tl;dr: Negative expected return.

Long version:

I received the following email the other day from Tom Daula:

Interesting applied project for your students, or as a warning for decisions under uncertainty / statistical significance. Real money on the line so the length of time and number of entries required to get a winner may be an interesting dataset after this is all done.

I replied that I think the question, “the increase in global temperatures is probably not due to random natural variation,” is fundamentally unanswerable.

Daula wrote back:

True, but the objective function is well specified: “correctly identifies at least 900 series: which series were generated by a trendless process and which were generated by a trending process.” The subject matter that motivated the problem is largely irrelevant. Although that could be a blog post on how this is the wrong way to state the signal to noise problem.

And I replied:

From the standpoint of climate science I don’t think this is so interesting because, from what I’ve seen, the evidence for climate change does not come from any single series but rather from many sources. But I agree that it would be an excellent teaching example.

And so I was going to post on it but then I thought I’d take a careful look. $100,000 on the line! Sure, Damon Runyon, Jack of Spades, etc. But still, let’s take a look. The webpage is from someone named Douglas J. Keenan and it starts like this:

It has often been claimed that alarm about global warming is supported by observational evidence. I have argued that there is no observational evidence for global-warming alarm: rather, all claims of such evidence rely on invalid statistical analyses. Some people, though, have asserted that the statistical analyses are valid. Those people assert, in particular, that they can determine, via statistical analysis, whether global temperatures have been increasing more than would be reasonably expected by random natural variation. Those people do not present any counter to my argument, but they make their assertions anyway. In response to that, I am sponsoring a contest: the prize is $100 000. In essence, the prize will be awarded to anyone who can demonstrate, via statistical analysis, that the increase in global temperatures is probably not due to random natural variation.

That’s the famous $100,000. And now for the contest:

The file Series1000.txt contains 1000 time series. Each series has length 135: the same as that of the most commonly studied series of global temperatures (which span 1880–2014). The 1000 series were generated as follows. First, 1000 random series were obtained (via a trendless statistical model fit for global temperatures). Then, some randomly-selected series had a trend added to them. Some trends were positive; the others were negative. Each individual trend was 1°C/century (in magnitude)—which is greater than the trend claimed for global temperatures. A prize of $100 000 (one hundred thousand U.S. dollars) will be awarded to the first person who submits an entry that correctly identifies at least 900 series: which series were generated by a trendless process and which were generated by a trending process.

But also this:

Each entry must be accompanied by a payment of $10.

OK, now it’s time to get to work.

I’ll start by downloading and graphing the data: