Monday, April 16, 2012

Likelihood of Global Warming Given X.

Introduction:

I’m going to profile a rather wacky article here. A Norwegian physics student applied Bayes’ Theorem to a number of things in a peripheral way in order to provide a basis for applying the theory to global warming. In “Testing Hypotheses about Climate Change: the Bayesian Approach”, Kristoff Rypdal applies Bayes to Russian roulette, the learning process of individuals, hurricanes and global warming and the melting of arctic ice caps. Essentially the author applied probability theory and hypothesis testing, where the concept of probability is defined subjectively as “a degree of knowledge" about a hypothesis. He defines knowledge as something generated by four processes: 1) the inspired formulation of new hypotheses 2) prediction (here deductio

n enters a central element) 3) collection of new data through experiment or observation 4) verification/falsification by comparing predictions and observations.

Summary:

I’ll go ahead and skip Kristoff’s lengthy explanation of what Bayes’ theory does via a parable about Mafiosos and their desire to watch him play Russian roulette. After by passing his .38, Kristoff takes us to Section VI. Hurricanes and Global Warming. He essential states that for the sake of the formula, the existence of human caused global warming is bivalent, 50/50 (H,HN). The scientific community (again for the sake of the formula) thinks that the odds of a massive hurricane occurring more than once per century in the absence of global warming is 10%, i.e. p(B|HN)=0.1. He also states that the scientific community believed that in the presence of global warming, massive hurricanes will occur more than once per century is 50%, i.e. p(B|H)=0.5.


Kristoff then basically applies the exact same theory to the arctic ice caps, in Section VIII: Bayesian Learning and Arctic Ice Cap Melting. He states that there has been a well-documented scientific effort regarding the monitoring of the arctic ice caps (which is true) and that these scientists have observed a large reduction in summer sea ice (which is also true). He then gives the “scientific estimates of probability” for the sake of applying the situation to Bayes’ Theorem. He states that the probability of the arctic ice caps melting w/o human caused global warming is 10% or, p(C|HN)=.1. He also states that the odds of this kind of melting occurring in conjunction with the presence of human caused global warming is 50% or, p(C|H)=0.5. These two measurements are identical as the one above and result in p(H|C)=.83 or 83%. When combined however, the author states that p(HN)=1-p(H)=.17. When combining this to p(H|B) we get .96, thus turning the results of the previous equation from ‘highly likely’ to ‘virtually certain’.

Conclusion:

Overall I thought Kristoff’s application was interesting though only theoretical in nature. It would be interesting to conduct polling studies on the topic of global warming in both the scientific community and the general public and apply Bayes theorem to the results. This could actually be applied to any polling of public perception really, so long as there was actual information to prove something correct or incorrect. As a study of ‘the causes of global warming’ Kristoff’s article is speculative and not particularly edifying, but as a study of human perception and likely, it is rather interesting.

Source:

Rypdal, K. (2008). Testing hypotheses about climate change: the Bayesian approach. Department of Physics and Technology, University of Troms, 9037 Troms, Norway

http://web.me.com/kristofferrypdal/Themes_Site/Courses_files/Bayesian%20approach%20to%20Climate%20Change.pdf

2 comments:

  1. How confident are you in the probabilities that the author assigned? I realize they're necessary for Bayesian analysis, but how does one determine that ice caps melting without human caused global warming is a "10%" probability?

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  2. This is really just an exercise in public opinion polling and probability. It's not exactly a science based measurement. You could apply it to the science community and see what percentage thing global warming is human caused or not in order to get a semi-scientific measurement of the accuracy of the study.

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