Biologist; Climatologist, Stanford University; Author, Laboratory Earth

I believe that global warming is both a real phenomenon and at least partially a result of human activities such as dumping greenhouse gases in the atmosphere. In fact I can "prove it"—or can I?—that is the real question.

What is "proof"? In the strict old fashioned frequentist statistical belief system data is direct observations of the hypothesized phenomena—temperature increases in my case—and when you get enough of it to produce frequency distributions you can assign objective probabilities to cause and effect hypotheses. But what if the events cannot be precisely measured, or worse, apply to future events like the warming of the late 21st century? Then a frequentist interpretation of " proof" is impossible in principle before the fact, and we instead become subjectivists—Bayesian updaters as some statisticians like to refer to it. In this case we use frequency data and all other data relevant to components of our analysis to form a "prior"—a belief about likelihood of an event or process. Then as we learn more we update our belief—an "a posteriori probability" as the Bayesians call it—or simply a revised prior.

It is my strong belief that there is an overwhelming amount of evidence to form a subjective prior with high confidence that the earth's surface has warmed over the past century about 0.7 deg C or so and that at least half of the more recent warming is traceable to human pressures. Is this " proof" of anthropogenic (i.e., we did it) warming? Not in the strict sense of a criminal trial with "beyond a reasonable doubt" criterion—say a 99% objective probability. But in the sense of a civil proceeding, where " preponderance of evidence" is the standard and a likelihood much greater than 50% is adequate to have a case, then global warming is indeed already " proved". So as a frequentist I concede I believe it is real without full "proof", but as a subjectivist, my reading of the many lines of evidence puts global warming well over the minimum thresholds of belief to assert it is already "proved".