2005-09-10

Probably not betting on climate with Lubos Motl

James Annans stuff refers.

Lubos Motl is a string theorist who thinks his opinions on GW are worth something [1]. Normally they aren't, but since he believes that warming and cooling are equally likely in the future, there is scope for a bet in which both sides think they are getting good odds.

James already has even odds on warming/cooling over the next decade from some unwise Russians, which is a good bet if you can get it (I've offered to share the exposure with him but he isn't taking; I'd even offer a premium). Lubos doesn't offer even odds (he isn't stupid, after all). He is looking to bet on a straight warmer/cooler from 2003 to 2013. He reasons that those who accept the consensus would think the odds of this to be about 1:100 on warmer; his odds are 1:1; so splitting the difference with a geometric mean gets 1:10 and he offers a bit less than this.

The trouble is interannual variability. The shorter the time period, and the fewer years for your endpoints, the more chance of the "wrong" result coming out even if the overall trend is upwards. To illustrate this, here is the CRU annual global temperature record (click for larger version). The bottom pic is a blow-up from 1970 (arguably the warming didn't start till the mid-70s due to sulphates, so I'm slightly doing myself down by starting from 1970, but no matter, I fudge that later), the two red stars (and the green ones ten years later) show the (as it happens, two) pairs of years when the temperature 10 years later was cooler. Since we all agree that the data since 1970 show warming (even those who believe the data is contaminated by UHI, alien spaceships and bits of string still agree that the data displayed show warming). If you choose a predition-time of 5 instead of 10 years, then there are 12 such pairs (5 is particularly bad: the values are (13=0; 12=1; 11=2; 10=2; 9=3; 8=3; 7=2; 6=9; 5=12).

So anyway, a rather rough calc (projecting the past into the future) then gives odds of cooling between 2003 and 2013 at about 2-3 to 25. Lets call it 1:9 (i.e. I think a fair bet is me putting up 9X for a chance of winning X; then my expected gain is 9/10*X-1/10*(9X)=0). So taking geometric averages (which Lubos asserts is "fair") gives odds between me and Lubos at about 1:3.

Lets do a quick sanity check on whether 1:3 seems fair to us both. If Lubos is right (in his assesment of the odds as 1:1), his expected gain is 0.5*3X-0.5*X = X. If I'm right (at 1:9) my expected gain is 9/10*X-1/10*3X = 6/10*X. Oops. Wrong: they should be the same. So we require odd 1:y such that 0.5*y-0.5 = 9/10-1/10*y, i.e. (y-1)/2 = (9-y)/10, i.e. 12y = 28, y = 7/3 (quick check: (7/3-1)/2 = 2/3 ?=? 2/3 = (9-7/3)/10 yes). In which case our expected gains are both 2/3 of our stake. So it looks like geometric averaging is wrong. Interesting, because it sounded plausible. I think that equalising expected gain is the way to get a fair bet, and the error in my calc above isn't immeadiately obvious. Also it pushes the odds into my favour, so I'll leave it for the moment.

So there we are: I offer Lubos (or anyone else credible) odds of 3:7 that 2003 is cooler than 2013 (ie, if 2013 is cooler I pay over 7*X; if its warmer I get 3*X; X negotiable but at least 500; currency dollars or pounds). I have (rather faint) hopes of getting better odds out of Piers Corbyn, so anyone interested had better strike now while the iron is hot & before I discover the flaw in my logic above...

OTOH difference-of-two-years is a noisy statistic. A better bet is on trends. From the above data, the trend is about 0.18 oC/decade. For the future, Lubos predicts a trend of 0; I predict same-as-the-past; splitting the difference, what about an even-odds bet on a trend, between 2003 and 2013 (inclusive; standard LS fitting) of above/below 0.09 oC/decade? As it happens, doing that since 1970 produces 3 11-year periods when the trend has been less than 0.09. I'd be more comfortable with trends. For one thing, it makes the bet more interesting, as you can compute the trends out at 5,6,7,8,9 years with some hope of guesing the 10th; whereas with diff-of-years the last is less predictable so the tension is less.

23 Comments:

Blogger Lumo said...

A slightly more comprehensible and coherent text about the very same topic is here.

12:53 am  
Blogger James Annan said...

"I offer Lubos (or anyone else credible)"

Anyone else credible? Thanks for the chuckle...

2:58 am  
Anonymous Steve Bloom said...

According to Lubos such a credible person would be... Bjorn Lomborg! Of course he also refers to Lomborg as a scientist. What kind of world do we live in when a string theorist agrees that political science (Lomborg's actual academic field) is science?

3:25 am  
Blogger Belette said...

A reminder that the comment policy here prohibits stuff like "xeroxed copies of a bigot". Sadly blogger won't let me edit comments, only delete them, so I'm afraid yours had to go, but I'll reproduce the substance here just this once:

From Lumo:

Dear Steve Bloom,

I completely agree with your last sentence. What kind of world do we live in when a string theorist agrees that a political scientist is doing a better natural science than those paid as climate scientists?

Well, unfortunately we live in a world in which many average climate scientists [insults deleted] while the actual politics-independent research must often be done by political scientists and mining consultants. What a strange world.

9:36 am  
Blogger EliRabett said...

FYI, Lubos is sitting on a sticky wicket. String theory is in a nasty blind alley looking for the next miracle drug http://www.math.columbia.edu/~woit/blog/

1:26 am  
Anonymous Jo Calder said...

Excellent wookie, Eli.

Cheers, -- Jo Calder

11:28 am  
Blogger Belette said...

Nigel wouldn't be interested in a flutter, would he? Last I heard he was still keen on an upcoming ice age.

12:40 pm  
Anonymous iso42 said...

I found your webpage(s) after reading Lubos' post . Your weasel - link is quite funny.

2:03 am  
Anonymous Jo Calder said...

Nigel wouldn't be interested in a flutter, would he? Last I heard he was still keen on an upcoming ice age.

I don't know. You could always ask him. I think it's clear which way we're headed on geological timescales, but it's not much fun to bet when the winning party's not around to collect.

I did seriously try to place some climate-related bets with Willy Hill's a few years back, most recently, "that the IPCC FAR will not be published or will show a reduction in the forecast lower bound for global warming". (I now realize that such a bet would be stupid, because either scenario is politically unacceptable.) Hill's said that they would not be able to find anywone to set odds.

If we're into bets, how about the following, which is a bit more modest in scope. A bottle of good single malt says that the following is true: Using the data and methods of MBH '98, the value for the R2 statistic (or "squared Pearson dot-moment correlation", if you prefer) for the period 1856-1901 is less than 0.05. As proof of this, I'll accept your word: you seem to know the guys, it's clear from the source code that R2 was calculated and so it should be easy, a matter of a minute's work, for you to get a straight yes/no on the above proposition from the people concerned. You could also use the response to illustrate your answer to John Fleck's "Ask Stoat" question.

Cheers, -- Jo Calder

9:07 am  
Anonymous Jo Calder said...

Sorry, for proof, read disproof in the above.

Cheer, -- Jo

9:11 am  
Blogger Belette said...

Jo - sorry, I don't even understand the question yet. This is Bartonism, isn't it? Feel free to provide sources, if you like, it might help me write the post.

But even if I did understand the question, I would still consider it a rather contrived bet. Are you interested in beting on 10 year temperature trends? You sound rather skeptical. What X would you insert in the following sentence: "I am prepared to bet on the cooling side at 1:1 odds for the temperature trend 2004-2014 (inclusive) is less than X oC/decade"?

As for betting on the FAR... that was published in 1990. Assuming you really meant AR4, I'll give you pretty good odds on it being published, and on a reduction in the forecast lower bound. But given that the AR4 text is now available for review, betting on what it says would be cheating, really. So: how about he temperature trends then?

3:17 pm  
Anonymous Jo Calder said...

I'm not entirely sure what you intend by Bartonism, and I didn't raise any questions in the comment to which you respond, but no matter.

For a start on R2, see the replication by Wahl and Amman, and Michael Mann's statement here.
I'll monitor this page to provide more references in case you get stuck.


If you take my bet, I'll take yours on the cooling side of 0.01 degrees per decade over the period 04-14, with a bottle of single malt as the stake.

But you say my bet is "contrived". What do you mean by that?

Cheers, -- Jo

5:01 pm  
Blogger Dano said...

William,

the Stevie Mac PosseTM is trying out their new narrative.

They have been told recently that the low r^2 in the early time periods of the MBH98 reconstruction was purposely and evilly hidden from public view, and thus these two things negate the findings of the paper. This negation, see, has a domino effect and crashes the results of all subsequent papers, see, and the foundation for the AGW religion is therefore undermined.

That is why you don't understand the question: you don't know the contextual narrative.

HTH,

D

5:05 pm  
Blogger Belette said...

Hmm - Jo, Dano - thanks for the context. Maybe I'll try to understand this sometime.

Jo: 0.01 oC/decade would be fine (indistinguishable from 0, though - it wasn't a typo for 0.1 was it?) but a bottle of malt is down in the noise. 1000 GBP is the minimum stake for being taken seriously.57898

5:20 pm  
Anonymous Jo Calder said...

indistinguishable from 0, though -- absolutely.

a bottle of malt is down in the noise -- nope, it's a luxury for me and there are many better claims on that amount of cash. Good for you if that's not your situation.

Maybe I'll try to understand this sometime. -- I think it's worth the effort.

Cheers, -- Jo Calder

9:01 pm  
Blogger Belette said...

Jo - errm, remember, you're not tying up the cash - you just have to be prepared to stump up in 10 years time. If you're not confident of your forecast, then by all means back out.

10:43 pm  
Blogger Belette said...

[A small apology for a part of that last comment, which was written late at night. Since Jo never offered to stump up a substantial sum, "back out" was rather unfair]

9:06 am  
Anonymous Jo Calder said...

I appreciate your last comment.

I have a very good idea what I'll be required to stump up for around 2014. I'm sure I'll need a stiff drink as well.

Cheers, -- Jo

9:09 pm  
Anonymous Anonymous said...

I have been making a regular, annual bet with my environmental science and biologist friends (as a paleo-climatologist I am of course a skeptic on AGW, and my friends in these fields of science many times use their hearts more than their brains) that goes like this. In 1998 my friends were wringing their hands and claiming the sky was falling as temps hit a "record". Of course in earth history it was a very short term set of temps to base it on, and the reproduceablity of the temp records until the 1970a was very doubtful and of dubious credibility. But I made them a bet, every year from 1998 we would look at the earth average temp, if it was up from the previous year, I pay, if it were down, they pay, I have not lost yet, 2005 was a push. Are you a betting man? No odds, just a simple bet that climate is not simple at all nor is it being driven directly by human CO2.

5:44 pm  
Anonymous Anonymous said...

Oops, should have proofed it, my bet has been that each year after 1998 would be cooler, I win that way, if it were warmer, they win, sorry.

5:49 pm  
Blogger Belette said...

Sorry anon, this is a closed blog now... though obviously I'm still monitoring it. But I doubt anyone else is. See http://scienceblogs.com/stoat/2006/07/betting_on_climate_change.php

8:08 pm  
Blogger Brian said...

Hello anon, I'm interested in joining your circle of friends that bet against you. I posted a comment on William's 7/11/06 post at scienceblogs if you care to follow up.

4:44 am  
Anonymous Anonymous said...

Jan: I cannot understand why Lumo should accept a 1:1 bet if he believes the odds are 1:1. Would you bet all your fortune in flipping the coin?

He seems to be a risk-averter, as most of us are. So if he believes the odds are 1:1 he must be, naturally, offered a bet better than 1:1.

8:54 am  

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