Wednesday, June 25, 2014

"Finite chance"

The phrase "finite chance" (see Google) seems to be consistently used to mean a a nonzero chance, or maybe a chance that is neither zero nor one. The phrase is very commonly used in the longer phrase "small but finite chance" (oddly, Google has more hits for the longer phrase).

Yet zero is as finite a number as you can get! So what is going on? Maybe people are implicitly thinking in terms of something like von Neumann's log odds (log p/(1−p)), where probability zero is represented by −∞ and probability one by +∞? In that case, "finite probability" would indeed mean what Bayesians call "non-extreme probability", i.e., a probability strictly between zero and one.

By the way, it seems to me that when we connect probability with evidence it is natural to think in the von Neumann way (the force of new evidence will be additive then), while if we connect it with statistical expectations it is natural to think in the classical way.


Austin said...

I think what people really mean when they say "finite chance" is "non-negligible chance," or "significant chance." That's how it seems to be used in context, at least.

Alexander R Pruss said...

That may be an implicature. Why bother noting that the probability is greater than zero if the probability is negligible?

Here is a hit where clearly "non-zero" is meant. Here is another. Note that both are from somewhat philosophical discussions, but that's to be expected.

William said...

Perhaps folks are getting their vocabulary from teachers of the Bayesian rule of thumb that none of the posterior data probabilities are allowed to be zero, so that in the Bayes formula no divisor can be zero, even though they don't know why they would use the term.

So this would be sort of a cargo cult style use of terminology.

SMatthewStolte said...

I don’t know what the importance of this would be, but here is a Google NGram graph of “finite chance” and “finite probability.”

Alexander R Pruss said...

A lot of hits for "finite probability" may be for "finite probability space", a different kettle of fish ("finite" modifies "space", not "probability").

Alexander R Pruss said...

Here's another explanation. Maybe "finite probability" means for people something like "one out of a finite number", i.e., in a probability x/y, the "finite" describes the denominator.