The Button Collector or When does trend predict future values?

I think that makes it very clear. It was also a fun read. Thank you.

He will have between 0 and a googleplex of buttons. I’m 95% certain of it.

author is getting on a high horse over words. I’ve used trends to predict the future b4. Distinguishing between models and statistical trends is a grey area.

Based on current trends, how many months until WUWT reaches 2 billion views? I guess this cannot be safely predicted as unforeseen events may change current viewing habits.
I am astounded, as a dedicated visitor since well before Climategate, at how rapidly the number of views is mounting – around a million a week. Astounded, but not surprised. Congratulations, WUWT!

Two weeks on, the number of buttons was found to have been constant for 17 days. I understand that this matter was then considered by the IPCC (Intergovernmental Panel on Clasps and Closures) and they reached a consensus opinion that, as 10 of the highest observations of number of buttons were made in the previous fortnight, the collection of buttons was clearly continuing to grow.

So, just because there has been a pause in rise of global mean surface temperature does not mean we can reject the physics of global warming? Rats.

Climate variables are not Martingale variables.

Trends which are stable despite a variety of potential disruptive events over the observed period will induce some confidence that it will continue. Trends which wobble in response to interventions may give some indication of causality. Climate science has neither.

It was interesting and informative to read the comments at Dot Earth Kip Hansen. Even relatively intelligent posters have difficulty understanding this simple concept that trend of the past is not necessarily predictive of the future especially at longer time scales. It is clear that many do not understand the complexity of the solar, ocean, atmosphere coupled dynamics. It was especially interesting that your link to Marcia Wyatt’s new paper was ignored. Much has been ignored regarding the oceans while focusing on the atmosphere over the last twenty years.

OMG buttons cause global warming.

Trends are an illusion

But half the articles on this site back predictions based on trends, usually of the form “it is going to get colder”. Are you saying all these articles are worthless?

“The trend is utterly useless as a predictor — always.”
This is absolutely incorrect. In the absence of any other data, past trends are the BEST predictor of future values.
This entire article shows a complete failure to understand statistics. Statistics can be used to make predictions, based on certain assumptions. If those assumptions are correct, the prediction is MORE LIKELY to be correct. If the assumptions are wrong, then the prediction is LESS LIKELY to be correct. No where are guarantees made.
The correct prediction in the article would have been “Given the assumptions we are making (iid, normal, etc), we predict that it is most likely that there will be 110 buttons, give or take (a very large number).” No statistician would EVER say “There WILL BE 110 buttons.” Because statisticians actually understand statistics.
“We can’t know the future” is an utterly silly argument. Will the sun rise in the East tomorrow? I hope you didn’t say “yes”, because you can’t know the future! If I let go of this pencil I’m holding in the air, will it fall to the ground? I hope you didn’t say “yes”, because you can’t know the future!
Bah. The only thing this article shows is how many supposedly educated people can utterly fail to understand simple concepts. Statistical predictions are not Truth, they are well formed Guesses. And guesses can be wrong. Anyone, like the author, that fails to understand this should stay well away from statistics.

Mark XR says:
October 17, 2013 at 8:23 pm
So, just because there has been a pause in rise of global mean surface temperature does not mean we can reject the physics of global warming? Rats.
If you mean, post modern IPCC physics, that CO2 is the key driver of modern climate change, yes we can. Historical evidence has all but debunked the correlation between global temperature and CO2.

You are correct – stats are only as good the information entered. And as always there are as many economists predicting the future as there are economists. One may as well watch Star Trek. No matter what anyone says here – whatever their forward programing it is a guess based on a past that may or may not be anywhere near accurate. Regards to inventory – how often shelves are without a product is common. If climate is an indication then it is no wonder why models are next to useless. What we do know is there are ice ages and interglacial periods. The rest our present understanding is next to nil – like the weather.

How do you know that BC is reporting the number of buttons accurately? What if his buttonometer hasn’t been calibrated. What if he is in an Urban Button Island. Maybe he adjusted the count to conform to the Summary for Button Makers.
Heh – there haven’t been any buttons for 17 years.

In the UK, I think the few minutes spent reading this article would be of great benefit both to Ed Davey (if he is capable of understanding it) and Sir Mark Walport, as well as several members of Parliament’s Energy and Climate Change Committee.
“Back to basics” on the use of statistics, with a reminder of the number of potential interconnected variables that might contribute to a model of global climate, should get them to pause for thought. Clearly this will not happen, because we are dealing with a religious type of belief (which history shows us is all about the political power to soak the poor), not statistics or science.

Past performance etc does not guarantee future returns, is a caution given to any small investor in the UK. However past behaviours do indicated the likelihood of future behaviours. When working in forensic mental health we used various tools to assess the risks patients with mental health problems who were also offenders posed to society. These assessments were in the main pretty useful. These type of assessments can also extend to how a person will react to a given piece of research. If they have always rejected a certain stance in the past, they are likely to do so again whatever the quality of the study. This underpins my belief that there is one heck of a lot more subjectivity in Climate science than we recognise, and a stance that makes me unpopular with both the consensus and skeptic side, many of whom like the reassurance of definite indisputable facts. From a personal perspective I see two general trends in opinions, but millions of different specific views on the issue, a number usually correlated to the amount of people who are asked.

If you think this is wrong – consider investors in stock markets whose whole living is dependent on picking trends in data and then working out when the data has gone off trend in a significant way. Like climate researchers and climate , each investor does not need to know the detailed internal workings of a company to be able to see when the data is straying off trend and a buy/sell decision be made. I dont need to know anything about the science of climate change to see its drifted off the IPCCs trend and the whole AGW/CO2 business is now a SELL option. There was an excellent post just the other day on this very topic.

In my humble opinion, whenever anyone compares any scientific statistical argument to the stock market, they’ve lost the plot.
When I take a hot caserole pot from the oven, I use oven gloves so that I don’t burn myself. An hour later, then I take the same caserole pot from the table to sink, I don’t use oven gloves. I have successfully predicted the future. Sure, I can’t know the exact temperature, but I can be pretty sure it will be close to room temperature. I can even take a few temperature readings soon after removing it from the oven, and make a pretty good guess at when it will be comfortable to hold the pot.
Note that unlike the stop market, this is unlikely to be affected news of some CEO having an affair, or by whether the Republicans and the Democrats agree on some particluar financial arrangement. Unlike the stock market, the pot is unlikely to be impacted by whether some trader had a headache this morning. Comparing the two is stupid
In fact, the author of this posting completely agrees. He says:

Armed with this secret formula, which is precise and immutable, we can now adjust our model of this button collecting process.

And here we get to the climatology comparisons. Some climate scientists seem to believe that they know the secret formula – in fact, they go further and claim it isn’t secret, but common knowledge based on physical principles – and using this formula they can predict the future using computer-based models. Other scientists, and much of the WUWT readership, believe that the formula is too simplistic, that it doesn’t allow for a variety of internal and external influences, or that it is tuned incorrectly so that some real influences (such as CO2 forcing) are assigned too much of an influence.
But it isn’t the stock market. And it isn’t some random collection of buttons. So don’t make a silly comparison to ‘prove’ a point.

In the example given, by analysing all past data, you would be able to make a prediction to some level of confidence (say 90%) what the minimum & maximum number of buttons the next day was likely to be. This is done all the time in many fields – for example we don’t know how many particles a radioactive source will emit in the next minute, and we don’t know the underlying mechanism which causes a particular atom to split, but we can estimate a range of values and we can use that knowledge for useful purposes (in a nuclear power station for example). To characterise this nuanced outcome as “We have no idea how many buttons he will have Friday night because we cannot see into the future” is absurd and just plain wrong – we have an “idea” but we don’t know for certain.

On statistics, it is estimated that 50% of all people who have ever lived on earth are alive today. Does this mean I only have a 50% chance of dying? 😉
Of course this post is overly simplified, it’s loosely applying the ad absurdum rhetorical tool. I’m sure most folk frequenting this particular virtual space are perfectly aware that in practice we can attach PROBABILITIES to certain potential outcomes based on HISTORICAL trends derived from hard data.
Nothing wrong with that, and many people base important decisions (investment, policy, research, travel, etc.) on that very concept. In fact we all do this constantly. It’s an integral part of human existence. From the moment we wake up of a morning, we expend a great deal of mental energy throughout the day subjectively assessing risk on the basis of the cognitive models we have constructed over time in accordance with the lessons life has taught us (just take the drive to work, for instance). It’s part of the subjective cost/benefit analyses that life demands of us all continually, and we are all far more adept at it than many people realize. (Indeed, the better we are at this, the more Antifragile we become.)
The point is, there is a huge difference between modeling probable outcomes of physically quantifiable processes, and modeling trends arising from human action. The former entails a higher objectivity quotient, the latter a great deal more subjectivity, thus making it less predictable based on existing trends. And I think that that is an important distinction to make in this thread. (I call this distinction the Light/Life Ratio.)
However, both types of forecasting are at all times subject to Taleb’s now proverbial Black Swan Event (meteor impact, unforeseen geoplitical event, etc.). Obviously, therefore, even the highest probabilities properly assinged to a given trendline can miss the mark completely. And it’s this fact that I think Kip Hansen is getting at here when he asserts we cannot predict the future using past events.
I imagine that the above is as plain as a pikestaff to most folk here, but I suspect that there are a great many others for whom this is not so obvious. And it’s their hearts and minds we seek to win from the prophets of the Great and Terrible Day of Global Thermageddon!
Just remember, “He is no friend that guides not, but ridicules, when one speak from ignorance”.

I would add a caution to the author’s conclusions. No matter how perfectly one understands the underlying causes of a phenomenon, models will still utterly fail if the phenomenon being modelled is inherently nonlinear. As a simple example, consider orbital mechanics. We understand Newtonian mechanics (as modified by relativity) with sufficient precision to be able to predict the ground paths of solar eclipses, the trajectory of Voyager or Cassini, or the return of Haley’s Comet. These are linear systems and thus can be modelled with some predictive accuracy. However, a nonlinear system (like weather) cannot be modelled over any significant duration because it is sensitive to infinitesimal changes in starting conditions. Nonlinearity prevents prediction over anything beyond the shortest timelines. Lorenz recognized this in the 60s, and the IPCC acknowledged it decades ago (and then promptly swept scientific reality under the carpet and spent the next several years desperately clinging to a politically approved but empirically falsified hypothetical linear relationship between anthropogenic CO2 emissions and delta T).

This issue was treated once very well by Karl Popper, e.g. in The poverty of historicism. Is has nothing to do with statistics as it can be summarized by his statement that regularities or not laws of nature. Even the sun-rise tomorrow is not a law of nature and cannot be predicted. We do not even know the probability of this event.

Hi, Kip. I’m afraid I agree with Fred (the Statistician) above, and others who have made similar comments. I think you have gone quite overboard by saying we have “no idea” what will happen next. This is the sort of black and white thinking that gets a lot of people into rhetorical trouble. Statistics is not about black and white – it is about quantifying the grey.
On a related point, you said “Models, not trends, can predict, project, or inform about possible futures, to some sort of accuracy.” This is true, about models, but it is (of course!) also true about trends. You then add, “Models must include all of the causative agents involved which must be modeled correctly for relative effects.” This is absolutely incorrect.
Models *never* include “all of the causative agents involved.” Never. A model is a simplification of the real world. By definition, some things are left out. We hope, when building our model, that only trivial causes (or trends) are left out, and what we have is a pretty good approximation. But models are always a simplification of the real world.
Further, it is entirely reasonable to sometimes leave out ALL causative agents. This would be an empirical model – i.e., a model based only on data, and one that tries to capture or describe the trends found in our data set. Absent any other knowledge, an empirical model will be the best predictor of future values – i.e., better than random guessing (which – absent any other knowledge – would be our only other option.)
Finally I would submit that empirical modeling is always the first step of any attempt to understand a phenomenon. That is, it is the first step in the scientific process. You first notice a pattern in nature or society. You try to describe that pattern, and – if it persists to some degree – you then investigate the pattern to look for causal agents – the underlying mechanisms that produce the pattern. But you have to notice the pattern first, and “noticing a pattern” is another way of saying “building an empirical model.”
The Theory of Gravity is the classic example of this. The empirical results are so thoroughly robust and understood that we even call it a Law. But we don’t know what “causes” gravity … we can model it very, very well, but we don’t know the cause. (Yes, there are a few hypotheses of late; but these are as yet uncertain.)
Cheers.

If every event is causally related to every other event, past or present, forming a compete model is a forbiddingly large enterprise. Worse if the causal relations are non-linear. In brief – trends and models are just masks to conceal our ignorance. However all is not lost – we can and do form very accurate predictions – so accurate that they are ALWAYS correct.
If I am x% (it does not matter what value ‘x’ has – this does not affect the accuracy of our prediction) certain that the sun will or will not rise tomorrow. So long as I do not claim perfect knowledge or absolute certainty, I shall always produce correct predictions; even better, I can never produce wrong ones!
This is why IPCC and all the other quacks playing with models/ and trends to produce forecasts/predictions can continue to syphon money from tax payers – they are never wrong! Even if their predictions never correspond to the events, they can (and do) claim increased confidence in the skill of their models and they can justify whatever causal relations they may fancy – yes – even that Great Greenhouse in the Sky!

@acementhead
Point taken, sorry for being so sloppy! However, it was only meant as joke about how statistics can be used to assert any nonsense (hence the winking smiley). But I consider myself suitably chastised…
Here’s a good link to support acementhead’s correction of my spurious nonsense:
http://www.prb.org/Publications/Articles/2002/HowManyPeopleHaveEverLivedonEarth.aspx
Do you agree though, acementhead, that statistics can and are used to support all manner of claptrap?

mhx says:
October 18, 2013 at 2:06 am
“Suppose that a car at a distance of 500 meters starts driving in your direction and for 490 meters it drives in a straight line at constant velocity. What would you do? “
—————
I would predict that the right-front tire would “blow-out” at the 492 meter mark and the car would veer off the road and crash. That is unless my earlier prediction proved to be correct that it would run out of fuel at the 491 meter mark. 🙂
Predicting earth’s climate for the next 100 years is akin to predicting Super Bowl or NBA winners for the next 10 years. Iffen you think you can, …. go for it, ……. place your “bets” today.
If one could magically remove all of the CO2 from the atmosphere there would be no measurable effect/change in the near-surface air temperatures and that is because 398 molecules of CO2 are irrelevant when intermixed with 20,000 to 40,000 molecules of H2O vapor.
Thermal energy in the near-surface atmosphere is NOT cumulative from one (1) week to the next and surely not one (1) year to the next.

@ William Abbott
Yes, William, of course you are right. But I was trying to tie off a potential off-topic discussion started inadvertently by myself due to my own laxity. Accepting I had been sloppy and acknowledging that an acceptable guesstimate might be closer to acementhead’s 7% was my way of willingly giving ground on matters of little consequence so we could all focus on more important aspects of this discussion.
Though I’m sure we could all have a jolly interesting and constructive discussion on estimates of earth’s past population, this is neither the time nor the place…

” Fred the Statistician says:
October 17, 2013 at 10:38 pm
“The trend is utterly useless as a predictor — always.”
This is absolutely incorrect. In the absence of any other data, past trends are the BEST predictor of future values.
This entire article shows a complete failure to understand statistics. Statistics can be used to make predictions, based on certain assumptions. If those assumptions are correct, the prediction is MORE LIKELY to be correct. If the assumptions are wrong, then the prediction is LESS LIKELY to be correct. No where are guarantees made.
The correct prediction in the article would have been “Given the assumptions we are making (iid, normal, etc), we predict that it is most likely that there will be 110 buttons, give or take (a very large number).” No statistician would EVER say “There WILL BE 110 buttons.” Because statisticians actually understand statistics.”
__________________________________________________________________________
And don’t Climate Alarmist Scientists say there WILL be catastrophe? And do statisticians actually understand statistics? I doubt it. Some statisticians understand some statistics and that would be as far as I would go.
“A Crooks says:
October 18, 2013 at 12:30 am
If you think this is wrong – consider investors in stock markets whose whole living is dependent on picking trends in data and then working out when the data has gone off trend in a significant way. Like climate researchers and climate , each investor does not need to know the detailed internal workings of a company to be able to see when the data is straying off trend and a buy/sell decision be made. I dont need to know anything about the science of climate change to see its drifted off the IPCCs trend and the whole AGW/CO2 business is now a SELL option. There was an excellent post just the other day on this very topic.”
___________________________________________________________________________
But are you a stock investor? Do you have any idea how many 100’s of different types of charts there are and you are trying to line up a trend? I personally used about 5 different stats charts and still would get it wrong about 20% of the time. These days the really big boys use their computers and very fancy algorithms to fire out buy and sell orders but the basics are still the different statistical methods.

Having read both the DotEarth page (and its resident commenters are something else…) and the comments here, I’m somewhat bemused by the number of people who do not understand Kip’s simple message. I’m particularly intrigued by the apparent correlation between those with advanced knowledge and skills, and their lack of understanding of what Kip has written. What I do read in many posts, are rationalizations for beliefs that are based on the statistical analysis of past events.
Probabilities are not certainties. Statistical analysis allows us to take past facts and develop beliefs about future facts, but it never allows us to actually know the facts – that only happens when the future is past, and we add the future facts to the dataset.
Knowledge is always based on history. Knowledge of the future doesn’t exist. A belief about some aspect of the future is all there is. Statistical analysis and modelling provide us with degrees of comfort that our beliefs are, or are not, likely to happen, but the uncertainty is never completely quantifiable. It’s improved by the causalities we know and understand, and therefore our beliefs have a higher degree of comfort, and mathematically a higher probability of certainty, but they are never certain. Even the probability of tomorrow is not a certainty, however likely the probability is.
I note that in many comments on both sites, that individuals with high skills appear to have a stronger belief that their future knowledge is more certain. That’s a rationalization for their beliefs abut the future.
In the climate science realm, as I suspect in many sciences today, the faith in these models and tools has allowed beliefs to take precedence over facts, the implied point of Kip’s argument. As a consequence, we have predictions (beliefs) presented as certainties. and some of the most convinced that these beliefs are certainties are scientists, the group most expected to understand they are not.

Paul Coppin says:
October 18, 2013 at 5:27 am
“Knowledge is always based on history. Knowledge of the future doesn’t exist.”
Ya well, the number of buttons of the collector, just like global average temperature, is brown noise, because there is an integrating element (the existing collection / thermal inertia resp.).
That gives us a probability distribution for the result on day today+n.
Mark XR says:
October 17, 2013 at 8:23 pm
“So, just because there has been a pause in rise of global mean surface temperature does not mean we can reject the physics of global warming? Rats.”
The opposite is true. Because the Null hypothesis (that warming out of the LIA proceeds as it always has) still suffices to explain everything, we can apply Occam’s razor and discard the CO2AGW theory as unnecessary, it does not add explanative power, more likely, it WORSENs our ability to forecast.
So you warmists, predict something that we would not have been able to predict with the Null hypothesis and then you MIGHT have something. Refute the Null hypothesis. For now you have NOTHING.

The author plays with words . A trend can be a model.
Trends might indeed show the future and might indeed predict future values. The most common situation is when the trend itself affects people behavior.
We can also discuss mob or pack behavior, and “If you tell a lie big enough and keep repeating it, people will eventually come to believe it”.
After a string of defeats i can predict that a certain trainer will not be at front of that team for much longer. Will be this true in all cases, no.
Can i predict the increasing odds of a divorce based on increasing discussions between a couple? Yes i can.
Or if a new technology appears,even if i don’t know anything about it but many adopt it then it might show a trend which mean that there are odds that the current increasing trend is repeated in the future.
Of course using just this kind of prediction is typically of inferior quality in most cases, but it has its value and sometimes it is the only or less worse solution.
Quantity has a value of its own.

The thesis of this post is correct. It is also irrelevant – very few people would confuse an extension of a past trend into the future for an infallible prediction.
Consider for a moment how the intelligence of animals and, finally, humans evolved. Did it start with sophisticated statistical methods and philosophical rigour? Of course not. We have two cats at home – one smart, the other not so much. The smart one is extremely good at picking up cues. For example, at the breakfast table, I first have some toast and jam, which she doesn’t seem to pay any attention to. However, afterwards, I make some salami or chicken sandwiches for my brown bag – and she is immediately on it and reminds me of her presence. Her cue? A little break between toast and sandwich. If I happen to pause a bit longer between two slices of toast, she will show up prematurely. (This is a simplified version – she follows a whole set of cues, she really is a smart beast, and as a consequence, too fat.)
What happens if she is wrong? She walks off to return again later, and the next day she will still try the same – because this strategy soundly beats a random guess. That’s what our brains give us – educated guesses. Of course, it’s nice when we can go beyond that, but much of the time, this is what we do, and as the course of evolution shows, there is nothing wrong with it.

The academics will tell you that you are describing a purely empirical model and therefore extrapolation is not accurate. Now the learned academics build “first principles” models and therefore extrapolation is possible. For example, one can theoretically calculate the trajectory of a projectile based only on velocity and angle of departure from the horizon (assuming no air resistance, etc.)
But that’s where the learned academics fool themselves: they don’t really ever know the complete first principles model. Friction, air resistance, etc. combine to make the full calculation impossible for all but the most idealized cases. Even artillery calculations utilize “fudge factors” that are required to dial in the targeting calculations for the given situation. Accounting for powder charge, mass, velocity, wind speed and direction, temperature, etc. can get you close but not guaranteed “bullseye”.
The climate is no less complex and no one has a crystal ball.

Fred the Statistician says:
October 17, 2013 at 10:38 pm
Will the sun rise in the East tomorrow?
========
The sun will rise in a direction that is mostly eastward, but this will change day to day and if you based a prediction of where it would rise in the future months based where it was last month, you would be right or wrong largely as a matter of chance.
Cyclical data does provide predictability, based on the observation that nature tends to be cyclical, otherwise extinction events at the extremes would have long ago made us the observer extinct. Trying to fit linear approximations to cyclical data is a statistical nonsense.

fhhaynie says:
October 18, 2013 at 6:59 am
Weather forecasters generally hedge their bets and limit their “predictions” to a few days.
=====
Climate forecasters make their “predictions” so far in the future that no one can check their accuracy.

This entire article is categorically untrue. Correlation is not causality, agreed, but it is all we ever have to make sense of the Universe. Science is nothing but systemetized observations of correlation that are indeed interpreted as probably being causality. The author should really a) learn some statistics; and b) read Jaynes’ Probability Theory, the Logic of Science.
The point isn’t that one cannot be mistaken in e.g. the extrapolation of a linear trend. The point is that one can often make some fairly powerful statements about how probable it is that one will be mistaken. If the author’s primary point above were true, then just because we’ve observed that objects released from rest close to the Earth’s surface consistently have fallen down according to what appear to be simple, predictable rules that fit consistently into a framework of similar rules for our entire life, we would still have no good reason for believing that the next time we drop a penny or throw a baseball, it will follow a trajectory consistent with those past observations. I will cheerfully bet the author $1 a trial for as many trials as he likes that if either of us drop a penny, it will fall down. I’ll even give him odds. Hell, I’ll just plain give him a dollar the first time it falls up.
There is so much more that I can say that is mistaken about this analysis. It ignores Bayes’ theorem entirely and the value of priors and their effect on estimates of future marginal or conditional probabilities. It ignores all of the mathematics associated with functional analysis (e.g. the Taylor series) which basically asserts that if there is an underlying non-stationary distribution from which any set of statistical samples is drawn that meets some very, very broad requirements — continuity, differentiability — that in fact one can almost invariably extrapolate a linear trend for at least some time, simply because the linear term often dominates a Taylor series expansion of the underlying distribution. That doesn’t mean that it always will, or that there don’t exist distributions and processes where it never will, but that there is a very, very broad class of processes for which it will, in fact, work. Broad enough that I dare say it will probably work nearly all of the time.
Even in climate science, this trick works remarkably well. What’s one of the best predictors of tomorrow’s weather, one that doesn’t rely on satellites or all of the tricks given in Anthony’s lovely book on predicting the weather (which, by the way, are also a direct contradiction of the top article, as the top article is basically saying that Anthony’s book is nonsense because just because certain cloud patterns were observed to have a linear correlation with future weather in the past doesn’t mean that those correlations will persist into the future)? “The weather tomorrow will be pretty much like the weather today”. Why? Because if one computes the autocorrelation of a variety of aspects of the weather, the autocorrelation time is longer than a day for many of them. Large temperature shifts don’t occur daily, they occur every few days (and even then, usually occur within fairly narrow ranges). Sunny fine days are often clustered (because high pressure systems are usually large enough and move slowly enough that they take days to pass over any given point). Ditto rainy/cloudy weather. Note that we cannot be certain of any of this, and that at some times of the year and on some parts of the globe the autocorrelation is smaller (in the middle of the Sahara or Antarctica I imagine it is positively huge, but in the temperate zone springtime it is comparatively short) but even this is known, approximately, on the basis of observed, extrapolated linear trends buffed up only in the modern era by additional Bayesian prior knowledge such as an understanding of the physics underlying moisture and the movement of air masses and cloud formation and so on.
Red sky in the morning, sailor take warning dates back 2000 plus years and is nothing but a linear extrapolation of observational data in weather systems. Now we actually understand things like Rayleigh scattering and why the rule — more often than not, but not at all certainly — works.
So sorry, if you want to actually learn about the statistical science of the improbable, you are far better advised to rely on Taleb’s book The Black Swan, who makes the same point the author is attempting to make, only far, far better, and in a context that fully appreciates that even black swan events don’t invalidate the assertion that autocorrelation in systems with an internal (hidden) dynamics is usually long enough that linear extrapolation of their behavior is valid for some time (times less than the empirically observed autocorrelation time, in fact), they simply mean that one should hedge one’s bets taking into account the possibility of comparatively rare but highly costly exceptions.
rgb
[Should “because just because” be “just because” . ? . Mod]

2. Models, not trends, can predict, project, or inform about possible futures, to some sort of accuracy. Models must include all of the causative agents involved which must be modeled correctly for relative effects. It takes a complete, correct and accurate model of a process to reliably predict real world outcomes of that process.
The rigor specified here is overstated and in the end entirely false.
Ancient astronomers were able to predict lunar and solar eclipses without knowing all the causative agents. They might have even been wrong is important aspects of the causative model. The Farmer’s Almanac makes useful predictions about where and when to plant, not from accurate causative non-linear models, but from historical records and employing trends.
An accurate prediction based upon causative agent models, of Breckenridge snow base on Dec. 26, 2013 would be most difficult. An accurate prediction for Dec. 26, 2053 would be even harder. Nevertheless, using only trends based on historical data, you can have extremely high confidence in a prediction that snow base for Breckenridge on July 4, 2054 will be much less than it will be Dec. 26, 2053.
[PREDICTIVE] Models can and should be tested by their abilities to correctly predict already known values within a data set of the process and then tested again against a real world future.
The value of any model must be measured by the difference it can make to you with the prediction in hand[1] compared to without the prediction. No matter how mysterious, if a model had a 60% chance of correctly predicting BLACK on a roulette wheel the model would have great value indeed.
Note 1: Sometimes your value in a model lies solely in fact that you found some sucker to pay you for a prediction.

Kip Hansen said:
October 18, 2013 at 8:09 am
An Observation: I am pleased to observe that here at WUWT, as opposed to the Dot Earth blog, in the 104 comments so far, there has not been a single instance of rank name calling or bullyism — not one. Marvelous.
———————————————–
Idiot.
Now gimme your lunch money.
😉

rgbatduke says:
October 18, 2013 at 7:46 am
Agreed, more or less. The author has shown a particular type of behavior is not predictable using trends. However, a linear regression is actually the optimal mean-square estimator for a particular type of random sequence: that of a deterministic affine variable with random slope and intercept, with measurements polluted by uniform independent noise. That is, in fact, the model for which a standard linear regression is derived.
He would be on much more solid ground if he said that climate variables, particularly mean surface temperature anomaly, do not behave like such a sequence and, as a result, are not predictable to the desired level of accuracy using such a model. To the degree that your model fails to capture the dynamics of the actual process, statistics derived based upon that model are dubious, to say the least.
A better model for mean surface temperature anomaly could be constructed. It would include a process model for the 65 year dynamics observable here, and possibly the 21 year process as well. The 65 year process is key – it was the upswing of that dynamic which was mistaken for an anthropogenic effect in the latter decades of the 20th century, and it is that process which is currently driving temperatures back down again. All independently of egocentric humans who, like a flea on the elephant’s back, think they control the beast because he happened to turn when the flea thought “turn!”.

Kip, as you and others acquainted with this subject no doubt know: Statistics is the language of science, but Probability is the logic of science. Most people have never come into contact with either the language or the logic, and therefore fill in the gaps in their education with arm waving and emotion.
How many people do you know who are familiar with Hume, Jaynes, or others of that caliber?

I’m not sure what the frequent reference to being able to predict a rising sun has to do with a description of the nature of what a trend is? Instead of using a phenomenon that is modelled VERY well and then claiming the hypothesis that trend has predictive value is validated (c’mon man!) why not pick an actual test of your hypothesis?
Take the last 100 months of temperature data from any station you want, fit a trend to that data and bet me 5 quatloos that you know what the tempature will be tomorrow. Afterwards, I’ll give you the money back if you promise to read this essay again.
see this arcticle by statistician William Briggs for more on what trend means and what it doesn’t mean.
http://wmbriggs.com/blog/?p=6854

Richard S Courtney: Sorry, but the human brain is very good at assessing trajectories (i.e. trends in the spatial changes of objects). Ball games would not be possible if this were not so.
Today we are in agreement. That’s an excellent example.

@ Doug Huffman says:
October 18, 2013 at 11:40 am
Re: Jaynes
Good to know someone else who has studied him. 🙂 I’m sure, then, that you’ve also heard the following:
“Probabilities do not exist.” And: “In the absence of Reality, Probability rules.” Both of which require considerable explanation which I won’t go into here, and the concepts can be difficult for many to wrap their heads around.

@ Kip Hansen says:
October 18, 2013 at 11:28 am
Some random replies:
“How many people do you know who are familiar with Hume, Jaynes, or others of that caliber?” None, including myself 🙂 I am a lowly “practician”.
****************************************************************
As was I for many years. But, I’d recommend Jaynes to you anyway. Here’s a link you can pursue at your leisure: http://omega.albany.edu:8008/JaynesBook.html

Kip Hansen,
Your ‘Buttons’ has attracted an excellent statistical audience with lively metaphysics / epistemological discourse. Thanks. It doesn’t get more enjoyable than this.
Hey, just yesterday I started on Jaynes’ book and rgbatduke’s partial draft of his book project ‘Axioms’. So, my statistical paradigm is being tested right now. I’ll need to get back to you later on your ‘Buttons’.
Personal Note=> I was quite critical of Popper’s science theory related thesis starting in the 1980s after reading Brand Blanshard’s ‘Reason and Anaylisis’ but now with Jaynes and Brown input I anticipate becoming more critical of Popper.
John

@ John Whitman says:
October 18, 2013 at 1:09 pm
Kip Hansen,
Your ‘Buttons’ has attracted an excellent statistical audience with lively metaphysics / epistemological discourse. Thanks. It doesn’t get more enjoyable than this.
****************************************************************************
Indeed. 🙂 Of course, all of this is our feeble human attempt to discern future Reality. So from a probabilistic pov, we must first define what reality is. The prevailing definition is when P=1, which is commonly termed an “Event” (hopefully a desired outcome). So the decision is one of choosing the set of probabilities that will result in the desired outcome, based on our level of knowledge and our influence over the process that (we hope) will lead to that outcome. Since we don’t have perfect knowledge we cannot have perfect confidence in our actions to attain that desired outcome. The Black Swan is always hovering. You pays your money, and takes your chances. 🙂

John Whitman: Do you have a link to “rgbatduke’s partial draft of his book project ‘Axioms’.”?
http://www.phy.duke.edu/~rgb/axioms.pdf
There’s a still earlier version under one of the menus at the top of my personal website as well.
rgb

“How many people do you know who are familiar with Hume, Jaynes, or others of that caliber?” None, including myself 🙂 I am a lowly “practician”.
(Raises hand…)
I have no idea what a “lowly practicianor” is in the context of statistics. Either you understand the concepts and have worked through the math (in which case you understand precisely how, and in what sense, and under what conditions statistical trends are predictive) or you are just saying lots of things that are not, as I pointed out, true. In which case you would be well advised not to write entire untrue and misleading articles.
Myself, I’m on my second company founded on predictive modelling. We sell a service that is worth money — quite a lot of money — because you are incorrect. If you were, in fact, correct, we’d instantly go out of business. Not only do we build predictive models, we do so without any strong underlying assumptions concerning the nonlinear function that describes the joint probability distribution we are modelling. They are effectively almost purely empirical models, in other words, with only a few Bayesian assumptions that go into the structures. I understand this stuff very well indeed.
Hence my suggestion that you START by learning some actual statistics before you make egregiously incorrect claims about statistics (which not only I, but pretty much every person knowledgeable about the subject have tried to correct you on, in many cases with nearly identical comments and yet independently — in fact, there is a trend here that I expect to continue as we continue to sample the knowledgeable fraction of WUWT readers…hmmm:-).
Again, if your goal is to justify a statement such as “GCMs suck!” feel free to make the statement, and there are many ways to justify such a claim. But don’t try to justify it by stating “predictive models, statistical or otherwise, never work”. That’s nonsense. As a previous poster noted, if one builds a model correctly, the “trends” it extracts from the data are indeed in a mathematically rigorous sense the best prediction of the future, almost always able to an assumption of complete ignorance of the future. There is literally a century of statistical theory, maximum likelihood, maximum entropy, Bayesian reasoning, and more to justify this. Exceptions to this principle are empirically rare — indeed, truly “unpredictable” means “maximum entropy” in a sense that is rarely realized in nature, in the sense that outcomes are completely, truly, random. If you read David MacKay’s online book on Artificial Intelligence and Information Theory (which is hard going, be warned) you will learn about information redundancy and compressibility and perhaps get some insight into why your assertions are not only wrong, they are deeply wrong.
rgb

A better model for mean surface temperature anomaly could be constructed. It would include a process model for the 65 year dynamics observable here, and possibly the 21 year process as well. The 65 year process is key – it was the upswing of that dynamic which was mistaken for an anthropogenic effect in the latter decades of the 20th century, and it is that process which is currently driving temperatures back down again. All independently of egocentric humans who, like a flea on the elephant’s back, think they control the beast because he happened to turn when the flea thought “turn!”.
Dearest Bart,
We don’t always agree, but Damn! We agree on that. Indeed, as I’ve been posting elsewhere, HADCRUT4 can be modelled almost perfectly (well within the visible noise in the underlying process with a four parameter fit — a straight line with a roughly 0.2C sinusoid with period somewhere in the 55 to 70 year range (the data is too imprecise to do much better) Since HADCRUT4 is indeed an anomaly, the base of the linear part is irrelevant, so this is really a three parameter fit as one degree of freedom doesn’t count.
If one counts the degrees of freedom that are CLAIMED to be important in GCMs, there are at least ten — one can list things like TOA insolation, albedo, shortwave and longwave absorptivity, heat capacity of Earth and atmosphere, and that’s six parameters in a single slab model that averages over all rapid processes, in the simplest POSSIBLE model that actually illustrates a GHE. It is claimed that CO_2, that did not change in any relevant way until roughly 1950, is responsible for the sudden temperature upturn in the 1980-2000 era, when it could not have possibly been responsible for the almost identical upturn in the 1920-1940 era, when a single THREE parameter fit works across the entire interval with no change in functional form precisely where we have to expect one if CO_2 is indeed a proximate cause of global warming.
This requires a stunning coincidence between multiple nonlinear parameters in order to work numerically, and that coincidence is, in fact, rigorously statistically unlikely.
rgb

Hi, Kip. Okay, I understand now. You think a three-day trend has absolutely no information. As you say, “Nothing else — nothing possible, nothing probable, nothing about tomorrow’s value at all.” Extrapolating from that, if – as you say – there is zero information in a three-day trend then, similarly, there must be zero information in a 30-day trend, or a 300-day trend.
Don’t you see that if your friend adds two buttons a day for, say, 342 days, then it’s a pretty good bet that he will add two more buttons on the 343rd day? It would have to be something quite exceptional, by the common-sense definition of the word, for this trend to end at exactly the point when you make a one-day prediction.
My brother has tried to argue something similar. He believes that all polls are useless; that it is impossible to survey 500 or 1000 people, and assume the results of that survey can give us any information about what the rest of the country thinks.
My brother is very smart, but he doesn’t understand statistics at all. Cheers.

@rgbatduke at 2:54 pm
I don’t know about the frog….but your story was enchanting.
The layers of logic were as rich as a pastry.
Especially that last: “All doors lead to certain death. Some perhaps sooner than others…”

@ Ted
You said:
“Extrapolating from that, if – as you say – there is zero information in a three-day trend then, similarly, there must be zero information in a 30-day trend, or a 300-day trend.”
And you are absolutely correct. A 30-day trend has absolutely zero predictive value for day 31!!!
Do we have to go back to flipping a (close to truly random) coin heads or tails to get the point that a trend is NOT predictive at all?
10, 100, 1000 heads in a row, does not change the fact that it is just as likely to be a tails as a heads, on the next flip, even though the trend screams heads.
I certainly hope that no one on this board would posit that the trend of 10000 heads in a row has even 1 infinitesimal bit of predictive information regarding the outcome the next flip.
If one argues that many heads in a row may indicate a trick coin, it may — but the law of large numbers supports 10,000 heads in a roll even for a random coin.
Either way — we would need knowledge of the fairness of the coin (underlying causal agent !!) to make the trend a useful predictor — it must be a trick coin for the trend to be predictive.

Unfortunately, the alarmists do not see ‘truth’ in quite the way ‘realists’ do. Many ‘Realists’ believe, and some even claim to know, that ‘out there’ there exists an objective world – the ‘true’ world that is available for observation by seekers after truth (normal scientists). The contrary view is that our view of the truth is socially constructed and that science is just another vehicle for imposing one world view on others – this is rather quaintly called ‘post-normal science’. Heavily disguised as truth seeking, this is no more or less than a fraud contrived to achieve some political aim – such as the realisation of Agenda 21 – if that is strange to you, just Google it up for a big surprise. That is only one example of the host of ’causes’ riding the post-normal bandwagon. Indeed anyone who thinks that the Hand of Destiny is on his/her shoulder is a welcomed passenger. Even Paul Nurse, President of the Royal Society, contributes to this simple pragmatic view in the name of drumming up cash for research such as his microbiological research centre being established in the heart of London and incalculable cost to taxpayers (i.e. everyone).
I have suggested elsehwere that it is not reason that drives the emergence of ‘institutions’ from conversations but the comforts of togetherness that arise from participating on language games (yes old LW again), that these institutions colonise and consume human lifetime is the cause of their own survival and this goes for all belief systems however zany.
All this is quite ‘natural’ and simply a feature of humanity – but it really is perverse and if we think that ‘institutions’ serve human interest, we probably have fairies at the bottom of the garden too.