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orthonormal comments on New Year's Predictions Thread (2011) - Less Wrong
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Comments (224)
10%: the United States has a historically hot summer.
This is only notable because it's the only factor that could get cap-and-trade legislation through a Republican House. (Whose bright idea was it to have the 2009 Copenhagen climate change summit in winter? The juxtaposed headlines with the winter storm may have set back the legislation indefinitely.)
If you'll give me 9:1 odds on this summer being, say, the hottest summer in the US in a century, I'll take it!
I was thinking along the lines of Skatche's reasoning above. 10% is my break-even point; if you were willing to go against me at 19:1, I'd take it.
I didn't make myself clear - it's the other side of the bet I want!
Oh, in that case I'd take the "no" side at 5:1 odds or lower. (I'm metauncertain enough that I wouldn't dare make bets in either direction close enough to my break-even point.)
At those odds a bet is almost but not quite worth it I think!
OK, so it seems our estimates are within the same bid-ask spread.
EDIT: Or rather, our bid-ask spreads intersect.
The meta-uncertain excuse doesn't make a lot of sense to me- it's enough that you want enough expected gain to justify the transaction cost.
Or is there some kind of rigorous notion of meta-uncertainty you're appealing to?
Hmm. Actually, it's because I haven't bothered to collect all the information I could, and so my bid-ask spread serves as a confidence interval. If it were too small, then I'd actually find it probable that someone else could do the research I haven't, figure out that the true value is on one side or the other of my interval, and exploit me.
This makes sense. So the interval at which you were willing to bet would increase given higher stakes (as that would give someone more incentive to do the research)?
What I'm trying to understand is what confidence interval means in a Bayesian context, a 'credible interval' seems to be the analogous concept but even after reading the article I'm still quite confused as to what a credible interval is in the context of subjective probability. I've seen also seen people here refer to the 'stability' of their beliefs- a concept which seems to function similarly. It definitely feels like it would be useful tool- it just don't quite get what it would mean as a way of describing beliefs instead of repeatable trials.
And if we can talk about credible intervals for beliefs... isn't that really relevant information for predictions? Shouldn't we give intervals in addition to p values? I'm not sure it makes sense to assume normal distributions for casually calculated probabilities on one-off events. This is especially the case since humans are really, really bad at distinguishing between probabilities at extremely high and low levels.
One way to think about the bid-ask spread, is that while orthonormal's current probability is 10%, he'd consider someone offering to bet him actual money on one side or the other to be sufficient evidence to adjust his belief significantly in that direction.
According to NOAA, 4 of the years from 1980 to 1997 were the hottest years so far of the century. So this summer has a 1/5 - 1/4 chance of being the hottest year of the century.
That's global temperature - I'd guess US temperature has more noise.
Intrade gives 2011 a 34% chance to be the warmest year on record, so 10% seems low.
But that's global annual temperature, not US summer temperature. The closest thing I could find to US summer temperature with a 5 minute search is the NASA GISS dataset for the average northern hemisphere land-surface temperature in June-August. The record summer high for the northern hemisphere was broken in 2010, 2005, 1998, 1995, 1990, 1988, 1987, and 1983, which also suggests that the probability of a record-breaking US summer is around 30% rather than 10%.
A little more searching turned up this NOAA/USHCN data set, which shows that the hottest summer (June-Aug) in recorded US history (contiguous 48 states, since 1895) is still 1936, so maybe 10% is closer to the truth. The 10 hottest US summers on record are 1936 (74.64 F), 2006 (74.36 F), 1934 (74.18 F), 2010 (73.96 F), 2002 (73.96 F), 1988, 2007, 2003, 1933, and 2001.
To make this needlessly precise, I fit a little model to the data and estimated that there's a 7% chance of breaking the 1936 record and a 12% chance of topping the 2006 temperature. For the past few decades, it looks like there's a linear trend plus some random noise. Fitting a line to the past 30 data points gives a .04/yr increase and puts the trend line at 73.35 F for 2011. The residuals have a standard deviation of .87. The record (74.64) is 1.29 degrees above the trend line for 2011, which makes it 1.48 standard deviations above the trend line. If the noise has a normal distribution, that would give a 7% chance of breaking the record (since p(z>1.48)=.07). A similar calculation gives a 12% chance of having the hottest summer of the past 70 years (breaking the 74.36 F mark set in 2006, which is 1.15 SDs above the trend line).
Thanks! I had a sense that the global warmth of recent years hadn't necessarily translated into a record-breaking summer in the US, but I hadn't looked into the data like this.
Since when are 10% of summers historically hot?
Since climate change began pushing up average temperatures. See for example: http://www.google.com/hostednews/afp/article/ALeqM5jbK6a-zNlRk3Az-Upzue83KHF5Bw
It's hard to get a good sense of precisely what the probability is, given that I'm not a climate scientist, but 10% sounds about right - perhaps even a little low.
It's not climate science, it's mathematics. The probability of a specific number being the highest in a sequence goes down rapidly as the number of items increases. And it's not like the temperature is doubling every year, either.
That's only true for a stationary series, which temperature isn't. For a random walk series you can have a 50% chance of each new observation being the highest ever in the series. For a trended series it can be higher than 50%.
Every year of the last ten years is among the top 15 warmest years on record. The other years are '00 '99, 98', '97 and '95. It seems very likely 2011 will be in the top 10, there is of course variation but you'd be crazy to expect a normal distribution. "Historically hot summer" is somewhat ambiguous but I'd say >.5 2011 is a top 5 warmest year (I don't have summer data- we might presume more variability there). ~10% for the hottest year on record doesn't sound crazy to me.
Okay, forget everything I just said; that probability does seem reasonable after seeing that data.
Not so. It is not mathematics itself that assumes a neat random distribution. Your assertion is about climate science.
I was simply going by remembered frequencies: every year since I started paying attention I've heard, at least once, something of the form "This year/season/month/day was (one of) the hottest on record in Ontario/Canada/America/the world." I therefore take the probability that at least one of these things happening to be quite high, and so the probability of specifically the U.S. having specifically a "historically hot" summer, although small, is by no means negligible. 10% is a reasonable rough estimate.
Did you know in certain parts of Europe, this winter was the first winter since 1945 where it has snowed for more than (some number) days before (some date) ?
Media like records, so they will report quantities that attain a record value.
That's true, but irrelevant. The fact that they're being reported doesn't change the fact that record values are, indeed, being attained.
It depends on how natural the records in question are. If there are 100 different records to be broken, you expect every year to break one and you should never be surprised when someone reports on it.
If you are choosing random properties and finding them to be extremal with reasonable probability, then you are getting a totally different sort of data.
This is also true but irrelevant. Skatche wasn't making predictions about whether he would be surprised by reports of records being broken. Just a specific prediction about weather.
Looks like I was underconfident in retrospect: according to the source that I agreed on when I made the prediction, 2011 was the second-warmest US summer on record.
(Even though it wasn't the warmest on record, the fact that it came in second is evidence that I probably should have estimated this at somewhere around the Intrade global temperature figure of 34%.)
http://predictionbook.com/predictions/2098 ; what data source do you plan to use?
The NOAA's State of the Climate report, I think; I'll look for the September 2011 version of this news release on the June-August summer.