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A physicist does Bayes

Physicist and science writer Jon Butterworth has written a layman's introduction to Bayes' theorem, touching at one point on its use in climate change:

If you have a prior assumption that modern life is rubbish and technology is intrinsically evil, then you will place a high prior probability on Carbon Dioxide emissions dooming us all. On the other hand, if your prior bias is toward the idea that there is massive plot by huge multinational environmental corporations, academics and hippies to deprive you of the right to drive the kids to school in a humvee, you will place a much lower weight on mounting evidence of anthropogenic climate change. If your prior was roughly neutral, you will by now be pretty convinced that we have a problem with global warming. In any case, anyone paying attention as evidence mounts would eventually converge on the right answer, whatever their prior - though it may come too late to affect the outcome, of course.

The use of Bayes' theorem in climate science is so much more interesting than this: as readers at BH no doubt know, the IPCC's use of a uniform prior in ECS for its "neutral" starting point biased the posterior towards higher estimates of future warming. Secondly, do we really have "mounting evidence"? Surely what we have is comparisons of unvalidated physical models to observations.

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Reader Comments (36)

Interesting that he says that a neutral prior leads you to believe we 'have a problem' with global warming not that there is/has been global warming.

I think _his_ prior is skewed.

Sep 29, 2014 at 10:02 AM | Unregistered CommenterClovis Marcus

I like the extreme nature of his typical a priory 'denier'. How about a little survey, how many of you here drive around in a Humvee exactly? Personally I drive a Saab 93 diesel estate, it does about 50 to the gallon and during the summer I don't even drive it that much because I commute on a push bike. I became an unbeliever as the evidence mounted that climate alarmism is nonsense.

Sep 29, 2014 at 10:17 AM | Unregistered CommenterStonyground

Yet again the false dichotomy fallacy.

Rather if you know that fossil fuels are necessary to avoid mass starvation whether we like them or not and that they have afforded us the time and opportunity to obsess about 0.6K/century of warming plus the media to vent our angst rather than spending every waking moment just surviving on this hostle planet, then you are more inclined to be suspicious of doom-mongers who have been consistently wrong in the past.

The only mounting evidence in the real scientific results, as opposed to pessimistic anecdotal evidence and flawed assumptions, is that the poorly-founded notion of CO2 as a climate driver is holed below the waterline. It is not the skeptics causing the trouble to this simplistic 2-variable linearised reductionism of a complex, multivariate, nonlinear, chaotic system, it is only mother nature making fools of the hubristic once again.

None of this would matter though if it was just an academic dispute and it didn't cause an energy crisis so that the most vulnerable have to now choose between heating and eating. Whither all this sanctimonious hypocrisy when that happens? What does he drive, how does he heat his home and where did he holiday this summer?

Sep 29, 2014 at 10:18 AM | Unregistered CommenterJamesG

I have a prior assumption that modern life is rubbish and (some) technology is, if not intrinsically evil, then certainly of dubious value to human progress and in some cases detrimental and restrictive of the right to a private life. I also have a prior assumption that science works by the progressive confirmation of theory based upon the accumulation of supporting evidence, or the dismissal of theory based upon the accumulation of contrary evidence. This, rather curiously, does not result in me placing a high prior probability on Carbon Dioxide emissions dooming us all.

"On the other hand, if your prior bias is toward the idea that there is massive plot by huge multinational environmental corporations, academics and hippies to deprive you of the right to drive the kids to school in a humvee, you will place a much lower weight on mounting evidence of anthropogenic climate change." Doesn't say half as much about the prior bias of sceptics as it says about Jon Butterworth's prior bias, methinks.

Sep 29, 2014 at 10:26 AM | Unregistered CommenterJaime Jessop

"In any case, anyone paying attention as evidence mounts would eventually converge on the right answer, whatever their prior - though it may come too late to affect the outcome, of course."

I thought what was pretty objective and very well stated.

Sep 29, 2014 at 10:30 AM | Unregistered Commentermrsean2k

"In my last post I dipped my toe into some statistics, ...."

This sums his Guardian article up. Perhaps he should stick to high energy physics.

Sep 29, 2014 at 10:37 AM | Unregistered CommenterCharmingQuark

The only 'mounting evidence' is mounting evidence of alarmists unjustly and repeatedly arguing by assertion that there's 'mounting evidence' to support agw theory - when in reality there's mounting evidence that the theory is collapsing right in front of us due to diminishing (or non-existent) evidence from observations.

Glad that's sorted, then.

Sep 29, 2014 at 10:41 AM | Unregistered CommenterCheshirered

'evidence mounts'

Well, there IS and Evidence Mountain, and AGW is getting pretty thoroughly buried beneath it. Not quite sure that is what he meant, though.

Sep 29, 2014 at 10:41 AM | Unregistered CommenterOtter (ClimateOtter on Twitter)

The point of Bayes is that by updating the estimate (which begins life as the prior) with successive observations, it iterates to eventually converge on an actual (probability).

In this sense it like any overdamped feedback control system, and thus familiar in a different guise to engineers who play with such beasts on a fairly regular basis.

Things like a "uniform" prior are all fine and dandy, but what matters a great deal is the observations, the and the continual updates made. It might be claimed that the prior is uniform but that of itself might be subjective. In the end with enough observations it also does not matter what it was. However, honesty in the observations (as well as having enough of them) is jolly important.

Sep 29, 2014 at 11:19 AM | Unregistered CommenterWally

Can it be a Bayesian problem when the questions is it CO2, is it us and is it catastrophic are all capable of being answered without a statistical model? Or is my idea that there is such a thing as truth merely a delusion?

Sep 29, 2014 at 11:22 AM | Unregistered Commenterrhoda

Butterworth should look in a mirror and ask himself about his priors.
Otherwise, one might easily confuse him for a fool.

Sep 29, 2014 at 11:29 AM | Unregistered Commenterhunter

He can't even spell his name correctly. How can we take his views seriously?

Sep 29, 2014 at 11:34 AM | Unregistered CommenterJohn Marshall

Apparently if you are a believer then your 'prior' is zero and won't be changed by evidence, such as a lack of actual Global warming despite introvertible 'evidence' from the models, people hiding declines and the fact that the '97% of climate scientists' story is clealy bollocks.

On the other side of the argument, íf we tend to be sceptical of all new evidence that contradicts our viewpoint, then are we not guilty of the same?

Sep 29, 2014 at 11:38 AM | Unregistered CommenterFarleyR

I must confess I did not have a neutral prior - given all the Chicken Little scares which have come and gone in my lifetime, I was somewhat biased against it. But, then I read a little of the evidence, and became slightly in favor. Isn't that, on average, the same as a neutral prior?

Then, of course, I read a lot of the evidence, and took a decided turn to the Dark Side.

Sep 29, 2014 at 11:45 AM | Unregistered CommenterBart

Jon Butterworth's own “priors” are very much on display: “…you will place a much lower weight on mounting evidence of anthropogenic climate change.” What “mounting evidence”?

If your prior was roughly neutral, you will by now be pretty convinced that we have a problem with global warming.” Do we? Please explain WHAT problem we are having with global warming. One would have thought that a physicist of reasonable quality would have been sufficiently neutral not to conclude that a cessation of rising temperatures does indicate that there really is no problem. For a problem to exist, it has to actually... well, exist; just saying that it exists is not sufficient for its existence to be so.

…though it may come too late to affect the outcome…” Now, he is assuming that it might be possible to affect the outcome, as well as the implication that the outcome will be dire.

That said, he has spawned some interesting comments, which is a refreshing change from the usual crop of bile.

Sep 29, 2014 at 11:46 AM | Registered CommenterRadical Rodent

I was trying to recall the details of the meeting at which climate scientists were (allegedly) invited to give extreme priors as input to the climate sensitivity problem. Can someone jog my memory?

Sep 29, 2014 at 12:39 PM | Unregistered CommenterDr Slop

If it is in the Guardian, my prior is to be skeptical.

Sep 29, 2014 at 1:30 PM | Unregistered Commenterbernie1815

Bayes is often the last resort of a sociologist. So why am I not surprised to see someone using it to make claims about global warming in The Guardian?

Sep 29, 2014 at 1:50 PM | Unregistered Commentermichael hart

My prior is that the climate system is insensitive to CO2 concentration. The evidence is mounting that I was correct all along.

Sep 29, 2014 at 1:51 PM | Registered CommenterPhillip Bratby

It is funny that Clutterworth did not mention the exception that a prior with probability 1 is meaningless as well.

When P(B) =1, P(A|B) always is P(A). So assuming that Clutterworth takes the extreme sceptic having a prior 0 for AGW, the believer in all things green would have a prior 1 about AGW, resulting in the probability of AGW being the probability of AGW.

Also a closed mind? Then that should have been mentioned in the treatise as well.

Sep 29, 2014 at 1:58 PM | Registered CommenterAlbert Stienstra

Bayes' theorem is just one aspect of the mathematics of probability and statistics, but somehow it has acquired almost mystical and religious significance, as in "I'm a Bayesian". Surely a marriage made in heaven with climate science, though of course hell for everyone else.

There is NO branch of mathematics (not even the fabled maximum entropy method) that can make silk pulses out of crappy data fed into crappy hypotheses. Religions and cults have no problems with such inputs.

Sep 29, 2014 at 2:28 PM | Unregistered CommenterMikky

I don't understand his point. I don't believe in something unless I am convinced by the evidence. That's how science works isn't it?

Sep 29, 2014 at 2:39 PM | Unregistered CommenterTIm

Apologies for writing "Clutterworth". I should have written "Butterworth", but my memory slipped...

Sep 29, 2014 at 2:42 PM | Registered CommenterAlbert Stienstra

My 'prior bias' is I have seen no evidence which supports CAGW, but some evidence which contradicts the assertion and suggests nobody really understands how the Earth's climate works.

Where do I fall with respect to the neutral line?

Sep 29, 2014 at 3:04 PM | Unregistered CommenterJohn B

Cheap access to abundant fossil fuels.

"deprive you of the right to drive the kids to school in a humvee"

or perhaps deprive the third world the chance to fully industrialize and lift themselves out of poverty.

Sep 29, 2014 at 4:54 PM | Unregistered Commenterjamspid

Sounds like waffle. If you're using Bayesian inference to test whether one or two hypotheses is correct, and as long as you use Bayesian recursion (update the prior with each new posterior) I'd think,and no matter what the nature of the original prior was, the use the answer will drift toward "not a problem". If we'd done this experiment from 1998 on wards that is what you'd find.

Sep 29, 2014 at 5:00 PM | Unregistered Commentercd

Butterworth says towards the end of the article:-

There is an exception to this, worth noting.
A prior assumption of zero probability can never be changed. Thus, for example, if you absolutely believe that the Earth is 5000 years old or so, no amount of evidence can change your mind.

However, this is not an exception, but the most extreme example of bias. When more objective data comes along, then true Bayesians should update their estimates. As a result the impact of subjective priors should diminish, and convergence occur between different priors. But if people have a bias towards one set of results, then confirmatory data will be accepted, and divergent data will be rejected. So the low Arctic sea ice minimum of 2012 was for the climate consensus a confirmation, and for sceptics explained by extreme storms. Conversely for the current hiatus in global warming the climate consensus has numerous ad hoc justifications, whilst for sceptics it shows the climate sensitivity assumptions in the climate models need revising downwards.
For Bayesian methods to work well requires positive attitudes towards eliminating bias, not excuses to maintain existing beliefs. That in turns means developing standards of evaluation and having an openness to criticism. Instead we have PR consultants keeping everybody to the doctrine by attacking “misinformation”. What we end up is not a convergence of subjective estimates to the real world, but evermore entrenched positions based on claiming they have science on their side.

Sep 29, 2014 at 5:01 PM | Unregistered CommenterKevin Marshall

Having some experience of Bayesian statistics I must say that I am somewhat confused by the term ”neutral prior”, since as far as I know there is no such thing. If Butterworth means a non-informative prior it would indeed be very useful to have one. Unfortunately while a non-informative prior can be defined for cases with discrete outcomes, the search for a non-informative prior in continuous cases has been described as “the holy grail” of Bayesian statistics for good reasons.
Indeed the more perspicacious Bayesians accept this and openly state that Bayesian statistics is inherently subjective (see e. g. J. M. Bernardo & A. F. M. Smith Bayesian Theory, especially Ch. 5). This is something that most non-professionals are probably unaware of.

Sep 29, 2014 at 5:37 PM | Unregistered Commentertty

Perhaps a short note on the use of flat priors is also in order, since some people seem to think that they are somehow non informative. Nothing could be more wrong. A flat prior (which must have a finite length) implies that you know with absolute certainty that the value of the quantity you are studying is within a certain range, but that you have not the slightest idea where it is within this range, a case that virtually never occurs in practice.
IPCC:s use of a flat prior from 2 to 10 degrees for climate sensitivity would make an excellent textbook case. It implies e. g. that it is twice as likely that climate sensitivity is more than 9 degrees than that it is less than 2.5 degrees, and that it is infinitely more likely to be 10.0 degrees than 1.99 degrees. This is of course not “non-informative”, and I think that when formulated like this even most “climate scientists” would agree that it is actually a rather bad prior.
However it is very useful for adding a nice, fat hig-sensitivity tail to any measurements resulting in low climate-sensitivity figures.

Sep 29, 2014 at 5:56 PM | Unregistered Commentertty

Jamspid (Sep 29, 2014 at 4:54 PM): ah, but those in the third world are living the agrarian idyll that those like Butterworth would have us aspire to (probably while maintaining his “right to drive the kids to school in a Humvee”), they just don’t know it, dazzled as they are by the adverts pumped at them continuously by Big…. whatever, blinded into buying ever more of the luxuries we consider standard (good health, adequate food, electricity, clean water, clean air…).

Sep 29, 2014 at 6:07 PM | Registered CommenterRadical Rodent

Great posts by Kevin M and tty: there are a lot of people spouting nonsense and calling it Bayesianism. As one of (now Sir) AFM Smith's less diligent pupils I learned enough Bayesian statistics to understand the need for great diligence in incorporating new information, and it appears that as Kevin says people's prejudices show up at least as much in their selection and use of new data as in their selection of prior.
It may be my own prejudice here, but I can't see how after 18 years of effectively flat global temperatures anyone can honestly have increased their confidence that there is a dangerous underlying temperature trend or that CO2 emissions have caused most or all the warming over the last 100 years. You could go from near-certainty to strong confidence, or from strong confidence to weaker confidence, but I have no idea how an honest person calling him or herself a Bayesian could be travelling in the opposite direction.

Sep 29, 2014 at 6:55 PM | Unregistered CommenterDavid S

Sigh. In the Seventies (IIRC) people used to spout a whole pile of BS about the world based on some analogies to Heisenberg's Uncertainty Principle. Usually waffle along the lines of things basically being unknowable. Those people were taking a valid theorem, and applying it outside any meaning it might have.

I truly hope that people don't start waffling on about Bayesian Statistics the same way. The use of Bayes in a case like this, where it most certainly does not apply, is to astound the masses with your erudition. If he doesn't include any numbers, let alone equations, it's not maths, and so it's not probability.

Please don't argue with him about what your own "prior" was. Tell him to shove off with his pseudo-science BS and come back talking sense using clear language that everyone can understand.

After all, he is merely saying that some people start decided one way, some others the other, and some are undecided. After the passage of time a consensus will be reached. Like that needs Bayes in any way.

On top of that it is also dubiously true. People have been arguing about right and left wing political alignments for as long as the French revolution. Yet they show very little sign of coming to an agreement which is best.

Sep 29, 2014 at 9:26 PM | Unregistered CommenterMooloo

Vehicles: when I have a job requiring a real commute (at present it's from my bedroom to my spare bedroom) I use an 1100cc BMW motorcycle that though rather large gets 50-60 mpg. When more people and/or stuff requires transporting I have a medium sized 2.5l Subaru station wagon ("Grandwagon", which means early "Outback") which gets 30 mpg normally, 35 on a trip.

While newer vehicles may be slightly more efficient, the fact that my vehicles were made in 1995 and 1997 and I'll probably use them for another decade means the resources used in manufacturing are getting well and truly amortised.

As my fuel bill is about 1500 pounds a year, and the best current (non electric) car might save at most 500 pounds of that, it's not worth spending more than 5000 quid in capital to get that more efficient car. Which is, basically, impossible at this point.

And both my current vehicles remain reliable, capable, and actually quite fun.

Sep 30, 2014 at 3:51 AM | Unregistered CommenterBruce Hoult

If you think evidence for human-induced global warming is "mounting" you have a prior at odds with the actual evidence.

Sep 30, 2014 at 9:06 AM | Unregistered Commenterchip

I am a retired scientist and throughout my professional life, I regarded the Null Hypothesis as the Gold Standard for experimental science and it has been so for the past 250 years or so as far as I am aware. You design your experiments to prove your assumption is wrong, not right, hence avoiding any potential bias.

The trouble with 'in silica'-based modelling, such as climate change modelling is that it is based on a positive hypothesis, and, if you do get any real-time data that contradicts the hypothesis you just 'tweak' it to hide the anomaly.

It is fundamentally and absolutely bad science - you cannot develop an accurate computer model based on a positive hypothesis, unless you are 100% certain of the assumptions on which it is based - in which case you don't need the model, because you already know the answer

Sep 30, 2014 at 5:38 PM | Registered CommenterSalopian


you cannot develop an accurate computer model based on a positive hypothesis

It could be just a case of semantics, but is your model (computer or otherwise) not the hypothesis. The null hypothesis is that it is wrong. Run the experiment and test it. I suppose which is the best method to assess this is the main point being discussed (Bayesian vs Frequentist); and if Bayesian how do you select the hypotheses prior pdf.

Oct 1, 2014 at 12:17 AM | Unregistered Commentercd

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