ (the Jacobian of $\mathbf b$) is invertible. Second, even if it were invertible, we would only arrive at $$ \mathbb{E}[\mathbf T(\mathbf y)] = ([D_\theta \mathbf b]^T)^{-1}\nabla_\theta A $$ which doesn't give us any direct correspondence between the parameter $\theta$ and the linear predictor $\mathbf X^T\beta$, since the link function links $\mathbb{E}[\mathbf y]$ to $\mathbf X^T\beta$, not $\mathbb{E}[\mathbf T(\mathbf y)]$.  So, how are GLMs of this form implemented? Where can I go to read more about how this works?
Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference?
Are users notified when their questions are reopened? Do users get notified when their question is reopened? I know there are no notifications , and that makes sense because 1) you assume the user is paying attention to their open, unanswered question, and they'll probably notice it's been put on hold and 2) it follows with the SE policy of (in general) not sending notifications for negative events.  However a reopening is a good thing, and once a question is closed it becomes less likely that the OP will be coming back to check on it often (so they might not notice the reopening otherwise). If there are not reopen notifications, why not? Or can we add them? After I installed Ubuntu 13.04, I can't mount my NTFS partition.  Error mounting /dev/sda5 at /media/mrxfly/xFLyDiskData: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda5" "/media/mrxfly/xFLyDiskData"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda5': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option. How check with SOQL if a picklist value is available or not for a specified record type How check if a picklist value is available or not for a specified record type ( through SOQL)? Thanks in advance I'm reading Linear Algebra by Hoffman, Kunze where the authors explained that a $n\times n$ matrix $A$ being invertible is equivalent to the fact that $A$ is row-equivalent to $n\times n$ matrix $R$ which is an identity matrix.  In the proof of the theorem, they wrote:     $$R= E_k\ldots E_2E_1 A$$ where $E_1,\ldots,E_k$ are elementary matrices. Each $E_j$ is invertible, and so $$A = E_1^{-1}\ldots E_k^{-1}~R\,. $$  ... Since, $R$ is a (square) row-reduced echelon matrix, $R$ is invertible if and only if $R=I\,.$  [...]   I couldn't get the conclusion, since any row of $R$ can't be zero, it has to be identity matrix $I\,.$ Why is it so?  Isn't there any other row-reduced echelon matrix other than the identity matrix having no zero row and invertible? Why is it so? Least expensive way to boost DC voltage What would be the least expensive way to boost a DC voltage?   The aim is to convert 1.2&nbsp;V/1.5&nbsp;V (from an AA/AAA cell) to 3.3&nbsp;V to power a small 8-bit microprocessor, like Atmel ATtiny45 or ATtiny2313, and also (if possible) 6&nbsp;V to power a buzzer.  Also, what would be the maximum current one could draw safely from an alkaline battery, after boosting it to 3.3&nbsp;V/6&nbsp;V?  Finally, how I could compute the duration for which the alkaline battery would last, given a certain consumption? I'd like to write something in the shape of this "coat of arms".    I'd like to have the text filling the coat but with a hole roughly in the shape of the sword. I know there is the \shapepar command to create paragraph shapes so I tried to , a patch for XFig that allows you to draw the shape you want but it never worked on my computer (Mac OS X). I also know I can build the shape by myself with shapepar syntax but it seems really complicated and I don't think I'll make a lot of shapes. So if anybody has ShapePatch working on his computer or knows shapepar syntax very well, could he give me the code? In which way does quantum mechanics disprove determinism? I've heard this pop up in a discussion with my physicist/engineer roommates, but didn't care to ask at the time.  Now I'm mighty curious about it.   doesn't really seem to say much on this issue.  From what I understand about the Uncertainty Principle, it says that there are certain properties of electrons and stuff that cannot be measured, and are therefore uncertain.  Then Wikipedia (under ) states that Sir Arthur Eddington says that the Uncertainty Principle isn't really so because we can't measure these properties, but because turns out nature is indeterministic.  At least that's what I took from those paragraphs.  Even without my biased wording, it sounds more like an assertion than evidence.  I've also read a few things about how other scientific conventions perceive the issue, like how a ball on the peak of a perfect mound might randomly roll down in any direction, and I'm still unconvinced.  My belief of determinism is generally that if you knew every single variable that existed as a factor at the very beginning and birth of the universe, you could correctly determine all properties of any individual particle at any point in time.  Could anyone provide some more background about this?  Especially regarding quantum mechanics? Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how? Why won't my follower, Serana, follow me? I told my follower (Serana) to wait. But this is different. I told her to go somewhere and wait so it will activate the enemies. Well it did and I killed them. But Serana seems to be not following me anymore. I can't tell her to follow me. And she is constantly in a squatting position. The only thing I can do is tell her to wait somewhere else to move her. And I can't part ways because I'm doing a main quest and she has to be there. Can anybody give me a tip on what to do? Class teardown in junit 3? I'm listing some items for sale online, and have taken a bunch of pictures with my iPhone.  About half-way through the process, iPhoto '11 stopped downloading new photos into its local Photo Stream.  I've quit iPhoto and re-opened it.  I've gone into the Photos app on my iPhone and confirmed all the pictures are there.   Is this normal behavior? Is there any way to tell iPhoto to download my pictures? I used to work as a consultant and have been spoiled with nice looking slides. For instance, being able to create slides that have 2, 3, or 4 graphs (perfectly positioned and with nice headers!) at the click of a mouse button via macros.  Similarly, there are many other kinds of word slides that had multiple columns, etc. that would be nice to recreate as well as objects like "main point" boxes at the bottom that summarize a main point and ways to add a transparent highlight to any part of the screen.  Is this kind of functionality far beyond anything that LaTeX presentations can do or is there an archive somewhere of code for making more intricate presentations? Why do birds sitting on electric wires not get shocked? When we touch electric wires, we get shocked. Why don't birds sitting on electric wires not get shocked? biblatex: Full Citations in Footnotes on Every Page How can I create this sort of bibliography using biblatex, ie, bibliography at the footer of every page? Using Squeeze Theorem to show the following limits Consider a function f (x) defined on R satisfying:   for all x distinct 0.  Calculate: lim f(x) with x→∞ and limf(x) with x→−∞   Issue information:   if x → ∞ then we can consider | x | = x  if x → -∞ then we can consider | x | = -x  I can use x² = | x |? How are long-term capital gains taxed if the gain pushes income into a new tax bracket? How to get a record from within custom visualforce page? Where can I install ubuntu if I have 4 primary partitions? I want to triple boot Windows 7, Backtrack, and Ubuntu. Windows and Backtrack are already installed. The problem is that both of them take 4 partitions: 3 for Windows, and 1 for Backtrack. When I try to make another partition, it says I can't have over 4. How can I install Ubuntu with this problem? Note: The 3 Windows partitions are PQSERVICE, SYSTEM RESERVED, and eMachines. I don't really know if I can delete one. Why is inductance (L) proportional with turns-square (N²)? We start from the   $$ \mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0. $$  We take surface integration of both sides, for the surface (\$s\$) inside the mean path (\$c\$) of the core.  $$ \int_s \left( \mathbf{\nabla} \times \mathbf{B} \right) \cdot d\mathbf{s} = \mu \int_s \mathbf{J} \cdot d\mathbf{s} $$  We use the  to rewrite the left hand side; where \$c\$ is in the same direction with the magnetic flux \$\Phi\$.  $$ \oint_c \mathbf{B} \cdot d \mathbf{\ell} = \mu N I $$  (The integral on the left hand side results \$NI\$, because there are \$N\$ different wires on the winding.)  The magnetic field density inside these kind of cores are considered to be uniform. So, we can write  $$ B \ell_c \overset\sim= \mu NI \implies B = \dfrac{\mu NI}{\ell_c}; $$  where \$\ell_c\$ is the mean path lenght of the core.  We can find magnetic flux from the magnetic flux density we have found by using the cross sectional area of the core \$A_c\$.  $$ \Phi = BA_c = \dfrac{\mu NIA_c}{\ell_c} $$  By definition, inductance is the amount of magnetic flux generated per applied current, that is  $$ L \overset\triangle= \dfrac{\Phi}{I}. $$  So, we find inductance of the system as  $$ \boxed{ L = \dfrac{\Phi}{I} = \dfrac{\dfrac{\mu NIA_c}{\ell_c}}{I} = \dfrac{\mu NA_c}{\ell_c} }. $$  But, all other sources () give inductance of an inductor like this as  $$ L = \dfrac{\mu N^2A_c}{\ell_c}. $$  What is the mistake I did in my derivation? Please explain in detail. bash if not multiple conditions without subshell? I want to combine multiple conditions in a shell if statement, and negate the combination.  I have the following working code for a simple combination of conditions:  if [ -f file1 ] &amp;&amp; [ -f file2 ] &amp;&amp; [ -f file3 ] ; then   # do stuff with the files fi   This works fine.  If I want to negate it, I can use the following working code:  if ! ( [ -f file1 ] &amp;&amp; [ -f file2 ] &amp;&amp; [ -f file3 ] ) ; then   echo "Error: You done goofed."   exit 1 fi # do stuff with the files   This also works as expected.  However, it occurs to me that I don't know what the parentheses are actually doing there.  I want to use them just for grouping, but is it actually spawning a subshell?  (How can I tell?)  If so, is there a way to group the conditions without spawning a subshell?