Let’s suppose everything you have heard about global warming is true.
It really will warm by a half-degree Centigrade by 2050, or even by three-quarters of a degree, or whatever. Some areas will have slightly warmer nights, just like you’ve heard. And some places will find themselves just a bit wetter, others a bit drier.
Very well, global warming is true. Now what?
Well, not much. To understand why, we’ll have to understand conditional probability. But hold off on that for a moment.
Because first we have to comprehend the 2000 scientists who signed a letter demanding the Senate “take action” on climate change. Presumably, by “climate change” they meant global warming. But never mind.
Eight of the signers were “Nobel laureates.” Not Nobel winners in meteorology, climatology, or oceanography, of course, because old Alfred was unaware of those subjects. One Nobeler was Leon Lederman, 88, a retired neutrino physicist, who said, “if anything, the climate problem is actually worse than reported earlier.” Scary stuff.
Of most interest is that some of these “scientists” were not scientists. Many—I don’t know how many—were economists. And that is why we must understand conditional probability.
What do economists know about long-range climate forecasts? Nothing. Or, rather, nothing that the average citizen doesn’t know. In their training, economists learn the best way to disparage the Laffer Curve, but the equations of motion and radiative transfer never appear on their syllabi. So why did they sign?
Economists are like the Congressional Budget Office: they have to believe what they are told. Their models are conditional on assumptions given them from on high. So, if a climatologist says, “It will be a half-degree Centigrade warming by 2050” the economist has no choice but to believe him.
The economist says, “OK, it’s going to be slightly warmer. How does that affect my bottom line?” And off he goes, builds his models, and concludes “More study is needed. I’ll need more research funding.”
No, only kidding! They sometimes make definite, testable predictions which are rarely wrong.
But enough bad jokes. Time to understand conditional probability. Suppose we want to understand how global warming will affect something of interest to an economist, say, Social Security funding. We first have to accept that global warming is true, as we did at the beginning.
We then have to accept a whole string of assumptions of how slight changes in temperature will affect Social Security. We might theorize that people will live slightly longer in warmer weather: consider all those folks who head to Florida once their odometers pass 65. And longer lives lead to greater burdens on the Social Security trust fund. Makes sense, right?
Since this year is the first in which outlays are greater than income into that fund, people are living longer, and Lederman claims global warming is worse than we knew, this is certainly a plausible theory.
With theory in hand, the economist can then use probability to estimate the likelihood of various Social Security budgets, given the belief that global warming is real and given the string of assumptions tying Social Security to climate are true. This is a conditional probability estimate, and the conditions are those “givens” just mentioned.
He can then use the conclusion that, once global warming hits, higher payouts are likely. And after becoming bothered about this, he’ll sign a letter to the Senate.
The point is obvious: because an economist’s model says “Social Security in trouble because of global warming” it is not true that Social Security is in trouble because of global warming. It might not even be likely to be true.
Conditional probability works in a nested fashion. In order to fully quantify the probability of a theory, we have to string out the list of conditional statements, assigning separate probabilities to each assumption as we go along, and multiply them all together. Since probabilities of these kinds of events are numbers between zero and one, multiplying strings of probabilities together results in a much smaller chance the entire theory is true.
Even the IPCC says there is only a 90% chance that global warming is true. That’s our first conditional. Then we have to assign probabilities to the other assumptions in the economist’s model. People living longer will lead to higher Social Security payouts is true, but only conditional on payouts remaining at their same levels. And what’s the probability of that? Not high, even given no effect of climate of length of life. Say it’s only 40%.
With just these two estimates, using our multiplying rule, we have 90% x 40% = 36%. That’s the upper limit on the truth of the economist’s theory. And we haven’t even considered his other assumptions, all of which lower the probability that Social Security will be affected by global warming.
Most studies which claim “X will happen given global warming strikes” are in this boat. They all are subject to the rules of conditional probability. And the likelihood they are true are almost always overstated because the theory holders never multiply their probabilities out like we have.
This is much too complicated for one post: Next time, we’ll sort this all out.
Thanks for the writeup – I may point some people in this direction.
The other side of the coin for conditional probabilities is when you have a string of very likely occurrences that chain together, the probability that at least one thing goes wrong gets surprisingly high. For example, suppose you have a series of five independent events or stages in a process, that each has a 90% probability of success, and all have to happen successfully for the process to succeed. You have a 90% chance of getting through the first stage, but the odds of getting through all five successfully are 0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.59049 – less than a 60% chance of success!
Very interesting. Perhaps that is why EPA favors upper limit deterministic risk estimates vs probabilistic ones.
As a working economist – that’s opposed to an academic one, thank you very much – and as someone who has done a lot of work on long-term structural forecasting to map out changes in the world’s economy, at first I took umbrage to your critique of economists, until I realized you were, in fact, thinking of your typical academic economist, at which point I agreed.
But there are some of us out there that haven’t fallen to the dark force, if you may, just want to point that out. 🙂
Part of our problem is indeed that there are too few economists who actually think the problems through, instead they do some estimations, marvel at their mathematical abilities, and do whatever they are told to do.
Other than that: spot on.
When discussing ‘serious’ matters like the fate of the world following a degree or so of warming, it’s important to get the definitions right. Thats why simple phrases like ‘climate change’ never mean what they appear to mean. They have their own conditionals.
Climate Change is of course only ever used in the sense of the UNFCCC definition –
‘A change of climate which is attributed directly or indirectly to human activity that alters the composition of the global atmosphere and which is in addition to natural climate variability over comparable time periods.’
So, next time you’re about to agree that ‘Yes, of course I agree there is climate change, changes all the time’,
think about it.
Briggs,
Completely agree with the point of your post re: probability. Slight disagreement with your statement that the economist has no choice but to believe the climate scientist. Yes, we know he is likely to do so for tribalistic type reasons. [e.g. I’m a very smart, highly educated expert. I know what I’m doing. I need people to trust my opinion. He’s a very smart, highly educated expert. I can trust his opinions. Not healthy for me, if folks start questioning experts.]
But any reasonably intelligent person can make basic inquiries regarding the competence of the “experts” and the basis for their opinions (just as a trial lawyer cross-examining the opponent’s expert witness). They can also apply their knowledge of history and their own BS sensor. And if our economist expert is really honest with himself, he knows there are a whole bunch of supposed “experts” in his own field who don’t know their ass from a hole in the ground. Maybe climate science has the same problem! The longer he lives, the more convinced of this he will become. Or should.
Fortunately for us, the competence questions posed to climate scientists are so basic, and their failure so blatant, that trusting them shouldn’t even be an option.
— instruments aren’t calibrated? Aren’t installed properly? Never bothered to check?!
— models fail basic forecasting principles? No verification or validation?
— computer code is a disastrous mess? No quality control?
— Statistics are routinely butchered? Adamant refusal to get help from qualified experts?
— Refusal to audit or replicate studies? Or share data and methods?
— Peer review process manipulated? Assessments blatantly dishonest?
— false doomsday predictions have a long history. Always wise to view with suspicion.
Any economist who blindly accepts the opinion of supposedly expert climate scientists in the face of that level of incompetence should have his own competence viewed with deep suspicion. Rule #1 — don’t sign your name and put your own expertise on the line without some minimal level of due diligence. Anyone foolish enough to disregard this basic rule is raising a very large red flag regarding his own competence.
The base condition of the 1/2 degree of temperature rise is based on CO2 emission scenario’s.
India was believed to have 114 years of proven domestic coal supplies as recently as 2008.
Recent news is that India has become a net importer of coal and will need to import as much as 200 million tons/year beginning in 2012.
In 2006 China who had what was believed to be the worlds 3rd largest coal reserves became a net importer.
Of course the EU has been a net importer of coal for quite sometime, importing 40% of its coal.
Then if we look at the Saudi Arabia of Coal, the US, coal production east of the Mississippi has declined from 600 million tons of coal to 400 million tons of coal per year.
In the Atlantic basin, there are 2 major exporters of coal, South Africa and Columbia. Both China and India(pacific basin) are now importing from Columbia.
I am not a statistical person so I almost never comment at this site. However I would like you to discuss Polynomial Cointegration and how it disproves AGW. Michael Beenstock and Yaniv Reingewertz at Hebrew University in Israel say that AGW is now disproved. Thank you.
Climate science is closer to economics than any other field. Both fields face the same challenges to acquire data. There are mountains of it, and much of the time the data is measuring the wrong thing. The data is “dirty.” The anecdotes frequently contradict the trends. From this data, they build models of complex systems. The dynamics of which are controversial.
At least the economist understands the limits of his forecast.
@Torange – is this the paper you’re referring to? http://economics.huji.ac.il/facultye/beenstock/Nature_Paper091209.pdf
Harrywr2,
I have a few questions about your post. The first is what the relevance of your post is to what Briggs wrote. Are you simply giving an example of a conditional? It’s not clear.
Beyond that, I’m trying to think through the connection between coal reserves and importing coal. There’s a big gap there. Coal in the ground is not the same as coal that is being taken out of the ground and used. It looks like you forgot a conditional probability there.
Let’s examine the conditional information. First, before we discuss climate change, what is “climate” anyway?
cli·mate 1. meteorology: typical weather in region: the average weather or the regular variations in weather in a region over a period of years; the meteorological conditions, including temperature, precipitation, and wind, that characteristically prevail in a particular region.
Ergo, “climate change” must be, by definition, an alteration in the prevailing weather conditions.
Nobel laureate Lederman says “the climate problem is actually worse than reported earlier.” Where? How? Is there a single case of a measurable change in the prevailing weather conditions of any region?
The prevailing weather here in Oregon is just as it has always been in my lifetime. It rains in the fall, winter, and spring, but less so in summer. Summers are quite nice, actually. The climate is coastal temperate. Sometimes it rains more, sometimes a little less, and there are other variations from year to year. But basically, the climate hasn’t changed in any significant way over the last 150 years (ever since the weather has been measured and reported).
The climate in Oregon is not like Hawai’i. It’s not even like California. It’s not like Alaska, either. Oregon’s climate is what it is, and there has been no discernible change in that. A 1 or 2 degree temperature change, on average, will not change our climate, any more than shaving 1 or 2 feet off the tops of all our mountains will change the topography in any significant way.
Therefore, the conditional probability that the climate will change is extremely small. Multiply a tiny fraction by any other fraction will yield an even tinier fraction. The probability of a measurable impact from climate change is ridiculously small.
That’s not to say the economy will not change. Oregon’s economy has gone through wild gyrations, and it’s hard to see how it could get any worse than it is now. But when our economy does change (hopefully soon), it will not be due to the climate changing, because it isn’t going to.
Lederman’s “worse than reported” is without foundation. Nothing could be worse than reporters have hysterically predicted. In particular, the climate hasn’t changed perceptibly, and it isn’t going to in the foreseeable future. Maybe in 10,000 years, but not in the next 40.
“Even the IPCC says there is only a 90% chance that global warming is true. ”
Can someone explain to me how IPCC can put a numeric probability like this out there? Does that number really have ANYTHING to do with probability, or is it simply the result of a SWAG by the IPCC scientists?
JAE:
Let’s see: There were 10 experts, 6 said they were 50-50 and 4 said they were 150% sure – that averages as 90% sure. QED
I’m a thousand per cent sure Bernie’s math is spot on.
JAE, I’d suspect that 9 models said 10% each, but from the IPCC AR4 WG1 TS.2:
The standard terms used in this report to define the likelihood of an outcome or result where this can be estimated probabilistically are:
Virtually certain > 99% probability
Extremely likely > 95% probability
Very likely > 90% probability
Likely > 66% probability
More likely than not > 50% probability
About as likely as not 33 to 66% probability
Unlikely < 33% probability
Very unlikely < 10% probability
Extremely unlikely < 5% probability
Exceptionally unlikely < 1% probability
The terms ‘extremely likely’, ‘extremely unlikely’ and ‘more likely than not’ as defined above have been added to those given in the IPCC Uncertainty Guidance Note in order to provide a more specific assessment of aspects including attribution and radiative forcing.
Unless noted otherwise, values given in this report are assessed best estimates and their uncertainty ranges are 90% confidence intervals (i.e., there is an estimated 5% likelihood of the value being below the lower end of the range or above the upper end of the range). Note that in some cases the nature of the constraints on a value, or other information available, may indicate an asymmetric distribution of the uncertainty range around a best estimate. In such cases, the uncertainty range is given in square brackets following the best estimate.
Chuckles:
“Unless noted otherwise, values given in this report are assessed best estimates and their uncertainty ranges are 90% confidence intervals”
How can you construct a “confidence interval” on the likelihood that my SUV is contributing to warming? It looks to me like IPCC here is trying to look much more “scientific” than they are?
JAE,
Regrettably I am not a recipient of any largesse or bounty from the IPCC, I merely cut and paste the stuff from their documents. As I understand it, the table is a 2 way street.
Confidence Interval
e.g. If one of their authors, after careful consideration uses the phrase ‘Very Likely’ then they have great confidence in writing 90%, after consulting the table for a suitable interval of course
Similarly, if they read 30%, they could confidently state ‘Unlikely’.
Each of 6 models say that there will be catastrophic warming are 35% accurate. The probability than none are right is less than 10%.
(1-(1-0.35)^6) = 92%
“Climate science is closer to economics than any other field”
Indeed, neither is actually a science.
sorry :(.
kdk33,
Stan Kelly Bootle had a definition for Computer Science that I think could very eawsily be extended to ‘Climate Science’
‘It manages to combine aspects of Astrology and Numerology, without the success of the former, or the precision of the latter.’
Economics is a social science that likes to pretend that it is a hard science.
JAE:
They were using some kind of delphi technique – which is based on the assumption that all the experts cannot be wrong…except, of course, when they are. It never really worked for the Greeks and there is no reason to believe that it will work for the IPCC. Actual evidence includes this year’s NCAA men’s basketball tournament. Rankings are expert judgements.
Doug M.,
There is something amiss with your logic. The math is correct, I’ll give you that. Imagine a convention of 100 astrologers, and they all predict some event, let’s say an earthquake. Let’s also say they are kooks, and are only likely to be right 1% of the time.
The math: (1-(1-0.01)^100) = 64%
But let’s say instead that there are 1,000 astrologers at the convention. Then the equation
(1-(1-0.01)^1,000) = 100% — virtual certainty.
However, they are kooks. Just because 1,000 kooks agree on some prediction, it doesn’t make that prediction valid.
In this case we have 2,000 self-selected “scientists”. They don’t know the future any more than astrologers do. We can give each of them a 1% chance of being correct. The math is undeniable; their group consensus prediction yields virtual certainty that at least one of them is correct.
So there’s something wrong there. I can’t put my finger on it. Help me, oh you gurus of logic.
Uncle Mike,
Your example is so important, it will show up in Part II.
Pingback: William M. Briggs, Statistician » 2000 Scientists Demand Climate Action! Part II
Mike D. “Oregon is just as it has always been in my lifetime”
Sorry Mike, I would tend to disagree. I have an apple farm in NE Oregon. Shortly after I was born we had a freak fall freeze that killed the fruit trees (around 53 I think). All during my youth we had many spring freezes that killed the blossoms. After I went to college in the 70s, the freezes stopped. After my father died and I took over the farm, we haven’t had any bad spring freezes.
While I’m only talking about a 50 year variation, I believe the climate has definitely gotten slightly warmer in the spring. This year we expect to see blossoms about 2-3 weeks early.
Now the real questions is 50 years long enough to see a trend? I don’t think so. It could get colder in the near future. There is also the question is this caused by man made actions or is it natural warming from the last ice age?