I just love brownies, chocolate fudge cake and the like. As a result of eating too many of those –so my dietician told me- I have gained weight over the past years. According to my dietician, somebody’s body weight depends on the ratio of their caloric input and output (i.e. someone’s personal ‘energy balance’). I also believed that. Until recently.
Here’s a graph of my body weight over the past 32 years:
As you can see from this graph, I’ve been on quite a few diets. But often, as soon as I had lost a few pounds, they came back when I lost my appetite in carrots and hunted down the chocolate aisle again. In the nineties, I did quite a bit of sports, which prevented my weight from increasing too much. I’ve stopped since; it just makes me tired.
Over the past 8 years, despite the yo-yo effect of sometimes losing as much as 5 kg over the course of a few months, my weight has increased. My dietician told me that unless I change my eating and sporting habits in a sustainable way, my weight will probably keep yo-yo-ing up.
I was gonna go back to drinking carrot juice again, but then somebody pointed out that my weight increase had nothing to do with my eating too much chocolate or anything like that. Huh?
He pointed out to me that the timeseries of my weight versus time (as shown in the graph above) contains a unit root! No, that’s not a consequence of eating too much carrots; it’s a characteristic of the time series. So what, you my ask? Well,
Though admittedly,
“it can contain a drift parameter, which indeed predicts a ‘deterministic’ rise in a certain period”
According to this theory, my body weight just varies stochastically, e.g. between the blue lines in the graph below:
As you can see, the theory is valid: My weight has indeed remained between the blue lines. And for the next few years, my weight will be between 55 and 105 kg, irrespective of what I eat and how much I sport! After all, that would be deterministic, wouldn’t it? (i.e. my eating and other habits determining my weight)
Wow, if that’s the case, then I’ll stop my carrot juice diet right now and run to the corner store for a box of mars bars!! And I’ll cancel further consultations with my dietician. Energy balance… such nonsense. Never thought I’d be so happy with a root!
PS: This post is not meant to ridicule the arguments made in favor of a unit root. It is meant to draw attention to the fact that the physical (or biological in this case) context of the quantity we’re investigating is very important. If someone is riding a bike downhill, I could wonder if the bike could have gotten to where it is all by itself, and conclude that I cannot possibly predict when the bike will reach the valley. But that ignores the (deterministic) effect of the guy who is riding the bike. Share your favorite analogy in the comments!
[Some typos edited]
Tags: deterministic, random walk, stochastic, trend, unit root
My view on climate change 
April 1, 2010 at 15:46
very good post.
it is just a random walk, that lead you to the top of that interval.
don t worry, you ll be somewhere near that 55kg soon.
April 1, 2010 at 15:48
Bart
Shouldn’t you plot your weight anomaly instead of your weight?
The point is about validity of inferences from data which contain an unit root, not the negation of ‘physics’.
What the AGW consensus does is take a small-time frame within your lifespan, correlate it with your caloric intake and implying causation.
Best of luck in reconciling VS’ conclusions with your climatic worldview.
April 1, 2010 at 18:15
Shub,
The difference between an anomaly and the actual value is only the subtraction of a constant value; it doesn’t make any difference for the interpretation, conclusions or the plot.
AGW causation is based on physics; not on mere correlation.
April 1, 2010 at 20:05
Bart says:
“AGW causation is based on physics; not on mere correlation”
Hmm, so we are operating off of closed form solutions for all feedbacks and forcings these days ? I guess it is possible that I am just behind the times and missed those papers.
I notice that the point made by VS in the earlier thread seems to have been dodged because it is a bit iinconvenient to your viewpoint. If your model results are from a parametrized model, and if that model is from first principles of physics, why the parametrization (which actually varies across models).
Could it be that we don’t completely understand all of those processes and are making educated guesses ? Maybe these educated guesses are based on (gulp) observation and statistics not physics ?
If you want to write me a close form solution for something like aerosol effects, I am completely willing to be swayed to your viewpoint. On the other hand, if you are going to claim that I need to consider a specific set of forcings and feedbacks valid based on statistical observations (and call these physics because you prefer them to be true), to falsify yet another set of observations and statistics (because you don’t like the implications of those observations), I find this logic to be more than slightly circular.
April 1, 2010 at 20:51
Artifex says:
“If your model results are from a parametrized model, and if that model is from first principles of physics, why the parametrization (which actually varies across models).”
Of course!!!! Now why didn’t I think of that? Of course you’re getting heavier Bart, it’s because in the equation of gravitational attraction
F = (G * M1 * M2)/r^2
the G is just a parameter that we don’t know (mind you, we don’t really know M1, M2 and r that well either). What if this parameter G is not constant and is increasing stochastically with time (perhaps caused by cosmic rays or some such). Then we could account for your weight gain by the change in gravity. After all, G is just a parameter, nothing more.
Adrian
April 1, 2010 at 21:38
Hi Bart,
If you were trying to determine the effect of almonds on your diet and charted your intake–and noticed that they formed about 3% of your caloric consumption but that every time you ate them your weight ballooned by 5kg shortly thereafter, what statistical analysis would you use to prove or disprove that your consumption of almonds was as important or more so than the 35% of other high fat foods you consumed?
Is this analogy closer to that facing climate scientists and statisticians evaluating their work?
April 1, 2010 at 21:45
Hi Tom,
Good one. On first impression, no I don’t think so. If you want to get at the fact that human emissions are tiny compared to natural emissions, the point would be better made as follows:
Imagine that what you eat exactly balances what your body needs. As a result, your weight remains fairly stable. Now you start eating a bag of almonds each day. Even though it’s a small caloric intake compared to what you otherwise it, it does seem to cause your weight to increase (unit root or not).
April 1, 2010 at 22:52
Hi Bart. At issue is the prediction of your body weight into the future. Without knowing anything about you relevant to your weight it would be foolhardy to predict a linear increase into the indefinite future. A more reasoned prediction would be the same level as it is now, consistent with a unit root. After the fact rationalization (eg exercise in the 90’s) is not part of the “unit root” model. My question to you is, given the past history of your weight, what do you predict it to be in the future. My prediction would be — about the same as now — ie consistent with the unit root.
April 2, 2010 at 00:13
Adrian says:
“After all, G is just a parameter, nothing more.”
Absolutely, I agree with this, and If 10 different teams were measuring Bart’s weight using differing values of M1, M2 and R and they all seem to be juggling the value of G to stay in a specific range, I am not going to buy the physics argument there either without a really good explanation of how they are choosing their G. Even in this case, they don’t get a pass by claiming “trust us it’s physics”.
Bart:
After some thought and clarification, I think your analogy is a good one. There are going to be those who promptly conclude: “It must be the bag of almonds. They have lots of fats” and try to shout down anyone who thinks differently. Others are going to be fans of the Atkin’s diet and claim that the fats don’t matter, it is 100% certain that it’s the carbs that count. Don’t worry. I can’t be the almonds.
Those with a scientific outlook are going to take a look at a wider variety of factors. Given only the info you have given us, I don’t have enough info to conclusively decide that the almonds caused your weight gain. I would probably guess that the almonds were some form of contributing factor, but it is not enough for me to take an evangelical position. After all, I could decide that the almonds were the deciding factor, put you on a diet and promptly kill you due to missing the impending thyroid malfunction.
All in all, a very good analogy
April 2, 2010 at 00:45
Ahh, but suppose we know he’s eating a bigger and bigger bag of almonds every day, while keeping his exercise and other caloric input constant …
April 2, 2010 at 00:54
Bart,
The GISS temp anomaly fluctuation (“trend” as you would call it) is about 0.6K over a century, (about 1/20 of the daily fluctuation typically seen in temperature). In contrast, your body weight likely fluctuates less than 1 kg during the day. Yet you can measure a 20kg weight gain (20X the daily fluctuation) in a much shorter period of time. So there is much more “signal” and much less “noise” in your weightgain…no fancy statistics needed to determine a trend from a random fluctuation….A comparable trend for temperature (20X daily fluctuation) anomaly would be a rise of over 200K!…
April 2, 2010 at 04:13
Carrot Eater and Eli would gladly pay you Tuesday if you gave us those carrots today.
April 2, 2010 at 04:17
More to the point, the evil doc will also measure your blood sugar, cholesterol and blood pressure. She will note that all of these point to the fact that you are pigging out on chocolate (please, don;t tell Eli chocolate bunnies) and almonds. While the weight gain alone is only indicative everything together puts you back on the carrot juice diet.
April 2, 2010 at 04:54
“The GISS temp anomaly fluctuation (“trend” as you would call it) is about 0.6K over a century, (about 1/20 of the daily fluctuation typically seen in temperature).”
This idea that “the daily fluctuation is huge, so how can we measure the long term trend” sounds good but is totally misguided.
Did you know that people are shorter in the evening than in the morning.
If my kids are, say, 18 years old, they may not be growing any taller. Then again, maybe they are, but it is quite possible that their long term trend is very small – maybe 0.1 cm over a year, which is much smaller than the daily fluctuation of a 1cm or so.
Do you conclude from that that you can’t measure my kids growth?
Of course not. You just measure it many times and average over, um, how about months?
April 2, 2010 at 06:06
If you want to get at the fact that human emissions are tiny compared to natural emissions,
Good Lord, you folks are thick.
April 2, 2010 at 06:08
Even though it’s a small caloric intake compared to what you otherwise it, it does seem to cause your weight to increase (unit root or not).
What happens if your metabolism slows down, or you get sick?
April 2, 2010 at 06:12
Ahh, but suppose we know he’s eating a bigger and bigger bag of almonds every day, while keeping his exercise and other caloric input constant …
You can only eat so many Almonds, their effect is therefor limited.
April 2, 2010 at 08:08
pdj,
Nobody is claiming that my body weight (or global temperature) will increase linearly into the indefinite future. What I’m claiming is that my body weight (global temp) depends on my (the earth’s) energy balance. And making an educated guess about my future energy balance, I can indeed say something about how my weight (temp) will respond: If I continue eating more than my body needs (ie creating a positive energy imbalance for my body), my weight will continue to increase.
April 2, 2010 at 12:11
hahaha… this blog entry is funny.. :)
April 2, 2010 at 15:28
Ah, the old “the almond effect becomes saturated” argument :)
VS:
Better funny than pathetic like B&R.
April 2, 2010 at 17:06
Ya know, actually, you may have come up with a better example than you realize. Weight is influenced by a lot of factors, also, those factors change over time. For instance, metabolism changes as you age. Has the nature of the foods we eat changed in general? I dunno, here in the states the composition of stuff at the supermarket has sure changed in the last 20 years. We can’t tell your age from the chart. Were you mature when the chart started? What about exercise? What about employment? Has the nature of your job changed? Then you can get into calories, etc, etc. Now, the solution to a “weight gain” problem, if, indeed, it is a problem, is not going to probably be just one factor, but a combination of several of the listed factors. If there is a unit root in the numbers, there may be a good reason.
April 2, 2010 at 17:07
hahaha… this blog entry is funny.. :)
Better funny than pathetic like B&R.
For someone who is supposed to be a scientist, you are certainly small minded.
April 2, 2010 at 17:55
So Bart, further to Pofarmer’s questions, please answer:
1. How do you know your weight gain isn’t due to a metabolic disorder?
2. How do you know it isn’t due to a large, tumorous mass?
Weight change from either is independent of your caloric intake.
Sure you’ve accounted for all variables in your model?
Or are you just assuming you are healthy and is that a valid assumption?
April 2, 2010 at 17:58
ps – says a lot about a man when he exhibits such passive-aggressive behavior as this post clearly indicates.
April 2, 2010 at 18:13
Profarmer, KD
Other factors remained fairly steady, except perhaps for a 3 year oscilation in my metabolism. Over the past 8 years however there has been no discernable trend in my metabolism except for this oscillation. Occasionally I got very sick and lost a lot of weight as a result.
KD, as for 2, its effect would be opposite. And leave unsubstantiated accusations at the door please. Thanks.
April 2, 2010 at 18:41
there have been recent studies showing that there are a couple of genes that dictate how you process fats and sugar (different genes for fat and sugar). So impact of more fats or more carbs is different for different people. We would probably need to get a dna sample from Bart to test him for which genotype he is… again we need better data!!
:)
April 2, 2010 at 20:24
Over the past 8 years however there has been no discernable trend in my metabolism except for this oscillation.
Really?
My understanding is for every 10 years over 30, your metabolism slows a certain amount. Sorry, I don’t have the numbers off the top of my head.
April 2, 2010 at 21:34
“You can only eat so many Almonds, their effect is therefor limited.”
Tell that to Michael Phelps. Or Donna Simpson.
April 2, 2010 at 22:29
Bart, I just love your ability to assume away the unknown. And as for your quip re; unsubstantiated claims, I guess that means you’re so enamored with the original post you can’t see the forest for the trees.
Well played sir, you have proved, once again, that you are the cleverest man in your own mind.
April 3, 2010 at 00:12
Bart,
Are you assuming that the presence of the unit root *excludes* the possibility of (caloric, sporting, DNA, etc.) “forcings” on your weight? That seems to be your assumption when you state: “Somebody pointed out that my weight increase had nothing to do with my eating too much chocolate or anything like that. … He pointed out to me that the timeseries of my weight versus time (as shown in the graph above) contains a unit root! No, that’s not a consequence of eating too much carrots; it’s a characteristic of the time series.”
But what VS is saying (if I understand him) is that if there’s a unit root in this time series, then it’s incorrect to fit a simple linear trend to the charted data. That makes perfect sense for your weight–if you could fit a linear trend to that data, it would be predicting that you’ll be buying a lot of new trousers in the future, as your waist grows ever larger.
The unit root doesn’t exclude the possibility that calories and sport (etc.) deterministically affect your weight, but it does have certain implications for how you have to correlate the data. And if you don’t correlate the data in accordance with those implications, your conclusions about the extent to which calories and sport (etc.) are affecting your weight will not be scientifically accurate. You might be right in your hunch that calories make weight go up and sport make it go down, but until you measure that effect precisely in accordance with appropriate statistical methods, that’s just a good intuition, not science. In this case, if your statistical methods don’t account for the unit root, the conclusions will be wrong.
April 3, 2010 at 03:41
It is as someone plotted a graph of a human condition for all time and claimed that God exists.
April 3, 2010 at 10:08
GDY,
I could wait for better data and continue eating loads of chocolate untill you’re satisfied with the data. I’m afraid what my weight will be by then though.
TT,
There is a (very) good chance that I misunderstood VS, but he did state (as I cited) that a unit root means that the trend is not deterministic (ie not caused by deterministic forcings). If I misunderstood him, I’m hardly alone, because a lot of people seem very eager to make that conclusion.
Nobody claims it’s necessarily linear (the linear fit just happens to visually describe the data half decent over a limited period of time).
April 3, 2010 at 10:09
Shub,
All my dietician is claiming is that if I eat more than my body needs, my weight will increase. No God involved. If you want to argue the opposite, you may be in need of a God to get rid of that pesky physical reality.
April 3, 2010 at 10:33
Age. Sadly most of us get fatter as we grow older.
The good news is that when you are really really old you will be as thin as a rake and you can eat all the chocolate you like.
The problem with the analogy for me is the scales. If I eat a huge amount of calories, say at Christmas, my weight gain might be as much as 20% of my overall weight in a very short period of time.
But when it comes to temperature we are not talking about a 20% gain we are talking in smaller numbers and over a much longer period of time.
That does not mean that temperature rise would be harmful but it does mean that the analogy is overly simplistic and therefore confusing.
Which tends to be the problem with climate science ;-)
April 3, 2010 at 10:35
corr.
That does not mean that temperature rise would not be harmful but it does mean that the analogy is overly simplistic and therefore confusing.
April 3, 2010 at 16:45
Bart,
I’m pretty sure VS is not claiming that a unit root excludes deterministic forcings. He’s just saying that it’s a mistake to visually fit a linear (specifically, an OLS) trend to your graph and to assume that whatever forcings there are, will be causally correlated to that (OLS) trend.
The fact that your weight gain has a unit root doesn’t exclude the possibility of causally attributing (some or all) of your weight gain to calories, genes, etc., and your weight loss to diets and exercise. It just means that, after you’ve gathered all the data points on forcings and the movement of your weight (up and down through time), you have to apply whatever statistical method is consistent with the presence of the unit root (e.g. co-integration).
Perhaps if VS is still lurking he can clarify this point.
April 3, 2010 at 21:11
“The fact that your weight gain has a unit root doesn’t exclude the possibility of causally attributing (some or all) of your weight gain to calories, genes, etc., and your weight loss to diets and exercise. It just means that, after you’ve gathered all the data points on forcings and the movement of your weight (up and down through time), you have to apply whatever statistical method is consistent with the presence of the unit root (e.g. co-integration).”
I think you clarified it pretty well :)
Best, VS
April 3, 2010 at 21:31
VS,
How do I square that with what you wrote:
And earlier on in the other thread you also wrote something along the lines of (sorry, can’t find the exact comment I have in mind) that the unit root is somehow inconsistent with a dominant GHG forcing, or with the temp increase being ‘forced’ at all by deterministic forcings.
April 3, 2010 at 21:50
Hi Bart,
I think it’s a matter of definitions:
When I say a ‘deterministic trend’, what I mean (and I did clarify that numerous times, although I see how the terminology could be confusing) is that the DGP is modeled as a trend-stationary process. Note that this ‘trend’ need not be linear.
Trend stationarity is ruled out by a unit root.
As for there being a deterministic expected increase in future periods (i.e. through various forms of ‘drift’), this is not ruled by a unit root (i.e. a stochastic trend).
That too I addressed, here.
:)
VS
April 3, 2010 at 21:53
PS. Note that ‘trend-stationarity’ includes ‘deterministic trends’ with various structural breaks. Stochastic trends can have structural breaks too.
We can test all of this, but we can’t start by making assumptions which are not supported by the data.
April 3, 2010 at 23:40
“I’m pretty sure VS is not claiming that a unit root excludes deterministic forcings. He’s just saying that it’s a mistake to visually fit a linear (specifically, an OLS) trend to your graph and to assume that whatever forcings there are, will be causally correlated to that (OLS) trend.”
Is this going to be like how McLean wasn’t claiming anything about longterm trends?
People just got the wrong end of the stick and assumed someone on the internet had disproved manmade global warming. It’s funny how that keeps happening..
April 4, 2010 at 07:07
blob,
I can’t tell exactly what you’re claiming about what VS said, but if you read the first few posts in the thread carefully, particularly the response to Scott Mandia, you’ll see he’s not claiming to have disproved manmade global warming. He’s saying that a lot of existing “proofs” for it use the wrong statistical methods, and one attempt to apply the right statistical method (B&R) rejected a long-term relationship between CO2 and global temperature. That doesn’t disprove the hypothesis that CO2 has contributed to global warming in the last 150 years, but it does, as VS says, raise a red flag about existing models that don’t account for the unit root.
April 4, 2010 at 09:35
VS, you CAN start by making assumptions which are supported by the underlying theoretical physics and other observations. Moreover, no matter what YOU said, certainly Beerenstock and Reingewurtz said
———————————————-
Therefore, greenhouse gas forcings, global temperature and solar irradiance are not polynomially cointegrated, and AGW is refuted.
———————————————
Eli takes it you now agree that this is nonsense
April 4, 2010 at 10:00
# VS Says:
April 3, 2010 at 21:53
“PS. Note that ‘trend-stationarity’ includes ‘deterministic trends’ with various structural breaks. Stochastic trends can have structural breaks too.
We can test all of this, but we can’t start by making assumptions which are not supported by the data.”
I get it now, VS. You never actually claim anything, only point out that anything is possible. I guess it is. When you actually have a claim to make, and evidence to back it up, let us know.
In the meantime, models which take into account the known climate forcings produce results which do not start by making assumptions, but work from observed and known physical processes.
April 4, 2010 at 10:27
“I get it now” .. lol
April 4, 2010 at 14:56
It’s like playing 20 questions with you VS. Is it bigger than a bread basket?
April 4, 2010 at 15:50
“”…but work from observed and known physical processes.”
If all the physical processes are ‘known’ why resort to statistical analysis at all? CO2 traps heat – end of story.
AGW theory has to become a grand unified theory of everything to prove itself. We all know where that took us (nowhere) the last time we tried that. I believe the physicists are still trying.
April 4, 2010 at 19:09
What has not been addressed here is the quality of the measuring instrument, its environment and the organisation that publishes Bart’s weight problem.
Actually the graph does not represents Bart’s weight, but an “weighted” anomaly against the averaged weight of his whole family some 40 years ago.
His family happens to be dispersed over the globe, so measurements are taken with many scales. Some scales are better than others, some are replaced or moved to places with a little different gravity. And of course not all of Bart’s family members do a great job in measuring and scribbling down the outcome. They sometimes even forget to report the results.
In those cases the missing data are filled in with the homogenized average result of relatives that live nearby.
This is also done for uncle Gradus and other black sheeps of the family who happen to live in places without scales. No problem, we assume their weight anomaly is the same as that of aunt Neeltje, even if she lives 1200 km away.
Some of Barts relatives life in places where over time there have popped up UHI outlets, comparable to a Mc Donalds. Giving in to the temptation they have endulged in many a juicy hamburger,resulting in an extra increase of weight which is not typical for the rest of the family that unfortunately has no access to UHI outlets.
And finally the responsibility for the reporting of Bart’s averaged weight anomaly is given to the Weight Watchers, who of course have a vested interrest in reorting increased weight.
So to me the discussion about unit roots or linear extrapolation of Bart’s future weight comes second to the discussion whether we can truly trust the data.
April 5, 2010 at 00:02
“Carrot Eater and Eli would gladly pay you Tuesday if you gave us those carrots today.”
Hmmm…Carrot Eater and the Rodent. Dr. Jekyll and Mr. Hyde?
April 5, 2010 at 00:55
Henk wrote:
What has not been addressed here is the quality of the measuring instrument, its environment and the organisation that publishes Bart’s weight problem.
Henk provides the “it’s not happening” argument. Others have provided the “it could not be caused by overeating but it could be caused by anything else” arguments. No doubt someone will be along shortly to claim high fat diets and/or being overweight is good for you.
Looks like it is a pretty good analogy after all. ;-)
April 5, 2010 at 01:17
This thread began on April 1st (April Fool’s Day) so I decided to weight before I posted a comment. At first I believed that the post was just nuts. The trend in the comments since then makes me believe otherwise. However, instead of posting anything significant here tonight, I will be rooting for the NY Yankees. They are quite a unit.
[Reply: I chose the date deliberately indeed, but in every joke is a grain of truth. As Frank also observed, the analogy is quite apt after all. BV]
April 5, 2010 at 03:43
Frank O Dwyer wrote
“Henk provides the “it’s not happening” argument””.
That is not what I am saying. My point is that if you ask people to make major changes to their lifestyle you better have your arguments backed by solid data.
And the particular data is not solid. Not in terms of quality of the equipment and the environment. Moreover the organizations that report the data are themselves part of the AWG selling machine.
The most amazing thing to me is that millions of Dollars are poured in building even more nifty, complex computer models that will project dramatic changes, and nobody seems to bother about improving the measuring system so that at least from now on the data will be correct and can be trusted.
But unfortunately AWG has become a religion; either you believe in it or you are an outcast, a denyer.
I do believe that our Earth is in a warming period, and that human activity plays some role in it. But if I look at the quality of the data, the large gaps in our knowledge of the climate and the strong feedback assumptions I am yet to be convinced that it’s all and only our fault.
Let’s say I am from Missouri: Show Me !
April 5, 2010 at 03:51
Henk,
“And the particular data is not solid.”
In terms of the analogy you cast doubt on the weighing scales but we can also note that other weighing scales give the same answer and that the subject needed to buy bigger clothes.
The same is true for warming. Multiple lines of evidence say it is warming.
The data on warming is solid enough to convince ice to melt. It is also solid enough that pretty much every animal and plant species on earth has responded to the warming, except libertarians and republicans.
April 5, 2010 at 09:52
Henk, I thought you were giving a good ironic ‘persiflage’ of Watts and his surfacestations. But no, you were serious…
April 5, 2010 at 20:14
The fundamental need in order that there be a random walk in global temperature is that feedbacks induced by temperature counterbalance the accelerated radiation loss at higher T. Otherwise higher heat loss does actually constrain the system not to change T (i.e., physics).
If you think about this a little bit, a random walk situation is actually scarier than what climate scientists propose, since the global system would be essentially unstable with respect to temperature until the the envelope of the feedbacks are reached.
April 6, 2010 at 02:57
Somewhat also to the point, Eli imagines that the blue lines represent a 95% confidence interval, but where would the purple lines representing a 90% confidence interval, etc. be? That would still be a fair amount of confidence
And besides it’s Dr. Jekyl and the Lagomorph, much cuter than rodents
April 6, 2010 at 13:11
Bart, I confidently predict that in 100 years your weight will be zero.
April 6, 2010 at 13:33
Alex H,
‘Bart, I confidently predict that in 100 years your weight will be zero.’
Perhaps with an uncertainty of 21 grams or so?
April 6, 2010 at 14:09
Chuckles,
Indeed. Although whether the 21 grams of matter in question actually would constitute Bart is a thorny question.
April 6, 2010 at 14:09
Mitch,
Good point. Arthur Smith noted the same here: That true randomness implies a very large (even infinite) sensitivity.
April 6, 2010 at 14:30
Temperatures are not a random walk (i.e. the discrete equivalent of a Brownian motion).
Both Alex and I separately tested that hypothesis (in the other thread), and firmly rejected it.
Can we now drop that straw-man please?
Thank you.
VS
April 6, 2010 at 15:07
VS,
I use the term perhaps more loosely than you, but since you claimed that the temps vary only stochastically; not determininstically, and have as much chance to be larger or smaller than the preceding value, I translate that as ‘random’ in the colloquial sense of the word.
April 6, 2010 at 15:30
Bart,
Please read this and this again.
Let’s try to stick to the agreed definitions. The discussion is already very cumbersome.
Best, VS
April 7, 2010 at 04:33
VS,
I am curious, and my apologies if you have answered this already. Do you agree, based on the overwhelming evidence, across many disciplines at hand that:
1) GHGs are increasing rapidly (relatively speaking) and primarily on account of anthro activities,
2) The resulting positive energy imbalance has caused and is causing an accumulation of heat in the biosphere (as quantified by thermometers, satellite MSU data, OHC, radiosondes).
My hypothesis is that this “unit root” hypothesis of yours has more to do with detracting from AGW, than it has to do with stats.
If you agree on 1 and 2, then I, for one, might be more inclined to believe that you are serious about understanding the quirky stats and behaviour of the global SAT record.
Otherwise, I think that you are the one guilty of arguing a straw man with your introduction of the “unit root”.
And yes, I agree, your single-minded focus on this is non-issue is indeed tiresome and cumbersome :)
April 7, 2010 at 07:07
Hi MapleLeaf,
You might want to read the thread in question, before jumping to conclusions.
Best, VS
April 7, 2010 at 18:27
VS,
Actually, I have read the thread, and I am not jumping to conclusions (about what?), that is why I first asked you some questions. Someone (TT) said on your behalf that
“…he’s not claiming to have disproved manmade global warming. He’s saying that a lot of existing “proofs” for it use the wrong statistical methods, and one attempt to apply the right statistical method (B&R) rejected a long-term relationship between CO2 and global temperature.”
Now that does not quite answer the questions that I put to you. You seem to be of the same ilk as Mosher and McIntyre, in one breath (perhaps) saying that AGW is real and a potential problem, and in the next breath obfuscating and floating contrarian ideas (which are almost always refuted).
VS, while some of your statistical musings may have some merit (although Tamino seems to have thoroughly debunked you and made you do some serious back pedaling), the WUWT crowd do not know how to separate the wheat from the chaff, and yet another transient contrarian hypothesis becomes another myth and another seed of doubt. This modus operandi is well understood.
That is why I’m curious about your answers, it will help place your musings in context and shed some light on your intent. In the end, the climate system does not care about “unit roots” or “random walks”. The physics behind radiative transfer theory of GHGs is well established and understood, and does not require using correlations between SAT data and CO2 concentrations. Me thinks this whole “unit root” silliness is just a rather elaborate ploy by you to get some undeserved attention and to obfuscate the science.
Prove me wrong, and publish your “unit root/random walk” work in a mainstream, peer-reviewed journal. That is what someone would do if they were truly interested in advancing stats and science, making their work widely available, and being open to critique by the community.
April 9, 2010 at 06:05
I still wonder why you guys are so fixated on “publishing”. This blog is also “publishing”, it makes ideas public.
You obviously feel uncomfortable with the fact that global temperature can walk randomly with no apparent reason, and frequently try to find a comfort in “physics”. As I tried to explain already twice in this blog, physics does not prevent the global temperature INDEX from walking.
I have presented a set of simple arithmetical examples that show that infinite multitude of combinations of spots with different spot temperatures can produce different global INDEX while energetically all these states provide the SAME radiative balance. Therefore, the INDEX can walk and can be random without any changes in overall energy balance. That’s simple physics.
April 9, 2010 at 07:49
But there *is* a positive radiative imbalance, making your argument moot. Plus, atmospheric temps are just one of the observables that is is changing in accord with a warming planet. THis whole discussion conveniently omits ocean heat content, sea ice, ice sheets, glaciers, ecosystems, sea level rise. etc. Are all those changes (which are in accord with a warming planet) due to random variations? You sure feel lucky.
April 9, 2010 at 08:14
Hi Bart,
I liked your analogy, but for me the following analogy is more helpful. Maybe people know the ELO-ratings that are used in chess. Every time when you win a game you earn raing points, when you lose you lose rating points. When your opponent has the same rating as you, you would gain eg X rating points as you win and lose X when you lose. However, when playing against an opponent who is stronger, you gain more points when you win and lose less points when you lose (and vice versa against an opponent with lower rating).
Now, what would we conclude when somebody’s rating curve contains a unit root? I believe (although I am not a statistician) that this is irrelevant. Because in this particular case (in contrast to climate or diet) the rules that govern the dynamics are precisely known, we can do not only statistics, but we can use probability theory. Although I don’t have time to do the calculations right now, I am sure that the null-hypothesis that a person has not become stronger, with a rating curve similar to the global temparature curve, would be firmly rejected. The reason for this is, although the rating at a particular time does depend on the previous timepoint, it becomes increasingly difficult to gain rating points if you are much weaker than your rating suggests. That is, there is a negative feedback incorporated. This is, I believe, very well comparable with the negative feedback of radiation imbalance. If temperature rises, outward radiation will increase in order to decrease temperature to equilibrium value.
For me this analogy was very helpful, when I thought it up. I strongly believe that the crucial point is that, although you cannot reject some null-hypothesis (i.e. the trend contains a unit root), that does not per se mean anything if the null hypothesis itself doesn’t make any sense wrt the problem that you are looking at. In the case of ELO ratings the nice thing is that you can do probability calculations to actually calculate the probability that a person who is actually say 2000 points strong will increase his rating to eg 2300 points and this probability is VERY low. Still, unit root testing could lead to the conclusion that a unit-root cannot be rejected, but that clearly does not mean the player in question has not become stronger (ie there is no trend)
I hope this is helpful and keep up the good work!
April 9, 2010 at 08:21
That’s a nice one indeed. If my chess rating were as the GISS record, I would like to play to someone who claims I haven’t improved. He would underestimate my abilities, and I woudl gain more points if I win.
On a related note, people who think the temp has an equal chance to increase or decrease (or perhaps even a larger chance to decrease, in order to remain within the 95% bound of the ‘stochastic trend’ or for whatever reason; PDO; sun; phlogiston) are cordially invited to take up a bet on future climate change.
April 9, 2010 at 08:26
“That’s a nice one indeed. If my chess rating were as the GISS record Iwould like to play to someone who claims I haven’t improved.
Yes, and take a bet on the outcome :)
April 9, 2010 at 11:00
Hmm, I thought this April Fools’ post was funny, but it seems that some people have taken it a little bit too seriously (i.e. they believe that the analogy actually makes sense).
Here’s the trend post for all those (apparently) confused as to what a stochastic trend actually represents.
VS
PS. Jel je Milanović naš čovek, ili jednostavno Nizozemac iz Utrehta koj je uspeo pogrešno da se potpiše kao (Milutin) Milanković? ;)
April 9, 2010 at 11:22
Hi VS
Actually, I am not from Eastern Europe, so I don’t have a clue what you meant, milanovic is just my nickname.
Indeed, I did not intend my post as April Fool’s post and I believe Bart also didn’t, so I am afraid you have more explaining to do. Where does my (or barts) analogy actually break down? What would finding a unit root in for example someones ELO rating imply? Shouldn’t your stochastic test also depend on the scientific hypothesis you want to test? Assuming nonphysical null-hypothesis does not help at all. Wouldn’t it be better to have (in the case of the ELO rating) a sensible null-hypothesis, namely someone has not become a stronger player and test for that?
April 9, 2010 at 11:28
Hi milanovic,
Actually, you’re a bit too late in asking for clarification, I’m done posting, see my latest post in the active thread. I sent a long e-mail to Bart yesterday explaining my reasons. Everybody else can infer these reasons from reading the long discussion.
In any case, I think that most of your questions are (implicitly or explicitly) answered in the 250,000+ words posted in said thread.
All the best, VS
PS. The Balkan is not ‘Eastern Europe’.
PPS. Not an April Fools’ post? Bart wrote something else to me in private… hence my lack of ‘response’ here.
April 9, 2010 at 12:44
Hi VS
i know I am late, but I did read most of the thread (at least your posts) and I am not the only one for who it is still not clear. But I understand that it is taking too much of your time.
April 9, 2010 at 12:55
The analogy makes a lot of sense in that the energy balance (either on the individual’s level or on the planet’s level) dictates how the energy content (and thus, the weight or temperature) will change. That is a ‘waarheid als een koe’ (‘true as a cow’), even though some people seem rather annoyed that the dieticians are not willing to give up their energy balance ‘dogma’ that eating too much will make you gain weight.
Of course the analogy poked fun at the far fetched conclusions some people are intent of making based on the presence of a unit root. As if energy balance considerations can suddenly be flushed down the toilet. Plus, that graph does not really represent my weight. In that way, it was an april fool’s joke.
April 9, 2010 at 15:52
I agree with Bart. Of course it is intended as a fun post, but I do think that the analogy makes sense. Sometimes such analogies make it easier to think about whether your assumptions actually make any sense.
April 10, 2010 at 14:08
Bart:
The problem is simple.
You say “in light of the physics and energy balance considerations, this increasing trend is real”
But in order to say that the increasing trend has to be real – irrespective of the physics and energy balance considerations.
Moreover there is some circularity in your argument. We have inferred/gained knowledge of some of the so-called physics and energy balance by looking at the supposed increasing trends.
Regards
April 12, 2010 at 01:01
I was directed here by comments on the RealClimate blog.
Please see our work on applying cointegration analysis and other time series econometrics to the climate issue which has largely (but not totally) been ignored by the climate science community. Here are all the relevant papers.
http://www.sterndavidi.com/topics.html#cli
Yes there are unit roots probably in the temperature time series but they are there due to the temperature being driven by the greenhouse gas series that almost definitely have unit roots in them.
April 13, 2010 at 06:55
Of course, if there is a physical basis to body weight or global temperature (why not?) then one has to look at what is driving changes as time goes on. Clearly energy balance, but in the case of global surface temperature we also have many more effects such as movement of heat into and under the oceans. But if the measurement is “noisy” the correct approach isn’t to throw up you hands and say “it’s too random, I can’t make heads or tails of it”, but rather to better understand the processes that are driving that randomness.
April 28, 2010 at 18:56
This is confused thinking.
From an empirical point of view, we can demonstrate using controlled studies that more food without increased metabolic demand or gastrointestinal problems is reliably associated by weight gain. We have done this not by single anecdotal reports, but by controlled studies with groups of people or experimental animals. We extrapolate from those studies onto individual people to explain apparent weight gain. We can differentiate real weight gain from measurement error easily. We can also differentiate weight gain from random fluctuations because we know what sort of random variations are possible in a healthy individual if caloric intake and metabolic rate are kept constant. We know from our large experience with human biology that weight gain is associated with other factors, but we also know from our experience that these factors are generally rare, or accompanied by other manifestations of disease or disorder, and generally reveal themselves given time. In other words: we are very very familiar with the workings of the physical system you are tracking, so using physical theory to interpret the time series as representing real weight gain (and making a number of reasonable assumptions about measurement techniques and your metabolism) is entirely reasonable. So in your individual case, we have a large body of validated theory and excellent measurement abilities with well defined errors we can use to evaluate the time series given. We do not need this specific time series to validate our basic notions of caloric intake and metabolism. This is inarguable.
In the case of the earth’s atmosphere, none of this is true. We have one good system, no good experimental models of it, indirect measurements with poorly defined error, and a fairly young body of observation and theory….In the case of climate change, you need this specific time series interpretation to evaluate the physical theory!
(!!!!!)
Your parallel is so badly thought out and wildly inappropriate from an empiricists point of view that (if I have interpreted your objection correctly) it is shocking.
April 28, 2010 at 22:00
Oh boy. Any analogy breaks down at some point. That’s the nature of being an analogy I guess.
Your choice to focus on those areas where the analogy is valid (the whole point of bringing up an analogy in the first place) or where it breaks down (it inevitably will at some point). The former could become a constructive conversation.
April 29, 2010 at 20:10
Your whimsical faux analogy was broken down from the beginning. And it certainly did not result in a constructive conversation. You should have posted in the Open Thread, where it would have been properly ignored.
April 29, 2010 at 20:52
DLM,
The analogy is spot on on the points where is matters: Energy balance considerations (e.g. conservation of energy) are not to be ignored when trying to understand a physical system where the energy balance is the driving factor. Feel free to add something sustantive for a change; your empty one-liners are starting to wear thin.
April 30, 2010 at 01:40
This is another straw man Bart: “Energy balance considerations (e.g. conservation of energy) are not to be ignored when trying to understand a physical system where the energy balance is the driving factor.”
Who said anything about ignoring energy balances.
I believe that somewhere in this thread I pointed out the same flaw in your in-appropriate analogy as Oh boy has done, no doubt more eloquently than myself. You people cannot give a good accounting of the earth’s energy balance. Half of your heat is missing. So we are supposed to trust you with our money?
April 30, 2010 at 20:30
Bart, my point is that if you think there is insight to be gained about how one interprets time series climate data in the light of physical theory from your weight gain example, you have entirely missed a very important point: In the case of your weight gain, people are NOT trying to establish the physical context of the quality you are investigating”: we already KNOW the physical context in detail, so we do not have to establish it from the time series data alone. In climate research people are trying to establish the appropriate details of the system (the “physical context of the quality you are investigating”) by examining the quality you are investigating.
This, of course, is not a criticism of climate science, but it does mean that in evaluating predictions you do not have a body of independantly derived detailed physical theory to fall back on in order to make predictions about how the system should behave when it is perturbed. so we can say confidently that, if you increase your intake, and do not get sick, and do not exercise, you will get fatter, because we KNOW the determinants of that system. It does not matter one bit if your weight data can be modelled as a random walk (or whatever). On the other hand, if you do not know, in detail, the determinants of the system by reference to an independently derived body of theory, then you first must establish if there is any evidence for determinants at all before you can do any prediction, and (more relevantly here) what the confidence intervals are for the estimates of the determinants.
(no, I’m not trying to say that the temperature data is a random walk, or that climate scientists don’t know any determinants, or that things are not warming up, or anything like that: just trying to make the point here that the relationships between theory, data and prediction varies wildly across scientific disciplines).
April 30, 2010 at 21:42
Oh boy,
A more relevant analogy would be an attempt to model the weight gain of several thousand people, chosen at random, let’s say from somewhere near each of the thousands of Gisstemp stations that are used to gather data that are massaged and then used to guess what the global temperature is on any given day.
First weigh each person, then determine each subjects daily calorie intake, with an accuracy of about 0.1 calorie, then increase each subjects food intake by about 3.9 calories/day. It shouldn’t be too difficult to ‘project’, within a pound or two, how much each will weigh in about thirty years. That should really be easy for those who know how to model the earth’s climate.
April 30, 2010 at 22:06
Oh boy,
In other words, we know nothing about the physical climate system?
Oh boy.
April 30, 2010 at 22:52
Bart, I specifically said ” no, I’m not trying to say that the temperature data is a random walk, or that climate scientists don’t know any determinants…”
The analogy you chose is poor because you are deriving specifics about physical theory from the specific time series data under examination in climatology: in the case of your weight gain, you are not. This is why the statistical model is crucial in climatology, but pretty much irrelevant in your particular weight gain problem.
This is a very, very simple point.
May 17, 2010 at 09:53
I’m not good in reading charts. But let me tell you one thing, body weight is something mysterious. I’ve been struggling to raise my weight for years. No matter how much I eat though, it’s just stuck in the same number.