The New Statistical Rhetoric of Climate Change

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This post comes at a good time since I am presently using subjective probabilities to estimate the odds of which sayings of Jesus recorded in the gospels really go back to him.

Subjective probabilities need not be "subjective". When we define the probability of either heads or tails in a coin toss as 0.5 we are making a "subjective statement by not basing it on a long number of trials. Instead we use the symmetry of the problem to define the probability.

Subjective probabilities also have validity when used relatively as in decision making. As long as the rule for defining them is consistent the absolute probability is not really important, only their differences.

SpiritSeeker:

I wonder if the coin toss example is really not subjective or if our idealized model has rendered it trivially subjective. This is not a rhetorical question -- I don't know a lot about this area, so I really do wonder.

Our statistical model posits a coin with two sides, essentially no thickness, falling unfettered in an otherwise still environment,

My thought is this: Suppose, when it comes time to apply the model, the coin tossed in not a fair coin. Suppose the coin bounces against something like a stalagmite (or our leg, for that matter) on the way down. What about powerful jets of air blowing crosswise across the path of the coin's descent? What if it lands on its edge? What if the dog eats it?

We don't suppose these things because we are dealing with a highly idealized model and we know that when it comes time to toss a real coin we can constrain conditions to reduce the necessity of our having to take variables into account. What I think we have done, though, is reduce the "subjectivity". I don't think we've fundamentally changed the character of the statistical model. That's why introductory statistics courses like to use such simple cases to begin with.

It would be really interesting to see a statistics textbook that moved from the very simple coin toss example to more complicated ones -- coins tossed by two divers underwater, coins tossed by parachutists jumping out of airplanes, coins dumped - one hundred at a time - from an automobile driving fifty miles an hour. My guess is that the authors would quickly have to progress to experimental trials.

HI Baslow,

I think what you are getting to here is what most people who deal with probability in terms of automated decision making would call the precision of the probability (precision is the opposite of your "subjectivity", a high precision means low subjectivity) The greater the number of experimental trials the greater the precision of the resultant probability. Yet, as you pointed out, if jets of air or other factors affect the coin toss in a semi-random fashion one would need more coin tosses to get an accurate probability number than one would in an idealized situation.

This area of probability does not seem to be very well developed as far as I can tell. And what is not well understood is not taught or even mentioned in non-graduate level courses.

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