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,H^N). 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|H^N)=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|H^N)=.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(H^N)=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

A Bayes factor analysis of Extrasensory Perception (ESP) claims

Introduction:
Daryl Bem a social psychologist at Cornell University has claimed that people can feel or sense important events in the future that could not otherwise be anticipated.  In Bem’s experiments he claimed that people can feel future reward and punishment events and were able to anticipate a random choice at a rate above chance.  Bem, in his experiment, used a conventional approach where the same basic phenomena was targeted from slightly different angles. Bem used null-hypothesis significance testing and p-values as evidence to reach his judgements.  The authors of this article, Rouder and Morey, employed a Bayes factor analysis to assess the evidence in the Bem experiments.   

Summary:
The authors’ of the article attempted to employ a Bayes factor measurement to evaluate Bem’s evidence.  A Bayes factor measurement is a method of model selection based on Bayes posterior odds and is used as an alternative to frequency hypothesis testing (which is what Bem used).  The posterior odds in a Bayes analysis is the probability ratio of data given hypothesis.  The formula for the posterior odds is usually given as:

Where:

• Pr(M|D) is the posterior odds, which describe the analyst’s degree of belief in the hypothesis after observing the data.  Usually described as the Probability of M given D.
• Pr(D|M) is a likelihood and represents the probability that some data is produced under the assumption of the model.

The basic assumption in Bayes factor analysis is that prior (Pr(D|M)) and posterior information (Pr(M|D)) are combined into a ratio that provides evidence in favor of one model versus another.   

The general form given for Bayes factor is:


The interpretation of K is given as:

Rouder and Morey’s analysis found that people can “feel” the future with neutral and erotic stimuli to be slight, with Bayes factor scores (K value) of 3.23 and 1.57 respectively.  There was, however, some evidence for Bem’s hypothesis that people can “feel” the future with emotionally valenced nonerotic stimuli. A Bayes factor of 40 was recorded for this type of stimuli.  The authors think the K value of 40 is noteworthy, but, they believe it is still a magnitude lower than what is required to overcome appropriate skepticism of ESP.

The summary of Rouder and Morey’s findings are below:

Conclusion:
Based on the number of articles read to create this summary, Bayes factors appear to be flexible and allow for the comparison of multiple hypotheses simultaneously.  Statisticians claim the Bayes factor is intuitive, however, the factors are difficult to calculate. Also, Bayes factor analysis is unlikely to be undertaken by someone with only a cursory understanding of statistics.   

Source:
Rouder, J., & Morey, R. (2011). A bayes factor meta-analysis of bem's esp claim. Psychonomic Bulletin & Review, 18(4), 682-689. Retrieved from http://drsmorey.org/bibtex/upload/Rouder:Morey:2011a.pdf