...to bits of evidence

We talk bits and bytes when buying computers and video games, but few think of bits and bytes as tools of gambling theory. Actually that's where information units got their start in the 1940's. The statistical ideas behind them had been in use long before that.

If you enjoyed our earlier note about using bits and bytes to track everyday risks, then you might also be happy to hear that "there's not a bit of evidence" has literal meaning too. The bits of surprisal discussed earlier work best for unlikely occurrences. If you have a yes-no statement, however, subtracting the surprisal that it's true from the surprisal that it's false gives you the evidence (ebits) in its favor.

If the odds of a question being true are 2:1 = for:against, there is only 1 ebit of evidence in its favor since ebits obeys for/against=2^ebits. If the odds for:against = 4:1, then there are 2 ebits of evidence for it, while if for:against = 1:4 then there are 2 ebits of evidence against it.

The cool thing about ebits is this: Independent chunks of information simply add (or subtract) ebits from any case that you are trying to make. Thus ebits follow the common sense about levels of proof developed by folks with no background in statistics at all.

That's a good sign! So then what does "beyond a reasonable doubt" mean, in bits? For example, do you think the standard of proof in a civil court is more, or less, than 14 ebits in favor to make the case?

The uncool thing about ebits is that it provides no clue as to whether it makes sense to ask the "yes-no" question to which it's being applied.