Posts from September 2013 (69)

The below is posted on behalf of Mark Holmes from the Department of Statistics at The University of Auckland. Colleague James Curran read this piece on Wired Science  and challenged him to respond to the following:

Suppose that two drunk statisticians leave a bar (located in the middle of an infinite forest) together.  They stumble around at random and get lost.  Will they ever find each other again?

Mark, helpfully, rose to the bait (thanks, Mark!)  This is what he says:

Assuming 1) that the drunks will live (and stumble around drunk) forever, and that 2) the forest is two dimensional (i.e. there is infinite space to move in both N-S and E-W directions, and the drunks can’t climb infinitely high trees!)  then the answer is yes, they will meet each other again.

Perhaps the best way to explain this is to consider the difference between their locations.  If after n steps the first statistician is at position X_n and the second at position Y_n, then let’s look at D_n=X_n-Y_n.  The two drunks will meet at any time n when X_n=Y_n, which is the same as D_n=(0,0) (the position at time n has two coordinates since we are in two dimensions).

It turns out that D_n itself is essentially a simple random walk, and that the two drunks not only meet again, but they meet infinitely often, because D_n returns to (0,0) infinitely often.  The posh way of saying this is that “simple symmetric random walk in two dimensions is recurrent”.  It is perhaps not surprising that if instead of stumbling around an infinite forest they stumble along an infinite footpath (one dimensional), they will also meet each other infinitely often (“simple symmetric random walk in one dimension is recurrent”).  Note that if the bar is located instead in an infinitely high, wide and long mall they might never meet again (“simple symmetric random walk in three dimensions is not recurrent”).

If the above was good news for the drunks, there is some bad news.  Although they will meet each other again in finite time, the  “average” time it takes them to meet again is infinite.  This is true both in the forest and on the footpath.

If you are interested in the relevant calculations, ask a graduate student in probability (they should also be easy to find on the internet).  If you are satisfied that you understand that, try to solve the following:

 “A physicist, a probabilist and a statistician walk out of a bar…..”

Suppose that we have three independent random walkers instead of two.  The above discussion says that each PAIR of walkers will meet each other infinitely often (in two dimensions).  Will all three meet each other simultaneously?

… so, dear readers, let us have it!  Don’t be shy.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday September 20 2013.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of September 14 – 20 2013 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

(more…)

If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!

On Friday, Stuff had a story about 10 pairs of twins in the same school in Wellington.

At this point I was going to break out the Stats New Zealand website and find out how many pairs of twins of school age there are in the country, and work how many schools you’d expect to have these sorts of numbers.  But when I went back to search for the story I found

• A Herald story from last September, with 14 sets of twins in a Dunedin school
• A Stuff story from last October, with 4 sets, in Timaru
• A Stuff story from April, with 9 sets, in Manurewa
• A Stuff story from June, with 3 sets in the same class, Palmerston Nth
• A Stuff story from August, with 5 sets of twins and two of triplets, in Timaru

That’s just the past year, since the stories go on back in the past, and even stretch to other countries: a Stuff story from June was about 24 sets of twins in an Illinois school.

At some point it must be hard to keep pretending this is a surprise.

• ChCh Press has a sensible story explaining that apparent clustering of murders is probably just chance variation
• Just when you thought I was getting tired of pie charts, here’s a beauty from a company that does exhibits for court trials

To be fair, the purpose of the chart probably is just to look ugly and complicated, not to convey quantitative information

• A fascinating statistic: 1/3 of emergency calls (111 number) are due to pocket dialing from mobile phones. Since nearly 50% are real, that means Kiwi butts are responsible for twice as many calls as pranks and cranks.

The Dominion Post has a story (via @LewSOS) on the Wellington mayoral elections.

John Morrison is leading incumbent Celia Wade-Brown in the race for the Wellington mayoralty, according to a poll of Dominion Post readers.

Mr Morrison, who has been a city councillor for the past 15 years, had support from 27 per cent of the 635 readers surveyed last week – while Ms Wade-Brown trails on 17 per cent.

They don’t say how the survey was done — it’s not clear how you would get a representative sample of Dominion Post readers.  For all we can tell, it might just be a bogus poll.  It’s also not clear, on this topic, why Dominion Post readers are even the population you would want, since the story continues

Of those surveyed, 275 were eligible to vote in the Wellington City Council elections.

You’d at least expect that the voting preferences would be broken out by eligibility.

Sadly, no.

According to the Herald, the ACC wants us to be careful about weddings — about getting injured at them, that is.

Weddings are supposed to be the happiest day of your life – try telling that to the hundreds of people who make ACC claims for injuries at ceremonies.

From tripping on the bride’s dress to swallowing the ring, nuptials can be surprisingly hazardous.

New figures show at least 600 people made claims to the ACC between 2010 and 2012.

So, how does the 600 claims over three years compare to what you’d expect from an average day?

The ACC accepted 1.7 million new claims last year, which gives about 0.4 claims per person per year, or about 0.001 per person per day.

There were about 20 000 marriages in New Zealand last year, so about 60 000 over 2010-2012, giving about 0.01 ACC claims per marriage.  The 600 reported claims would then be about what you’d expect if there were 10 person-days of exposure per marriage.

My experience is that wedding celebrations typically involve more than ten people, and, with setup and rehearsals, often more than one day.  It looks as though weddings, like Christmas, are actually safer than ordinary days.

An interesting piece in Slate on longevity (via @juhasaarinen).  Unlike the typical story using life expectancy, it’s by someone who seems to understand what it means. There’s also an interactive graph of how causes of death have changed over time, which is notable for having the best use of a creative y-axis scale I’ve seen in a long time.

If you look at ‘influenza and pneumonia’, there is a general decrease with a dramatic spike in 1919. It’s so dramatic that it pops out of the top of the lower panel and spikes into the upper panel. This is the famous Spanish Flu pandemic — the same  rate in today’s New Zealand would mean over 25000 deaths.  Fortunately the three flu pandemics we’ve had since then have all been much less nasty.

It’s also worth noting that nearly all the decline in infections as a major cause of death happened before antibiotics became widely available in the mid-1940s. That’s the reason I’m not really convinced that antibiotic resistances is going to kill us all, though it’s certainly worth avoiding.

Last night’s edition of Our Changing World had two segments by University of Auckland statisticians called James.

Allison Ballance and James Russell talked about seabirds and rat eradication

Ruth Beran and James Curran talked about forensic statistics

From this morning’s Twitter feed

• An animated GIF (click on it to wake it up) showing how to improve a barchart by removing junk. [from Darkhorse Analytics: Data looks better naked]

• Data journalism: how the data sausage gets made.  Jacob Harris describes how he collected and summarised data on meat recalls in the US
• The Royal Statistical Society has repeated the simple maths test they gave politicians last year, this time for senior professionals and managers. Less than half of them could give the probability of getting two heads from tossing two coins.
• However, the same Royal Statistical Society news item ends “The figures have been weighted and are representative of all GB adults (aged 18+)”. This seems to me to fall in the “not even wrong” category. The target group aren’t remotely representative of all British adults, and I’d be surprised if it was even possible to reweight them to the national age distribution.
• Cathy O’Neill (mathbabe.org) asks why rankings of eg, cars or universities don’t allow the user to change priorities for different attributes (as the OECD Better Life Index does, for example)