Over time I've learned that many (most?) methods used in classical statistics can be interpreted as evaluating a Bayesian model in some plausible way while I find the standard explanations much less intuitive.  So I was wondering whether there are any resources which explain standard stats methods in a Bayesian manner?
I'm a simple minded Bayesian who feels comfortable in the cosy world of Bayes.   However, due to malevolent forces outside my control, I now have to do introductory graduate courses about the exotic and weird world of frequentist statistics. Some of these concepts seem very weird to me, and my teachers are not versed in Bayes, so I thought I'd get some help on the internet from those who understand both.   How would you explain the different concepts in frequentist statistics to a Bayesian who finds frequentism weird and uncomfortable?   For example, some things I already understand:   The maximum likelihood estimator $\text{argmax}_\theta \;p(D|\theta)$ is equal to the maximum posterior estimator $\text{argmax}_\theta \;p(\theta |D)$, if $p(\theta)$ is flat.  (not entirely sure about this one). If a certain estimator $\hat \theta$ is a sufficient statistic for a parameter $\theta$, and $p(\theta)$ is flat, then $p(\hat \theta|\theta)=c_1\cdot p(D|\theta)=c_1\cdot c_2\cdot p(\theta|D)$, i.e. the sampling distribution is equal to the likelihood function, and therefore equal to the posterior of the parameter given a flat prior.    Those are examples of explaining frequentist concepts to someone who understands Bayesian ones.   How would you similarly explain the other central concepts of frequentist statistics in terms a Bayesian can understand?  Specifically, I'm interested in the following questions:   What is the role of Mean Square Error? How does it relate to Bayesian loss functions? How does the criterion of "unbiasedness" relate to Bayesian criteria? I know that a Bayesian will not demand that its estimators are unbiased, but at the same time, a Bayesian would probably agree that an unbiased frequentist estimator is generally more desirable than a biased frequentist one (even though he would consider both to be inferior to the Bayesian estimator). So how does a Bayesian understand unbiasedness? If we have flat priors, do frequentist confidence intervals somehow coincide with Bayesian ones?  What in the name of Laplace is going on with specification tests like the $F$ test? Is this some degenerate special case of a Bayesian update on the distribution over model space?    More generally:  Is there some resource that explains frequentism to Bayesians?  Most of the books run the other way around: they explain Bayesianism to people who are experienced in frequentist statistics.     ps. I have looked, and while there are a lot of questions already about the difference between Bayesian and Frequentism, none explicitly explain Frequentism from the perspective of a Bayesian.   is related, but is not specifically about explaining Frequentist concepts to a Bayesian (more about justifying frequentist thinking in general).  Also, my point is not to bash frequentism. I really do want to understand it better
Difference between staticmethod and classmethod What is the difference between a function decorated with  and one decorated with ? How to change the forgotten root password? I forgot my root password...actually I think I know what it is because it is the same password I have for pretty much everything but in the Terminal in tell me "Sorry, try again." Is there a way to reset the password? If so how? I don't mean people with low self esteem.  But there are people who feel happy at being able to make other people laugh at their own expense. I remember someone telling me there is a word for them, I can't find it.  Let me explain:  I sometimes, while sitting with a group of people, might just tell them a personal embarrassing story, which might be completely fabricated, to make other people laugh. And when they laugh, I feel happiness.  I'm also self deprecating, but not in a way that I hate myself, rather,  just my work (I'm a screenwriter) and knowing I can do better. I do not self deprecate myself in public (I don't praise myself either).   Edit: Now that its mentioned, I think the word I'm talking about was used to describe a person's sense of humor. Or it could be a word used to describe a psychological trait/disorder.  Edit: I just looked up humor styles on Wikipedia. And after reading it, I guess the word that closely matches what I'm looking for is 'Affiliated Humor' but in a 'Self Defeating' style. Disable browser 'Save Password' functionality One of the joys of working for a government healthcare agency is having to deal with all of the paranoia around dealing with PHI (Protected Health Information). Don't get me wrong, I'm all for doing everything possible to protect people's personal information (health, financial, surfing habits, etc.), but sometimes people get a little too jumpy.  Case in point: One of our state customers recently found out that the browser provides the handy feature to save your password. We all know that it has been there for a while and is completely optional and is up to the end user to decide whether or not it is a smart decision to use or not. However, there is a bit of an uproar at the moment and we are being demanded to find a way to disable that functionality for our site.  Question: Is there a way for a site to tell the browser not to offer to remember passwords? I've been around web development a long time but don't know that I have come across that before.  Any help is appreciated. Check if macro is fully expandable Question  Is there a way to check whether a macro is fully expandable (or rather "safe in an expansion-only context" )?    Consider this code:  \def\a{Just a string} \def\b{\a} \def\c{\def\unsafe} \def\d{\c}   How could I check which of the macros (a-d) are safe in an expansion-only context? By looking at them I know that a and b are whereas c and d are not but if I wanted to know the same for a macro I haven't written myself this could get quite useful.      Background  I am working on a way to detect whether some input is a valid number in PGF. For this I developed  which makes use of passing the input into \pgfmathfloatparsenumber. The problem I have run into is that said macro appears to somehow manages to expand the input until there is an error (if the input is in fact not safe in an expansion-only-context). I tried using protected, noexpand and similar but somehow PGF manages to circumvent those.    So the idea is to check whether the input is safe before actually passing it to PGF. The problem is: I don't know how I'd go about that... Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function? If a Continuous function $f(x)$ satisfies $f(x) = f(2x)$, for all real $x$, then does $f(x)$ necessarily have to be constant function? If so, how do you prove it? If not any counter examples? Double booked - User bookmarking question recorded twice In this  one user is shown as having bookmarked  twice:  This doesn't appear to be the same question as:  or  though it's certainly possible that the cause is the same. My linear algebra professor proved that      Diagonalizable matrices with complex values are dense in set of $n \times n$ complex matrices.   He defined a metric (I believe) that was somehow related to the usual metric on $\mathbb{R}^{n^2}$.  Then somehow proved that diagonalizable matrices were dense because for any matrix $A$ if $\det(A - \lambda I) = 0$ on an open subset, then $\det(A - \lambda I)$ was the zero polynomial.  I Googled around a bit and found some stuff talking about the Zariski topology, and I am not sure this is what I want. Most of what I have found on this topology is much more general than what he was doing.  Does anyone know any resources that would explain how to go about proving this statement?  Edit: I found out how to prove this the way my professor did.  We define the norm of a matrix by $$ |A| = \max\{|Ax| : |x| = 1 \}.$$ Now we have a distance $d(A, B) &lt; \epsilon$. You can prove that if $(A - B)_{ij} &lt; \epsilon/n$, then $|A - B| &lt; \epsilon$.  Let $p(x)$ be the characteristic polynomial of $A$, an $n \times n$ matrix.  $$p(x) = \prod_1^n (x - x_i) = x^n + (-1)\sigma_1 x^{n - 1} + \cdots + (-1)^n\sigma_n$$ where $\sigma_1, \ldots, \sigma_n$ are the elementary symmetric polynomials of $x_1, \ldots, x_n$ which are the eigenvalues.  The discriminant of the characteristic polynomial is a symmetric polynomial, therefore it can be written in terms of the elementary symmetric polynomials, which in turn can be written in terms of the entries of the matrix.  But since the discriminant is a polynomial, it only has finitely many roots. Therefore for $\epsilon &gt; 0$, by changing the entries of the matrix less than $\epsilon / n$ we can find a new matrix $B$ such that $|B - A| &lt; \epsilon$ and the discriminant is not zero.   The discriminant being not zero means $B$ has distinct eigenvalues, thus has a basis of eigenvectors. Therefore, it is diagonalizable.  Thus the set of diagonalizable matrices is dense in the set of matrices with respect to that metric. What is the difference between below variables assignments?   var=23 var =23 var= 23 var = 23   Is there any difference in space around the assignment operator? I accidentally changed /var owner/group to my username and then changed it back to root, but not all the /var folders' owners are root, so is there anyway to change back owner/group of files/folders to default state?  Or at least those files/folders that are created by packages? How to find relevant and new open research topics? How do I force Windows to check for updates? How do I make windows save their position on screen after re-attaching a display? MySQL Access denied for user 'root'@'localhost' What is a one-word synonym for "science lover"? I'm searching for a one-word synonym for "science lover". In my case, I love science and I self study it, but I never got a degree in Physics or Chemistry or any of these related subjects (except computer-science). But I enjoy experimenting stuff and see what's going on.  So, what would be a one-word good alternative for "science lover"?  The best one I found is learner, but that's more general I guess. Scientist is probably too much in my case. I saw sciencophile in another post, but I don't really like it–it sounds too complicated. Distribution of Dark Matter around galaxies It is well-known that measurements of the velocity profile in galaxies are not compatible with Newtonian laws. A way to circumvent the problem is to assume that galaxies are surrounded by a spherical halo of Dark Matter. The density of mass of this Dark Matter can then be computed from the velocity profile with Newton's laws.   My question is the following: the formation of a galaxy involves essentially only the gravitational interaction. According to Newton (and General Relativity too), the trajectory of a particle does not depend on its mass. As a consequence, I do not understand how usual matter and Dark Matter could have followed different trajectories leading to such different mass distributions nowadays. Can somebody explain this (apparent) paradox ? Why do people omit the definite article? I'm used to always hearing or seeing a  before certain nouns.  Yet on certain occasions the article is totally omitted, and it bothers me.  I'm wondering what the justification for omitting the article is, especially when the definite article would seem to be required, or if it is just bad English either on the part of the individual in question or more likely by tradition.  The most frequent place I hear this is at the doctor or dentist's office. In every one I have ever visited, the receptionist or assistant always says things like "Doctor will see you shortly" instead of "The doctor will see you shortly."  The wikipedia article linked above says this: "A definite article indicates that its noun is a particular one (or ones) identifiable to the listener".  In the case of a clinical setting, I know who the doctor is, especially if this is not my first visit.  The people in the office know the doctor even better than I, so it would seem to be inappropriate to omit the article. Even the indefinite article would be incorrect. It further says, under "Zero article":  "In languages having a definite article, the lack of an article specifically indicates that the noun is indefinite."  Since the noun is not indefinite, why are they omitting the article?  Another place I see the article omitted is with the word "bar".  Bartenders apparently don't say "I tend the bar" they say "I tend bar".  Unless a bartender works in multiple bars, it would seem like an article would be required.  Furthermore, "the bar" can mean any bar a person goes to, so even in a case like , it seems like the word "the" should be in the sentence.  The only thing I can think of in this case is maybe the speaker doesn't want to confuse the listener into thinking they work in the legal field.  Is this just a bad habit, a historical corruption or tradition, or is there really a valid reason (or perhaps more than one) for these omissions? Closure of identity element in a topological group is the intersection of its neighborhood system Consider a topological group $G$. I want to prove that      if $\cal{U}$ is the set of all neighborhoods of $e$ (the identity element), then $\overline{\{e\}}=\cap_{U\in \cal{U}}U$.   What I thought was:  i) If $x\in \overline{\{e\}}$, then every neighborhood $V$ of $x$ intersects $\{e\}$, hence every $V$ is a neighborhood of $e$ as well, i.e. $V\in \cal{U}$.  ii) On the other hand, if $x\in \cap_{U\in \cal{U}}U$, then $x\in U$ for all $U \in \cal{U}$, meaning every $U$ is a neighborhood of $x$ intersecting $\{e\}$.  Now, I think that the missing part is an argument justifying that there is no neighborhood of $e$ that is not a neighborhood of $x$ (part i)), and that there is no neighborhood of $x$ that is not a neighborhood of $e$ (part ii)). My idea for this is to argue that there is a homeomorphism taking $e$ to $x$, therefore the neighborhood system of one cannot have more elements that the neighborhood system of the other.  Is this correct? If not, is there a way I can fix it? If $\sum_{1}^{\infty}(a_n)^3$ diverges, does $\sum_{1}^{\infty}(a_n)$? Prevent Mac Terminal from reverting to default theme I can't find any way to change the Terminal theme and have that theme applied permanently.  I want to change to another darker theme other than the default 'basic' theme, and (most importantly) have it remain as the theme every time I open Terminal.