Open Thread #14

The last one is full, so here’s a new one for much faster loading.

Breaking Records

According to temperature data from GISS the hottest year on record is 2005, but according to data from HadCRU (the HadCRUT3v data set), the hottest year is 1998. You might wonder whether there’s any significance to the fact that, eleven years later, the HadCRU data set hasn’t yet set a new record. HadCRU data shows a much stronger influence from the very strong 1998 el Nino than does GISS data; hence the HadCRU 1998 record is considerably more extreme than the GISS 1998 record (it was the record at the time). How long should we expect it to take before breaking a record anyway? How long does a record have to remain unbroken before we have statistically significant evidence that global warming might have peaked in 1998?

Embarrassing Questions

The decade of the 2000s is almost over; there’s only a bit more than 6 months to go. This decade has witnessed the hottest year on record (2005), the lowest summer arctic ice extent ever observed (2007), and the highest sea level in recorded history (2008, although data for 2009 are not yet available). It has also seen a war against truth and the scientific community, waged by the forces of ignorance and dishonesty who deny that global warming is real, is man-made, and is dangerous.

A few of the assault leaders are scientists (but when they opine on global warming their scientific expertise and objectivity abandon them or is banished); many are capitalists attached to “free markets” as an ideology who see any attempt to mitigate climate change as a threat to the fossil-fuel-based economics which is the source of their obscene wealth; some are politicians, who are probably motivated by the same free-market ideology which, frankly, gives capitalism a bad name.

Key Messages

The synthesis report from the Copenhagen conference on climate change gives dire warning of the consequences of inaction about global warming. They emphasize six key messages, each with its own chapter:

Take it to the Limit: Part 2, the Central Limit Theorem

In the last post we introduced the moment generating function. It’s defined as a power series, with its coefficients determined by the moments of a probability distribution.

Take it to the Limit: Part 1, Moments

Probably the most important theorem in all of statistics is the central limit theorem. I’d like to give an explanation what it is, and show that it is indeed true (not rigorously but at least quantitatively), so I’ll take a couple of posts to illustrate it. In this, the 1st installment, I’ll introduce the concepts of moments of a probability function and of the moment-generating function.

It’s going to get worse

Since 1975 the planet has warmed at an average rate of about 0.017 deg.C/yr. If that rate is sustained, we’ll see at least another 1.5 deg.C warming this century. Add that to the 0.8 deg.C warming we’ve experienced over the last century, and the globe will be hotter than pre-industrial times by more than 2 deg.C — the amount which many consider to be extremely dangerous climate change. That’s a problem.

Dangerous Curves

There’s a saying about modeling data, that “with 6 degrees of freedom you can model an elephant.”

It expresses that fact that when we fit curves to data, or smooth it in any way, if we include enough degrees of freedom in our model we can fit just about any pattern. But, that doesn’t mean the fit represents what the physical signal is actually doing. Both your characterization of what the signal has done, and especially any forecast of what it will do, can be faulty, especially true if you don’t apply statistical significance tests to determine whether or not your model fit might be meaningful. It’s yet more suspect when the noise which is superimposed on the signal isn’t white noise. Hence one of the easiest, and alas most common, ways to fool yourself (and others) is to indulge in reckless curve-fitting.

Statistical Presentation: a Work of Art

Statistics is the mathematical science of the analysis, interpretation, and presentation of data. Like many with a theoretical bent, I tend to focus on the analysis and interpretation. But it should not be forgotten that the presentation can have tremendous impact, and add greatly to the clarity with which important conclusions are driven home.

A friend recently sent me a link to a presentation by Hans Rosling: Debunking third-world myths with the best stats you’ve ever seen.

Usually, the phrase “the best stats you’ve ever seen” would be nothing but hyperbole. But in this case … Watch the presentation, I think you’ll be impressed. I know I was.

Open Thread #13

The previous open thread is getting quite large … so here’s a new one. Lucky 13.