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Archive for December, 2007

Hurricanes have not increased: misuse of running means

Most statistics purporting to show that there has been an increase in hurricanes do not use the best statistical methods. I want to highlight one particular method that is often misused, and which can lead one to falsely conclude that trends (increasing or decreasing) are present when they actually are not. Read my original post to learn more about this.

That technique is the running mean. As you can see in the rather dramatic graphic from Science Daily, a 9-year running mean has been plotted over the actual hurricane numbers (up to 2005 only) in the North Atlantic. It looks like, in later years, a dramatic upswing is taking place, doesn’t it? This type of plot has shown up in many scientific, peer-reviewed papers.

Science Daily hurricane running mean
Source: Science Daily
Don’t be turned off by the equations! Something very surprising is coming at the end of this article and you will be rewarded if you read to the end.

What is a running mean? A p-year running mean converts a series of actual, observed numbers into a statistical estimate, or model, of what a supposed underlying trend of those numbers might actually be. Because it is a model, its use must first be justified. In math, a 5-year running mean looks like

Running mean equation

where the symbol y indicates the hurricane numbers, and the subscripts t, t-1 and so on indicate the time period: time t is now, time t-1 was last year (now minus one year) and so on. The superscript on the symbol y to the left of the equal sign indicates that this is the modified data value plotted, and is not the actual number. Even if you’re afraid of math, this equation should be fairly easy to understand: the current, modified, number is just the mean of the last 4 observations and the most current one.

Additionally, in the mathematics of time series models, an auto-regressive series of order 5 is written like this

Autoregressive formula

which shows how the current data point is predicted by a weighted sum of past values, and where the weights are the coefficients Φ. Just let all the Φ = 1/5 and you have a similar running mean structure like that above. The point is this: using a running mean implies an underlying statistical time series model. Which is OK, as long as the data support such a model.

Do they for hurricanes? No.

In order to justify using auto-regressive time series models, you start by looking at something called an auto-correlation plot, which is a plot of how each year’s number of hurricanes is correlated with the previous year’s number, and how this year’s number of hurricanes is correlated with the number of hurricane from two years ago and so on: the number of previous years is called the lag. If any of these correlation lags are significant, then you can use an auto-regressive time series model for this data. If none of these correlations are significant, then you cannot.

Here is a picture of the auto-correlation of hurricane number (number of storms s) for the North Atlantic using data from 1966 to 2006.


None of the correlations reach above the horizontal dashed lines, which means that none are significant, and so a simple running mean should not be used to represent North Atlantic hurricane numbers.

So far, so good, right? Now let’s look at some made up, fictional data. Take a look at the following pictures, which are all simulated hurricane numbers; one of them looks pretty close to what the real data looks like. The running-mean even shows a healthy upward trend, no doubt due to global warming. But what do these pictures really show?

Simulated data with 9-year running mean

To get this data (the R code to make it yourself is pasted bellow), I simulated hurricane numbers (Poisson with mean 10) for pretend years 1966 to 2005, four separate times. Each year’s number is absolutely independent of each other year: to emphasize, these are totally random numbers with no relationship through time. I also over-plotted a 9-year running mean (red line). Because all of these numbers are independent of one another, what we should see is a flat line (with a mean of 10). The reason we do not is because of natural variation.

I only had to run this simulation once, but pay attention to the lower-right hand numbers, I got something that looks like the actual North Atlantic hurricane numbers. The 9-year running mean is over-emphasizing, to the eye, a trend that is not there! Actually, this happens to two of the other simulated series. Only one shows what would expect: a (sort of) straight line.

Like I said, I am including the code I used to make these plots so that, if you are curious, you will see how exceptionally easy this is to do.

Good statistical models are hard to do. See some of these posts for more discussion and to find some papers to download.

R code to make the plots. You must first have installed the package gregmisc.

library(gregmisc)
par(mfrow=c(2,2))
for (i in 1:4){
x=rpois(40,10)
plot(1966:2005,x,type='l',xlab="",ylab="",axes=F)
axis(1)
lines(1966:2005,running(x, width=9, pad=TRUE, fun=mean),lwd=2,col="#CC7711")
}

1 comment December 30th, 2007

Were the cannonballs on or off the road first?

There’s something of a controversy whether photographer Roger Fenton placed cannon balls in a road and then took pictures of them. He also took a picture of the same road cleared of cannon balls. Apparently, there is a question whether the cannon balls were ON the road when he got there, or possibly they were OFF and he placed them there to get a more dramatic photo. This drama unfolds at Errol Morris’s New York Times blog.

Whether they were first ON or OFF (Morris uses the capitals letters, so I will, too), excited considerable interest, with hundreds of people commenting one way or the other, each commenter offering some evidence to support his position.

Some people used the number (Morris uses the ‘#’ symbol) and position of the balls, others argued sun shadows, some had some words about gravity, and so on. Morris compiled the evidence used by both sides, ON (cannon balls on first) and OFF (cannon balls placed there by Fenton), and he presented this summary picture (go to his blog to see the full-sized image):

Morris cannonball evidence pic

This is an awful graph: the order of evidence types is arbitrary, it would have been better to list them in order of importance; the use of color is overwhelming and difficult to follow; and, worst of all, the two graphs are on an absolute scale. 288 people supported ON, and 153 OFF, so counting the absolute numbers and comparing them, as this picture does, is not fair. Of course the ON side, with almost twice as many people, will have higher counts in most of the bins. What’s needed is a percentage comparison.

One of his blog’s readers provided just such a comparison, in the following pictures (again, go to his blog to see the full-sized images):

Cannonballs ON pie chart

Cannonballs OFF pie chart

These are, of course, pie charts, and while they are slightly better than the original bar charts, they are still awful. Three simple things wrong are again the order of evidence is arbitrary, the are an overwhelming number of colors, and the they needlessly print the exact percentages—down to the 10th place! Once again, there is a larger sin: The main purpose of these pictures is to compare the different percentages supporting each type of evidence, but to do that your eye must jump from picture to picture, find the relevant slice, and then go back to the original to check for the difference. This makes the reader work very hard to get the information.

I drew this:

Cannonballs comparison chart

The dark blue lines indicate that a larger percentage of ON people supported that type of evidence; dark red lines indicate that a larger percentage of OFF people supported that type of evidence. The types of evidence labels appear on the side with the larger percentage. The types of evidence are also ordered by importance.

For types of evidence Topography/Climate, Camera/Exposure, Cannon ball properties, Gravity and Physics, there is little difference between the two groups. But those who supported ON, thought Number and position of balls, Sun shadows, and Practical concerns were much more important. Those who supported OFF, thought Character (of the photographer)/Artistic, Shelling, and placement of Rocks were much more important.

I’m not certain how interesting, or relevant, any of this data is, but what is important to us is that graphs can find the interesting and relevant data, as long as you are willing to put in the effort to create good ones. Nearly always, the default graphs available in packages like Excel, fall short of the mark (yes, a very, very weak cannonball pun).

Oh, Morris guesses that OFF is the truth.

Add comment December 28th, 2007

Will Smith on reprogramming Hitler

Roger Kimball, in his blog, has an entry on the actor Will Smith’s “Reprogramming Hitler” comments. The subject is benevolence. It is well worth reading.

A quote: “The Australian philosopher David Stove got to the heart of the problem when he pointed out that it is precisely this combination of universal benevolence fired by uncompromising moralism that underwrites the cult of political correctness.” He goes on to quote Stove at length (go to the original site to read).

I thought it be helpful to extend Stove’s quote. To those who would suppose that, “Ought not wrongs to be righted?” is a rhetorical question, Stove writes:

It does not follow, from something’s being morally wrong, that it ought to be removed. It does not follow that it would be morally preferable if that thing did not exist. It does not even follow that we have any moral obligations to try to remove it. X might be wrong, yet every alternative to X be as wrong as X is, or more wrong. It might be that even any attempt to remove X is as wrong as X is, or more so. It might be that every alternative to X, and any attempt to remove X, though not itself wrong, inevitably has effects which are as wrong as X, or worse. The inference fails yet again if (as most philosophers believe) “ought” implies “can.” For in that case there are at least some evils, namely the necessary evils, which no one can have any obligation to remove.

These are purely logical truths. But they are also truths which, at most periods of history, common experience of life has brought home to everyone of even moderate intelligence. That almost every decision is a choice among evils; that the best is the inveterate enemy of the good; that the road to hell is paved with good intentions; such proverbial dicta are among the most certain, as well as the most widely known, lessons of experience. But somehow or other, complete immunity to them is at once conferred upon anyone who attends a modern university.

David Stove, On Enlightenment, Transaction Publishers, New Brunswick, New Jersey, p. 174

Add comment December 27th, 2007

How many false studies in medicine are published every year?

Many, even most, studies that contain a statistical component use frequentist, also called classical, techniques. The gist of those methods is this: data is collected, a probability model for that data is proposed, a function of the observed data—a statistic—is calculated, and then a thing called the p-value is calculated.

If the p-value is less than the magic number of 0.05, the results are said to be “statistically significant” and we are asked to believe that the study’s results are true.

I’ll not talk here in detail about p-values; but briefly, to calculate it, a belief about certain mathematical parameters (or indexes) of the probability models is stated. It is usually that these parameters equal 0. If the parameters truly are equal to 0, then the study is said to have no result. Roughly, the p-value is the probability of seeing another statistic (in infinite repetitions of the experiment) larger than the statistic the researcher got in this study, assuming that the parameters in fact equal 0.

For example, suppose we are testing the difference between a drug and a placebo. If there truly is no difference in effect between the two, i.e. the parameters are actually equal to 0, then 1 out of 20 times we did this experiment, we would expect to see a p-value less than 0.05, and so falsely conclude that there is a statistically significant difference between the drug and placebo. We would be making a mistake, and the published study would be false.

Is 1 out 20 a lot?

Suppose, as is true, that about 10,000 issues of medical journals are published in the world each year. This is about right to within an order of magnitude. The number may seem surprisingly large, but there are an enormous number of specialty journals, in many languages, hundreds coming out monthly or quarterly, so a total of 10,000 over the course of the year is not too far wrong.

Estimate that each journal has about 10 studies it is reporting on. That’s about right, too: some journals reports dozens, others only one or two; the average is around 10.

So that’s 10,000 x 10 = 100,000 studies that come out each year, in medicine alone.

If all of these used the p-value method to decide significance, then about 1 out of 20 studies will be falsely reported as true, thus about 5000 studies will be reported as true but will actually be false. And these will be in the best journals, done by the best people, and taking place at the best universities.

It’s actually worse than this. Most published studies do not have just one result which is report on (and found by p-value methods). Typically, if the main effect the researchers were hoping to find is insignificant, the search for other interesting effects in the data is commenced. Other studies look for more than one effect by design. Plus, for all papers, there are usually many subsidiary questions that are asked of the data. It is no exaggeration, then, to estimate that 10 (or even more) questions are asked of each study.

Let’s imagine that a paper will report a “success” if just one of the 10 questions gives a p-value less than the magic number. Suppose for fun that, every question in every study in every paper is false. We can then calculate the chance that a given paper falsely reports success: it is just over 40%.

This would means that about 40,000 out of the 100,000 studies each year would falsely claim success!

That’s too high a rate for actual papers—after all, many research questions are asked which have a high prior probability of being true—but the 5000 out of 100,000 is also too low because the temptation to go fishing in the data is too high.  It is far too easy to make these kinds of mistakes using classical statistics.

The lesson, however, is clear: read all reports, especially in medicine, with a skeptical eye.

8 comments December 26th, 2007

What faith is not

Archbishop Thomas Collins of Toronto, quoted in a Christmas newspaper article about the virgin birth of Jesus, said that he had “never seen a quark and nor has anyone else. They are, he said, like so many other things we take on faith, beyond our human comprehension.”

Another example: I have been on a plane and have heard a fellow passenger say that he has “faith” that the pilot will land safely.

These are common uses of the word faith, and the sense in which it is used in our two examples is well known. But I believe these uses are improper, are a distraction, and have caused much unnecessary argument.

I do not have faith in quarks nor do I have faith that the plane will land safely. I believe in quarks and safe flights based on evidence. Even stronger, quarks are not beyond human comprehension; statements like Collins’s are paradoxical. For humans in the first place proposed quarks, thus, they comprehended them.

I am most certainly not arguing that quarks are real, or that all planes will land safely. We know that some planes crash, and the evidence for quarks is elusive to most of us. But there is evidence, and an enormous amount of it, that most planes will make it home fine, and other evidence which shows that quarks are real. Both of these beliefs, therefore, are the result of reasonable inductive arguments (unarticulated, almost certainly, for most humans, but that fact does not matter here).

Another set of common misconstruals of faith are found in, for example, the Skeptic’s Dictionary:

Faith is a non-rational belief in some proposition. A non-rational belief is one that is contrary to the sum of the evidence for that belief. A belief is contrary to the sum of the evidence if there is overwhelming evidence against the belief, e.g., that the earth is flat, hollow, or is the center of the universe. A belief is also contrary to the sum of the evidence if the evidence seems equal both for and against the belief, yet one commits to one of the two or more equally supported propositions.

That web page also approvingly quotes Mark Twain, who said, “Faith is believing what you know ain’t so.” We can dispense with this blatant misuse of the word immediately. Believing what you know is false is idiocy or contrariness or obstinance, not faith.

The Skeptic’s Dictionary’s definition of non-rational belief, as “one that is contrary to the sum of the evidence” is not controversial, and the two examples it uses are fine. But it false, and against all experience, to say it is irrational to “commit to one of the two or more equally supported propositions.” According to this, it would therefore be irrational to carry an umbrella when the forecast is for 50% chance of rain. (It would also be irrational to weight propositions by how much you would gain or lose depending which turned out to be true; this is the technical subject of decision analysis.)

Moreover, it is mere abuse to say that faith “is a non-rational belief in some proposition.” This is no sort of definition at all, only an aspersion on a perfectly good word. This petulant definition is almost certainly the result of an overreaction to the gross misuses of faith from the “other side,” i.e., those who are religious. The Dictionary quotes one of these people, UC Davis Professor Richard Davis, who says, “A statement like … ‘everything evolved from purely natural processes’ cannot be supported by the scientific method and is a statement of faith, not science.” Davis is obviously wrong, and uses the word faith in the same sense as the person claiming the plane will land safely.

Misuse of faith by the religious is common, e.g., Archbishop Collins’s. When this misuse happens, it is usually because the religious are seeking to counter certain scientific statements which (often times with cause) threaten their beliefs. As a weak counterattack, some religious devotees attempt to argue that much of science is also taken on faith. Sort of a “We’re all in this thing together, so leave me alone” argument. This is unfortunate, but is no reason to dismiss the word altogether. For example, physicist Paul Davies, writing for the New York Times (quoted on the Skeptic’s Dictionary) said, “..science has its own faith-based belief system. All science proceeds on the assumption that nature is ordered in a rational and intelligible way.” Davies’s first sentence is true, his second is false (in the now familiar manner). Why is the first one true?

This is faith:

Faith is belief in some thing for which there is no evidence.

For Christians, misuse of faith most likely begins with Hebrews 11:1, a famous line, which reads, “…faith is the substance of things hoped for, the evidence of things not seen.” This use of evidence should be seen as lyrical, but some have attempted to take it literally by, perversily, requiring faith in evidence, which is what Davies is trying to do in his second sentence.

But Davies’s first sentence is true: every atheist, scientist, and mathematician has faith in certain statements, propositions they believe to be true, but cannot prove; further, they know that these propositions are impossible to prove. That is, there is no, and can be no, evidence for these statements. Nevertheless, they still believe that they are true. It is even necessary that they do so. These propositions form the very basis of probability and statistics, as well as physics, chemistry, and on and on.

What are these statements?

Stay tuned for my essay What faith is.

4 comments December 26th, 2007

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Add comment December 25th, 2007

Merry Federally Recognized Holiday of December 25 That, in Order Not to Offend, Shall Remain Nameless

Or just plain

Merry Christmas!

1 comment December 25th, 2007

Two differences in perception between global cooling and global warming

As is well known by now, a passel of climatologists in the 1970s, including such personalities as Stephen “It’s OK to Exaggerate To Get People To Believe” Schneider, tried to get the world excited about the possibility, and the dire consequences, of global cooling.

From the 1940s to near the end of the 1970s, the global mean temperature did indeed trend downwards. Using this data as a start, and from the argument that any change in climate is bad, and anything that is bad must be somebody’s fault, Schneider and others began to warn that an ice age was imminent, and that it was mainly our fault.

The causes of this global cooling were said to be due to two main things: orbital forcing and an increase in particulate matter—aerosols—in the atmosphere. The orbital forcing—a fancy term meaning changes in the earth’s distance and orientation to the sun, and the consequent alterations in the amount of solar energy we get as a result of these changes—was, as I hope is plain, nobody’s fault, and because of that, it excited very little interest.

But the second cause had some meat behind it; because, do you see, aerosols can be made by people. Drive your car, manufacture oil, smelt some iron, even breath and you are adding aerosols to the atmosphere. Some of these particles, if they diffuse to the right part of the atmosphere, will reflect direct sunshine back into space, depriving us of its beneficial warming effects. Other aerosols will gather water around them and form clouds, which both reflect direct radiation and capture outgoing radiation—clouds both cool and warm, and the overall effect was largely unknown. Aerosols don’t hang around in the air forever. Since they are heavy, over time they will fall or wash out. It’s also hard to do too much to reduce the man-made aerosol burden of the atmosphere; except the obvious and easy things, like install cleaner smoke stacks.

Pause during the 1980s when nothing much happened to the climate.

Then, since the 1990s, the Earth’s temperature noticeably began to increase. So back to the old argument: any change is bad, and it’s somebody’s fault. One of the main culprits everybody knows: increasing carbon dioxide, a gas which (fairly inefficiently, actually) captures outgoing radiation, leading to warming. Both CO2 and warming also tend to increase plant production (making a greener world), but never mind that. Aerosols are still in the game, but now are seen as mitigators: the sunlight they reflect helps to cool things off (the overall effects of clouds is still unknown).

Changes in orbital forcing still need reckoning, but these were and are largely ignored. These orbital changes, and their inevitability, form one of the two main differences in perception between cooling and warming.

For both global cooling and global warming, we were able to find a way to perceive it as being our fault: by ascribing the changes either to man-made increases in aerosols or CO2. But back in the cooling days, we also had unchangeable circumstance in the form of the Milankovitch cycle (or the earth’s orbit) and other obscure physics, which there was nothing anybody could do to change. Because of that, more people were resigned to their fate, so to speak, thus more ignored the scientists.

Overall, then, in the late 1970s it was hard to get people too excited about mankind’s effect on climate, though there was a consensus (a now favorite word) that some kind of global cooling was coming our way. But there just wasn’t enough substance to hold the media’s and the public’s attention.

So how did global warming become so well known? If it were only reports of man-made increases in CO2, as it was for man-made increases in aerosols, I doubt the world would have taken much notice of global warming. But there was one other difference between the two theories that I think accounts for the heightened importance of global warming.

That is difference models.

Computational power in the 1970s was, of course, trivial compared to that of today. Complex global climate models back then were no more sophisticated, actually even less sophisticated than, the algorithms in the digital wristwatches of today. In short, intricate computer models and, much more importantly, reliance and trust in these models, was an impossibility then. It is not so now.

Predictions of global cooling, then, relied more on observations of actual cooling, and gross—on paper—approximations to the physics of the atmosphere. Today, the predictions of global warming rely almost exclusively on the output of models. Computational power has certainly increased, and by orders of magnitude. Have the models themselves also improved?

Yes, but not as much as you would think, or hope. More of the physics is now known, but it is impossible (see this review) to completely insert this new physical understanding into the models. Many of the models’ “subroutines” are based on parameterizations, which are educated, but not infallible, guesses of how certain processes (like clouds) work. Other model components, such as how the atmosphere interacts with the ocean, land, and outer space, are increasingly crude approximations (the later, outer space, is related to orbital forcing, and is usually ignored). Other parts of the models are based on nothing more than assumptions of how the physics works in certain situations.

Too, we don’t have accurate actual measurements of all locations, levels, and components (like temperature, moisture, wind speed, and so on) of the atmosphere, land, ocean (and outer space). The number of measurements we do have is minuscule compared to the actual size of the earth. So it is hard to reconcile the output of models with what the actual state of the earth is, though, of course, this is a necessary step. The process whereby the models are adjusted so that they conform to both the actual measurements and to the scientists’ expectations is called tuning. All models undergo extensive tuning until the majority of it users are satisfied of the output.

The models are sophisticated; they rely on very difficult mathematics and require years of training in physics and computer science to understand and implement, thus model tuning is an art. People devote entire careers to just tweaking these models. Books and journal articles regularly appear suggesting changes or offering new interpretations. There is an entire culture built around these models. It is also safe to say that no one person has a complete understanding of the models. This is why organizations like the IPCC must cobble together hundreds of scientists in order to summarize what these models are saying.

We have now arrived at the second difference in perception. To believe in global cooling, we had to believe in the individual scientists who propounded the theory; we had to have trust in their capabilities, their ethics, their motivations. There were not so many climate scientists back then, and the theories they touted were complex and difficult to explain to the public, so we basically had to take their word that what they predicted would come to pass.

In global warming, we no longer have to believe in a single scientists, we can instead choose to believe in their collaborative models. Computer models, I should say. Because to say a model was done on a computer gives it a certain lustre and mystery, which in turn makes it difficult to question its results. Lustre and mystery that is undeserved, however, because computers, I unfortunately have to emphasize, do nothing more than what they are told to do by people. We still have to trust in scientists’ capabilities, motivations, etc., only now this trust is once removed, and it becomes more a trust in technology.

That trust is, in 2007, nearly complete. But it is a trust that is not deserved. It is true technology has done marvels in other areas of our lives, and is to be trusted in those areas. It is not true, however, that the climate models upon which scientists base their projections should be trusted. The models have not yet proven their capabilities; which is another way of saying that they do not yet make accurate predictions of actual observed conditions. Not even one-percent of the effort devoted to working on these models is set apart to measuring how well they actually perform. The evaluation and verification studies that have been done so far imply that the amount of uncertainty in output of these models is vastly underestimated.
But again, never mind, because there is also the shear number of people making cataclysmic claims. Most of these people are not, of course, climatologists. They are instead people who use the results of climate models as input to their own models of economics, ecology, agriculture, sociology, and on and on. Aynsley Kellow, Professor of Government at the University of Tasmania,

…describes one paper published in the journal Nature in January 2004 that “warned of the loss of thousands of species with a relatively small warming over the next century. But just how virtual was this science is apparent when we consider that the estimates of species loss depended upon a mathematical model linking species and area; modelled changes in the … distributions of areas of habitat depended in turn upon the results of climate models tuned to reflect climate changes as a result of increasing greenhouse gases … these in turn were driven by scenarios of what [such] emissions might look like over the next century, driven in turn by economic models.” Source http://www.smh.com.au/articles/2007/12/21/1198175338154.html

Model builds upon model which builds upon other models, all of which make approximatiosn and assumptions and so on. This is not the kind of work in which to put your beliefs. It it not the kind of work to write treaties or raise taxes. Yet it has become so.
(For an amusing article showing how some are trying to spin the old predictions about imminent cooling such that they actually were predictions of global warming, see this Wikipedia article. — Note: this article, like all on that site, are subject to change.)

Add comment December 24th, 2007

The impossibility of there being no truth.

One of the premises frequently used for the argument that “all cultures are equal” (multiculturalism), or for the argument that you should not be judgmental, is relativism, which is the idea that there is no absolute knowledge, that is, that there is no truth. Some would write it, “there is no ‘truth.’” The scare quotes indicate the author’s derision of the word. As the philosopher David Stove has made clear, the scare quotes turn the word from its obvious meaning, that something is true, to something that is only believed by so-and-so to be true. Thus, the quotes also serve to give their users a self-made patina of superiority.

Roger Kimball, in his blog Roger’s Rules, told of his attendance at a colloquium to honor the philosopher Leszek Kolakowski. In a session on “Enlightenment, Modernity, and Atheism,” one of the participants began her statement, “I know, of course, that there is no truth.”

And it’s in this sentence that we have the proof that its own conclusion is false. Which is another way of saying that the woman’s statement is paradoxical, and therefore nonsensical.

Why? If it’s not already obvious to you, “to know” can only mean that you are aware of a truth. And the truth that you know cannot be that there is no truth, because then you would not be able to know it.

The original sentence cannot be saved by changing it to “There is no truth” because, as Bill Clinton might remind us, it depends on what that meaning of is is. And the meaning is existential, which is to say, that the thing of which it speaks (truth) exists. In any case, the sentence “There is no truth” is either true or false. If it is true, then there can be no truth, and so the sentence cannot be true, hence a paradox.

All arguments against the idea of truth fail for the same reason. Because no matter how cleverly you couch your language, no matter the strength of your authority, in the end either your argument is true or it is false. If it is true, then there is no truth, and your argument cannot be true, and you’re right back in the same paradox.

The non-existence of truth is then an impossibility, thus true things exist. So the task becomes identifying what those truths are. And that’s no easy task!

What does this have to do with statistics? A lot, actually, because all statistics is based upon probability, the nature of which we first have to understand before we can use any statistical method. One view of probability, and the dominate one in Bayesian statistics, is the idea that probability is subjective, nothing more than a construct in an individual’s mind. In other words, subjective probability is a philosophy of relativism. Those who hold this view believe that there cannot be objective, i.e. true, probability.

Naturally, I believe this is false. Stay tuned for more.

Add comment December 22nd, 2007

Can increasing fuel economy standards result in more gas consumed?

Yes.

Congress recently passed an increase in fuel efficiency standards for cars, from 25 MPG to 35 MPG, a 40% jump. So you would expect that, when this law goes into force, gasoline usage will go down. That’s what various congresspersons and “environmentalists” are arguing, anyway.

Unintended consequences

Now, the mandated increase is a very large change, and complying with the law is probably beyond current engineering capabilities. That is, automotive engineers will have a difficult time implementing these standards in the time alloted, unless they do the one easy thing available to them, which is to make cars lighter. Lighter cars get higher gas mileages.

Making cars lighter is not hard. You simply take things out of heavy cars or make smaller cars. Problem solved!

Except smaller and lighter cars, all other things being equal, fare far worse in crashes. People know this, and tend to buy a larger vehicle instead. That is, confronted with a choice of a small, more dangerous, car, they will more likely buy a larger SUV or a truck.

Trucks and SUVs do not have to comply with the higher gas mileage requirements. Mileage for these larger vehicles is about 15 MPG (average of city and highway driving).

So instead of buying a safer car that now gets the required 25 MPG, people will be more likely to buy vehicles that are, on average, 60% less efficient!

Thus, more gas will be used than before the higher standards were in place.

Of course, I cannot prove that my scenario is certain to happen, but it is at least not impossible, and even somewhat likely. If I am right, this will be yet another example of good intentions gone bad.

Add comment December 20th, 2007

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