ryanmonroe

I think I may have misinterpreted your original comment. It's true, as you say, that in the Stein estimator some individual MSEs get worse to yield a lower overall MSE. I was focusing on your example and assuming you meant this was only possible because some individual MSEs were larger than others to begin with (under the individually optimal estimator).

> it's only really relevant when you have things that are associated with each other somehow

The proof of lower overall MSE assumes the variables are independent.

This is not why it works. The James-Stein estimator applies in the case of independently distributed Normal variables with equal variance, so the individually optimal estimators for each parameter have the same MSE.

Mercedes has the $40k B-Class electric car.

>Imagine that you just heard a mom tell her kid, 'Don't be so bossy!' What gender is the child that she is addressing?

Imagine if you heard a parent tell their child "don't be an asshole". What gender is the child? I think it's true that women are held to a different standard when it comes to assertiveness, but the existence of a female-specific insult is not evidence of that. There are plenty of male-specific insults of the same nature. Asshole, dick, douche, prick, bastard, etcetera

>Here's one: plot 360 degrees of a sine wave, and it's first and second derivatives. Then explain an Excel user how that works.

Seems pretty straightforward to me

    x  <- seq(from = 0, to = 2*pi, by = .05)
    y  <- sin(x)
    y2 <- cos(x)
    y3 <- -sin(x)

    plot(x, y, type = 'l')
    lines(x, y2, col = 'red')
    lines(x, y3, col = 'blue')

I would assume results rankings are based on how many people click the link after searching the given terms. Probably no one searches "search engine" on Google then clicks on a link to google.com .

For me personally, a simple animated version of this image[0] looping through rows of A and columns of B seems easier to understand.

[0] https://upload.wikimedia.org/wikipedia/commons/e/eb/Matrix_m...

Pretty amazing. If the outcome is determined by 100 million independent coin flips, the probability of a margin greater than one tenth of a percent is 1.5e-23. In R

    n      <- 100000000
    diff   <- 0.1/100
    a_wins <- n*(1-diff)/2
    b_wins <- n*(1+diff)/2
    p1 <- pbinom(a_wins, size = n, prob = 0.5)
    p2 <- pbinom(b_wins, size = n, prob = 0.5, lower.tail = F)
    p1 + p2 # = 1.523959e-23

>having to sacrifice IO for charging while mobile

You're not sacrificing anything. The old MBP had two usb ports and the new one has 3 available while charging. The only thing that has changed is now you can use the charging port for IO when not charging. Framing this as a "sacrifice" doesn't make any sense.

>make sure you carry the right USB-C cables, as your friend's might not work

With the old Magsafe chargers, and for laptop chargers in general, it's the same deal. If you want to charge your laptop, you have to bring your charger. The fact that the charger is USB-C doesn't make the situation worse.

"You see that we obviously cannot walk several of the indicated routes"

They may be using a public transit route which goes in only one direction or can only be boarded at the point on the other side of the loop.

If the police are trying to get you to talk without a lawyer, they're the ones being impolite. You're just trying to avoid being thrown in jail.

Wolfram Alpha has similar functionality (minus the home page)

http://www.wolframalpha.com/input/?i=days+until+doctor+stran...

In the book he notes that it started out as a derogatory term. Can't find the quote in the book but I found this

http://www.nytimes.com/2010/05/16/magazine/16FOB-OnLanguage-...

"When I asked Derman recently about his early years in finance, he said that at first he felt that quant, like rocket scientist before it, was largely a derogatory put-down for the brainy newcomers, many of them foreign-born: 'two-thirds pejorative, one-third grudging praise,' by his calculation."

I just wanted to point it out. The thread title is "Learn Advanced Mathematics Without Heading to University", which could be read with the implication "Learn advanced mathematics, at the university level, without going to university". Under this context, someone replied that this is possible because s/he learned it, but can't prove what s/he's learned. Of course not being able to prove the useful theorems you've learned doesn't render them useless (although perhaps less useful as you're less likely to know precisely when they can be applied and how to extend them to new situations), but in the context of the discussion it seems like an important distinction to make.

An added benefit to learning from a book that's more popular is that if you hit a wall and have a specific question about the material as it's presented in your book, you're more likely to find your question answered online. You might even be able to find course material that follows the book, whether from an official online course or just because the professor at some university didn't bother to make the course page blocked off from non-students.

I'd say the biggest benefit of being in the present year when learning math from a book is the availability of online resources like Stack Exchange where you can ask experts about the material you're learning if you get stuck. It's also nice that most books are available in pdf form so you can pick up multiple books on each subject you learn and easily switch back and forth between them.

>Just don't ask me to proof anything

I don't mean to offend, but being able to prove things is generally the main focus of advanced mathematics. If you can't prove what you know, or at least have a rough outline of a proof you could construct after referring to something, you haven't learned it in the same way those at a university have.

Okay, so it follows from completeness. Now prove that real numbers are complete (or provide a construction of the reals that uses completeness as an axiom) without using concepts foreign or confusing to someone with a middle school level exposure to math.

Google gives "an intentionally false statement" as the definition for lie. Wikipedia says "A lie is a statement that the stating party believes to be false and that is made with the intention to deceive".

>The unfortunate truth is that black people are more likely to commit violent crime in the US.

It doesn't make much sense to cite the proportion of black people convicted of a crime by US law enforcement as evidence refuting the claim that the US law enforcement's interaction with people changes according to their race. The proportion of black people convicted of [category] crimes could be high for many reasons, including actually higher incidence of such crimes among blacks, racial prejudices at various points along the legal path of alleged criminals, and any combination of those or other factors.

Siri gave me the same response for a few days but apparently they've reverted that change because it has since started working normally again.

Depends on the location. Many McDonald's have quite comfortable seating, like this http://www.giotile.com/wp-content/uploads/2014/09/McDonalds-... .

Lack of pistachios in grocery stores wouldn't affect me one bit, but I'd still be on the side of pistachio buyers (and pistachio salesmen) if my city decided to ban them. edit: or if my city decided that all cashiers checking out customers with pistachios must be fingerprinted.

I think I read a blog post about that somewehre.

Anyone else get an error when trying to add this extension?

>Package is invalid. Details: 'Could not load background script 'tracksy/tracksy.js'.'.

I'm not sure I understand how this works unless all objects being measured are on the same surface as the reference object. Take for example, this image https://lh3.ggpht.com/n3-JnvRAOTqSOwD7UriOo7ooPGQ0Nf8wueiK_U...

Imagine measuring a distance vertically along the side of the window. Now imagine a second image in wich, instead of a window, there is just more of the (now larger) desk. If you were to draw the same line in the same location in the second image, the actual distance of the underlying object would be different. Does TakeMeasure somehow account for this? I would assume the answer is no, and if so that would still make for a useful app, but then I saw this "TakeMeasure allows you to measure dimensions of any small or large objects that fit into your camera view. "

The logistic function maps to (0,1). The hyperbolic tangent tanh(x)=2*logistic(2x)-1 maps to (-1,1).

Linear models in R are also solved by QR factorization.