## Marginal solution

Okey dokey. Better reveal the solution to the stat-geek marginalisation quiz. There were sixty two votes.

The popular winner was the economics/marginal profits idea, with 31 votes. Plausible but wrong.

The second most popular was the “marginal interest” idea. Well… this is what the term has more or less drifted into meaning, because (almost) everybody has forgotten the true origin. So… wrong.

Nobody voted for “lost in the mists of time”, which proves you all care. How nice.

Only two people voted for EB Margin being the pseudonym of WR Gossett. This disappointed me, both because it is funny and because it was supposed to be a cunning false trail. WS Gosset in fact published his papers under the name of “Student”, which is why we have the “Student’s t test’.

So of course the correct answer was other. Sorry if that was an annoying tactic, but I think if I’d made the right answer one of the choices, it would have been too obvious. Amongst the 6 suggestions, two were for our amusement :

“I’d write the reason here but there’s not enough room in the margin”
“To marginalise those who don’t know”

and four were were spot on or more or less right

“Refers to margins of a contingency table”
“thought it was to do with averaging rows, with answer stuck in the margin”
“your are projecting the 2D pdf onto the “margin” of the plot”
“Sweeping the probability to the edge (=margin) of the paper?”

Sounds like the first two people knew, and the second two deduced the right answer. If you were one of those people, award yourself an extra biscuit at coffee time, and feel free to announce yourself.

Just to it spell out..  As physicists, we nearly always think in abstract mathematical terms, so we think of  “marginalisation” as a calculus problem – an integral. Even when thinking visually we picture a joint probability distribution as a smooth surface in three dimensions. But early statisticians were often concerned with tables of numbers, and worked on paper. Think of a joint frequency distribution as a grid of numbers in cells. Then  add up a row, and write the answer in the margin. When you have done this for all the rows, read down that margin, and – voila – the marginal distribution for y.

Don’t start me on regression…

### 8 Responses to Marginal solution

1. You are so cool! I do not believe I’ve read through
a single thing like that before. So great to find somebody with some original thoughts on this
issue. Really.. thanks for starting this up. This website is
something that is required on the internet, someone with some originality!

• Mark McCaughrean says:

While of course this is obviously generic spamflattery, it’s also obviously completely inappropriate on this particular occasion.

Sorry, Andy: couldn’t resist :-)

• Somehow spamflattery sounds like something from one of those eighteenth century picaresque novels. Why Mr McCaughrean, surely that is nothing but spamflattery! You do more me more justice in this manner than you imagine Madame. etc.

• Mark McCaughrean says:

Dear Mr Lawrence,

Following a tiresome delay, no doubt caused by my carrier pigeon having been waylaid by scoundrels aboard fishing smacks somewhere in the North Sea, I am delighted to be able respond to your missive.

Having done so, allow me to offer the desire that you and all of your correspondents who participate in this bulletin board enjoy a most excellent festive season.

Hoping that this final sentence did not, in fact, channel Bill and Ted, we remain

Sincerely yours,

Mr McCaughrean

• andyxl says:

Dear Mr McCaughrean

I am most grateful for your warm felicitations, and on behalf of all my correspondents, wish you in turn a joyful yuletide and successful 2014.

This thought however raises an interesting social conundrum. If your missive was indeed intended primarily for myself, then you form of closing address is most appropriate. If, however, as the most mildly curious reader cannot but suspect, you intended the communication to be primarily for my correspondents, most of whom are not personally known to you, then surely you should have concluded your communication “yours faithfully”?

In any case, good on yer mate and don’t get too pissed at Crimbo.

andy

2. “As physicists, we nearly always think in abstract mathematical terms, so we think of “marginalisation” as a calculus problem – an integral. Even when thinking visually we picture a joint probability distribution as a smooth surface in three dimensions.”

When doing things like this, I wear my Fortran hat, not my physicist or mathematician hat. The array operations introduced in Fortran 90 (and refined in Fortran 95) make this elegent to implement numerically. The common things one does when reducing a probability distribution to a lower dimension—marginalize, maximize, take a cut—correspond to single statements, and even things like projecting, say, 3-dimensional contours onto 2 dimensions can be done in just a couple of lines of code.

3. andyxl says:

Hmm. There were still a few votes after this solution was published!