It’s my belief that everybody’s a Bayesian, but not all admit it. Yet.

Their shared interest was compound uncertainty (although they did not entirely agree on the proper stat treatment of compound uncertainty problems). Compound uncertainty may be roughly defined as the increased chance of making at least one mistake when drawing more than one direct inference, for instance when many distributions (or statistical tests) are considered simultaneously.

Scheff? and others (like John Tukey) considered Duncan’s treatment too “liberal” because it fails to suppress enough Type I errors (false positives), meaning it fails to reject the null hypothesis when the null hypothesis is true. Duncan’s point of view might be crudely summarized as the null hypothesis is never really true, the accused is never really innocent, two phenomena are never really the same, you really are pregnant, despite the statistical significance of the test.

Both Scheff? and Duncan eventually became Bayesians. Bayesians conjecture that belief systems exist prior to collecting the data, and that those a priori beliefs influence the posterior probabilities that result from data analysis. Another way to say this is that Bayesians reduce the uncertainty through their a priori confidence in their (mystical?) predictive powers.

I think we are all Bayesians to some degree. We “know” what’s going to happen, or feel like we do. You need some Bayesian confidence just to get out of bed each day and give it another try.

Alan Watts, on the other hand, (who was not a statistician), preached the wisdom of insecurity. He held that we don’t know shinola about the future, and that’s what makes existence a wonderful adventure.

I hope all that helps, although I can see how it might not. Here’s another way to look at it: uncertainty aggregates.

Here is my stock statement on AGW

It is trivially true that man—and every other organism—influences his environment and therefore his climate. It is only a question of how much and to what extent, if any, AGW is harmful or beneficial, and to what extent its harmful effects can be mitigated, or its benefits exploited. We are not interested in trifles: AGW means discernible, large-scale important effects on climate.

I am trying to understand, or offer a framework for, quantifying the uncertainty of the entire process: how uncertain are our observations, explanations of observations, predictions of new ones, and the effects supposedly caused by AGW.

Briggs

At one time (the Eocene) there were boreal tropical forests and many more species than exist today. Indeed, for 99% of the past 300 million years, the Earth has been warmer overall than today. Warmer is the normative condition, if one takes enough paleo-history into account.

It is in nature of Man that change is held to be bad, precisely because the future is uncertain. Uncertainty itself is held to be a negative. But the mere fact that the future is uncertain does not imply (much less guarantee) that it will be bad.

Many have expended enormous effort in predicting the terrible consequences of climate change. Few have spent much time making optimistic predictions. However, the future is what we make of it, whatever it might be.

Usually works.

I asked a friend of mine for his opinion on the role of uncertainty a couple of weeks ago. He was at CERN when he got my e-mail. Probably forgotten by now. I’ll have to re-write him. Since his current focus is on strings, the role that uncertainty plays in modeling is something that he has to take into consideration on a daily basis. Something I wish more modelers would do. The most irritating feature of the current debate is the certainty expressed, and criticism supressed.

It just doesn’t make sense to me.

If temperature records in the US go back to 1880, roughly 1 in 128 should be broken each year. For a given date, roughly 1 in (128 *365) or 1 in 46,720 should be broken for each date of the year, assuming no trends. With a warming trend, new highs should be somewhat more frequent than that, with a cooling trend, less frequent than that.

Here I’m guessing, but I suppose the number of new records with a constantly increasing temperature trend should be rougly proportional to
time / (1 - (T/SD))
where SD is the standard deviation in temperature
from year to year, say about 0.1 degrees, and
T is the linear trend fit, say 0.01 degrees per year.

In my example, if the world was warming up at 1C per century, and the standard deviation in temperature is 0.1 C per year, you’d expect 10/9
as many records as the logarithmic prediction.

With constantly decreasing temperatures, again
given the above figures, you’d get only 9/10 as many new highs as a strictly logarithmic projection-

Since the real climate shows increasing from 1880 to 1940, decreasing from 1940 to about 1970, and increasing again from about 1970 to 2000, fudge factor adustments for new records will be slightly more complex than that.
A. McIntire

http://wattsupwiththat.wordpress.com/2008/03/13/to-tell-the-truth-will-the-real-global-average-temperature-trend-please-rise-part-2/

Good luck with the simultaneous translation - I find them very difficult. My one lesson from doing them in Latin America is to avoid making jokes - many do not translate and one’s sense of humor may not travel far from home!

Along with everything else, do you still play? My spring season starts in 10 days.