21 August 2011

More Fun With Uncertainty Guidance

Here is a another math exercise.  In its AR4 report the IPCC says:
The uncertainty guidance provided for the Fourth Assessment Report draws, for the first time, a careful distinction between levels of confidence in scientific understanding and the likelihoods of specific results. This allows authors to express high confidence that an event is extremely unlikely (e.g., rolling a dice twice and getting a six both times), as well as high confidence that an event is about as likely as not (e.g., a tossed coin coming up heads). Confidence and likelihood as used here are distinct concepts but are often linked in practice.
Here are some specific definitions to help you answer some questions.

A. "high confidence" means "about 8 out of 10 chance of being correct".
B. "extremely unlikely" means "less than 5% probability" of the event or outcome
C. "as likely as not" means "33 to 66% probability" of the event or outcome

So here are your questions:

1. If the IPCC says of a die that it has -- "high confidence that an event is extremely unlikely (e.g., rolling a dice twice and getting a six both times)" -- how should a decision maker interpret this statement in terms of the probability of two sixes being rolled on the next two rolls of the die?

2. If the IPCC says of a die that it has -- "high confidence that an event is about as likely as not (e.g., a tossed coin coming up heads)" -- how should a decision maker interpret this statement in terms of the probability of a head appearing on the next coin flip?

Please provide quantitative answers to 1 and 2, show your work.