Tag Archives: mathematics

Mission Failure

As many of you are aware, the launch of the Glory satellite was a failure. The mission would have studied solar irradiance, aerosols, and clouds — all of which are important data for climate studies. Alas, the satellite failed to deploy and the mission — if it happens at all — will have to wait. It’s surely a demoralizing blow to the Glory team, and a blow to climate science since it follows hard upon the launch failure of the OCO satellite two years ago. RealClimate has a post on the subject.

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Ridge Regression

Since the subject of “ridge regression” came up in discussions on RealClimate recently, I thought I’d give a very brief description of what the heck it is.

I tried to keep the math to a minimum, but I failed. There’s no getting around that fact that this is a mathematical topic so there’s lots of math anyway. But it’s still only a peek at the subject — I hope that it at least gives a little perspective on what ridge regression is and why it’s used. Oh well, at least the “rigor police” have been banished.

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It’s routine practice in statistics to apply a statistical model to some process. Often (I’d even say, usually) the model depends on a certain number of parameters. Sooner or later, we’d like to know what the parameters are (or at least be able to estimate them). One of the most powerful methods in statistics for estimating the parameters of a model from a given set of data is called “MLE” for “Maximum Likelihood Estimation.”

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It sometimes happens that we have only limited access to direct measurements of some variable of interest, but we have abundant data on some other, related variable. In such cases we can use the “other” variable as a proxy for our target variable. We attempt to determine the relationship between them, then use the measurement of one as input to that relationship in order to estimate the other. Voila! Of course such indirect estimates will be imperfect, but at least they’re an approximation, we hope a useful one. Why, such practice has even been applied to climate science.

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Bad Bayes Gone Bad

In the last post I discussed what I thought was a mistaken application of Bayesian analysis. I didn’t claim that Bayesian analysis isn’t appropriate for the problem, in fact I showed the kind of Bayesian analysis which I think is appropriate. But some readers objected to my claims; I think we have some Bayesian zealots out there.

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Good Bayes Gone Bad

A reader recently linked to a book about information and inference, which definitely leans toward the Bayesian rather than frequentist view of inference. I do too. But I’m not the avowed anti-frequentist that some Bayesians are.

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The Power — and Perils — of Statistics

A recent article in ScienceNews calls into question scientific results established by statistics. It was excerpted by WUWT at great length (I wonder whether Anthony Watts knows the difference between “fair use” and violation of copyright), apparently an attempt to discredit global warming science because, after all, it uses some statistics. Of course Watts fails to consider the outrageous statistical follies coming from his side of the fence (many from himself and his contributors). Lubos gets in on the act, purportedly defending statistics but insisting on a ridiculously high confidence level — and of course, getting in some potshots at global warming science himself.

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