Maximizing likelihood function of continuous normal distribution
In MLE for continuous rv, why is it ok to evaluate a pdf at a point?
Multiple Image in Canvas ItemsControl How to derive variance-covariance matrix of coefficients in linear regression I am looking for an adjective/noun for someone who is able to speak/ makes speeches very well and uses words effectively to influence/impress people. How to modify a specified commit? I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank? How can I find just the *.mp3 files with a recursive command like ls -R *.mp3 in a directory that contains several sub-directories and at the end copy these files in a directory that I choose.  Thanks for your support. I am kind of confused on the terminology of &quot;space&quot;. From  I am getting that  In mathematics, a space is a set (sometimes called a universe) with some added structure.  And from topological and metric spaces, I know that we a space is a a tuple of a set and a structure, e.g. $(X, \tau)$, $(X, d)$, where $\tau$ and $d$ are a topology and a metric respectively. On the other hand, in machine learning the term &quot;features space&quot; is used a lot for sets like $\mathbb R^n$, e.g.  and although it often refers to the set underlaying set itself, not the tuple of set plus the added structure. In fact, I have done the same in a previous publication (which the peer-reviewers accepted), but I would like to be both correct and precise in what I research, write, and submit. Is it just that machine learning researchers are imprecise in their terminology? Is it just an ? I think, what some people are doing, might be they consider a space to be a set, which is somewhat structured, instead considering the set with the structure (so, the tuple), to be the space.  I am not sure how to think about this. How do I deal with this in my writing? Especially since, what happens a lot is that I need subsets and element out of the underlying sets of all kinds of spaces.  Of course it would greatly help if there was a general name for a set that is the underlying set of a space, , but it seems that there is no dedicated name for such a set. Let's say there was a features space $(X, \cdot)$, (where I am not even sure, what structure we would add). Then it would be great to have a name for the set, let's call it an asdf. So we could say the feature asdf.  Afterthoughts: What makes it worse for me is that it seems ( and ) I am not even using the word &quot;structure&quot;, right, since it is about operations, so we are talking about an &quot;algebraic structure&quot;, while &quot;geometric space&quot; is... something else...? So apparently a &quot;vector space&quot; is actually not a &quot;geometric space&quot;, but an &quot;algebraic structure&quot;. I can understand that point, but the language gets even more confusing. Chain-calling parent initialisers in python How to set a shortcut for "Always on Top" for window? In 12.04 (Unity), I would like to assign a shortcut to the "always on top option" for a window. Probably something like Ctrl+Shift+Home to turn on and Ctrl+Shift+End to turn off, or whatever. Is there an option to do this somewhere in the Compiz Settings Manager?  This (old)  claimed that      For compiz, Enable Extra WM Actions. Check the properties, and insert ALT+A to Key field for Toggle Always-On-Top action.   But I couldn't find that. Are there any disadvantages to unusual RAM amounts for virtual machines? This is going to seem like a silly question, but many many years ago I somehow got it into my head, perhaps from reading an article or speaking to people 'in the know' that a computer should not be run with 'odd' amounts of ram, such as 3,  5, 7 etc...    Is there any truth in this whatsoever?  I have a vmware environment with many servers in it.  I want to go through and alter the amounts of ram to reduce the overall ram usage and in many cases I want to give a server 3gb of ram as opposed to 4 or 2. How to Logout of an Application Where I Used OAuth2 To Login With Google? I've been a Stack Exchange contributor for a couple of years now, currently most active on . One thing that keeps coming up is questions that would appeal to audiences on two different Stack Exchange sites but there are almost no features taking advantage of these questions. On travel.SE we have crossover questions most often with  and possibly next most often with  - but it can happen with almost any SE site. Today alone we had  with  and  had . I am absolutely sure that this must happen all the time between arbitrary pairs of Stack Exchange sites but the only feature that takes advantage of it is the possibility of migrating off-topic questions which leaves the original question acting as a redirect across the two sites. I think there is a missed opportunity to build the network between sites where users of one site don't realize they could make valuable contributions to a sister site they have had so far little to do with. At the very least there could be a way to &quot;advertise&quot; a question on a second site that could be interested in it. Probably by listing it in the sidebar where there are also links to meta questions, linked questions, related questions, new blog posts, and But there could also be some kind of features that make some sort of acceptable crossposting. There could be gamification/badges added around building cross-site questions or whatever else you can think up. I think this is a great way for people to spread their expertise from their main site onto other sites, to make the network stronger and more cohesive, to bring more attention to questions that would have a divided audience between two sites. I can think only of positives and no negatives. Does anyone else have some ideas to add or think this is a bad idea for any reason?  Example crossover questions: Here are some links to some crossover questions I've been finding in the Stack Exchange network here. (This was previously posted as an answer, but more people wanted it to be part of the question.)   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  : I have a Python module installed on my system and I'd like to be able to see what functions/classes/methods are available in it. I want to call the help function on each one. In Ruby I can do something like ClassName.methods to get a list of all the methods available on that class. Is there something similar in Python? eg. something like: from somemodule import foo print(foo.methods)  # or whatever is the correct method to call If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t Goal: I have a function $f(x,y)=z$ (two variables for illustration only) which I know almost nothing about--it has a compact domain which I can determine, it is non-negative, and bounded above.  My goal is to find the maximum value $f(x,y)$ takes on its domain.  I can query the function and I know the values at a few points: $f(x_1, y_1)=z_1, f(x_2, y_2)=z_2,..., f(x_n, y_n)=z_n$.  Optimization via Linear Regression:  I have used linear regression (and related methods like the lasso) to model functions like this in the past; this is the method that I am very comfortable with.  Typically, I might try to find a polynomial (of degree $k$) which relatively accurately models the data. The end result would be to say that:   $$f(x,y)\approx \beta_1 + \beta_2 x + \beta_3 y + \beta_4 x^2 + \beta_5 xy + \beta_6 y^2 + ... + \beta_{m}y^{k}.$$  Determining the coefficients is done by solving the .  The "best degree" for the polynomial might be determined using $k$-fold cross validation.  Once the "best" polynomial has been determined, one can choose any of a number of methods to optimize it (Newton's method, gradient descent, hill climbing, etc).  Then, if all goes well, the optimal value on the polynomial corresponds to an optimal value of $f(x,y)$.  Bayesian Optimization:  Recently, I was describing this technique (linear regression) to a colleague who asked: "What is the difference between that and Bayesian Optimization?"  I've been attempting to answer this question for the last couple days, and so far I don't have anything really conclusive.  After reading , trying to read  and getting stuck reading  I think I understand the following about BO:   Start with a prior (a guess as to what family of functions the black box belongs to... or at least some family of functions which you believe might be able to describe $f$ well).  It looks using a  as a prior is popular. Specify whatever is needed to build your prior (for GP this is a covariance function). As you go along, you maintain two evolving functions, a "mean" function $m(x,y)$ and a "confidence interval" function $c(x,y)$.  Basically, you can predict the value at any point by evaluating $m(x,y)$ and you are confident that $f(x,y)\in [m(x,y)-c(x,y), m(x,y)+c(x,y)]$. Bayesian optimization provides a systematic way of updating/exploiting the model by alternatively selecting points where the confidence interval is wide (you are very uncertain about the value) or at optimal points on the model $m(x,y)$.   My Question: Is it fair/correct to say that the major difference between Bayesian Optimization and simply optimizing the linear regression model is that Bayesian Optimization provides the systematic way of sampling with the goal of optimizing the model and reducing uncertainty whereas the linear regression model ignores the idea of uncertainty and doesn't explicitly provide a means of updating the model?  Said another way, is the linear regression model an example of what might be a "mean" function $m(x,y)$ in Bayesian Optimization?  If I stick with linear regression, specify how to compute the uncertainty, and provide a means of updating/improving the model (exploit/explore) am I just doing Bayesian Optimization (without calling it that)?  Background: My background is in pure mathematics (graph theory) but my new job has me working with a lot of data (so I'm self learning statistics).  With that in mind, my statistics vocabulary is somewhat limited (so I appreciate answers that either avoid technical terminology or briefly explain any technical terminology used)--for example, Monday was the first time I heard/read the word "prior" used in a stats sense and I'm still not 100% sure I understand that correctly. Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet? Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet."  I have a (not very mathematically intelligent) friend who presented it as if it were a mathematical fact, which got me thinking... Is this really true?  Of course, I've learned that dealing with infinity can be tricky, but my intuition says that time is countably infinite while the number of works the monkeys could produce is uncountably infinite.  Therefore, it isn't necessarily given that the monkeys would write Hamlet.  Could someone who's better at this kind of math than me tell me if this is correct?  Or is there more to it than I'm thinking? Why was a regular train used to transport students to Hogwarts? I have an iPhone 6 128 GB which is not jailbroken. The current version of iOS on the phone is 8.1.3 and yesterday I wanted to update to iOS 8.2.  The download went through without any problem but while installing, it gave the error:     Unable to Install Update   An error occurred installing iOS 8.2   Tried installing after switching Off and ON and also tried Hard Reset (Holding Home button and On/off switch).  Same error displays every time.  Also the Touch ID has stopped working and I find that the Settings - Touch ID &amp; Passcode - iPhone Unlock is OFF.  When I try to switch it ON, the system displays the error     Failed   Unable to complete Touch ID setup. Please go back and try again.   Is anyone facing this problem?  I live in India. How do I identify SMD components? (or how do I identify any component) How do I identify the markings on an SMT component and match it up with a part number so I can be a good designer and actually look at a datasheet (and read the whole thing)? Or identify a part to replace an unknown part on a PCB? I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out &ndash; at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case?