more binomial MADness

I posted earlier about the mean absolute deviation (MAD) of a binomial variable S_n with parameters (n,p). Here’s a little follow-up with plots. This is a plot of \mathbb{E}|S_n - np| versus p for different values of n.

The first is for n = 10. Looks beautifully scalloped, no? As we’d expect, the MAD is symmetric about p = 1/2 and monotonically increasing for the first half of the unit interval. Unfortunately, it’s clearly not concave (although it is piecewise concave), which means I have to do a bit more algebra later on.

When $n = 100$ the scallops turn into a finely serrated dome.

By the time you get to $n = 1000$ the thing might as well be concave for all that your eye can tell. But you would be deceived. Like a shark’s skin, the tiny denticles can abrade your proof, damaging it beyond repair.

Why do I care about this? If you take n samples from a Bernoulli variable with parameter p, then the empirical distribution (unnormalized) is (n - S_n, S_n). So \frac{1}{n} \mathbb{E}|S_n - np| is the expected total variational distance between the empirical distribution and its mean. More generally, the expected total variational distance for finite-alphabet distributions is a sum of MAD terms.

Linkage

Some interesting stuff has passed my way while being in India (and one or two things from before). Might as well post them before I forget, no?

Slavoj Žižek may be a curmudgeonly Marxist, but the animation helps soften it, I think. I don’t think I fully agree with him, but there’s stuff in there to chew on.

The Purdue anonymization project won a big NSF award.

Tips for tasks related to graduating (h/t Bobak).

Some interesting news about the future of the textbook market. It’s doubly interesting since I am in Pune, a treasure-trove of cheaper editions of technical books.

Apparently I sometimes wear a lab coat.

APIs for hardware : architecting cellphones and networks

We had two talks by here at UCSD on Tuesday. The first was Cell Phones: How Power Consumption Determines Functionality by Arvind, and the second was Software-Defined Networks by Nick McKeown. These talks had a lot in common: they were both about shifting paradigms for designers, and about approaching the architecture of hardware from a software point of view.

Continue reading

Linkage

More content-ful posts to come soon, I swear. I got sidetracked by job applications. ‘Tis the season, you know…

The REAL STORY of Alice and Bob. Classic investigative journalism (h/t Bikash Dey)

Tyler Perry’s For Colored Girls gets panned. I should mention that the play was done at MIT my first year there and I still remember it as one of the most affecting pieces of theater that I saw during my time there (and maybe after as well).

Scott McLemee on the poverty of the Rally to Restore Sanity.

Winners of the SD Asian Film Festival “Interpretations” contest. Like contentless scenes from your acting/directing class, but with film!

SAALT put out a report called From Macacas to Turban Toppers: The Rise in Xenophobic and Racist Rhetoric in American Political Discourse (PDF). Reading it is keeping me up past my bedtime. (via Sepia Mutiny).

Readings

The Hakawati (Rabih Alameddine) — an expansive novel, framed by the story of a son who has gone to the US coming back to visit his dying father in Lebanon. The sharply drawn tension and anguish of the present shifts rapidly through old family stories, to the story of Baybars (and parts in between). It’s hard to pick up the strands initially, but it’s a rewarding read once you get into it.

A Short History of the American Stomach (Frederick Kaufman) — a quick read, repeats of some stories from Harpers I had read. It might appeal to people who like Sarah Vowell’s writing, but it’s too heavy on snark for me. Good for picking up some cocktail-hour conversation pieces, if you enjoy talking about the puking habits of Puritans at cocktail hours.

The Magicians (Lev Grossman) — I enjoyed this book, even though some people call it Hipsters in Narnia. It is a bit of that, but I couldn’t really put it down (= brain candy). Recommended for those who want a jaded view of Harry Potter.

Ghostwritten (David Mitchell) — I read this one after reading Cloud Atlas, which I absolutely loved. It’s written in a similar style, with interlocking stories, but more direct storytelling going on than, say, if on a winter’s night a traveler. Maybe I just like the relay-race novel. In any case, definitely engrossing, if a bit… bleak? It’s simultaneously lush (descriptively) and bleak (psychologically).

Gaming the Vote (William F. Poundstone) — a popular nonfiction book about elections, the spoiler effect, and the history of voting systems. It’s larded with examples of elections from US history and makes for an engrossing read. Most of the focus is on the weaknesses of first-past-the-post and other methods of determining winners, but it’s a nice accessible read.

Nixing negative reviewers

A question came up while chatting with a friend — how do you tell the editors of the journal to not ask certain people for a review? Say you submit a paper to a journal and in the cover letter you want some language to the effect that “please don’t choose Dr. X as a reviewer, since they will be biased.” This must be a relatively common situation, especially where people have axes to grind, and what better way to grind them than while reviewing the other camp’s paper or grant proposal?

Let’s create a cartoon situation: suppose Dr. X really hates your guts (intellectually, of course) — this is actually the case, and not just your own misperceptions of Dr. X. I know that at some schools for tenure cases the candidate can give a list of people not to ask for letters. But in the context of paper submission, hows can you politely suggest that Dr. X may not be the most objective reviewer for your paper?