Isn’t this unit actually called the deciban, with the base unit being known as either the Ban or the Hartley? The WP article on Bayes factors also gives a table of qualitative interpretations, sourced from Harold Jeffreys. Note that your tables seem to give five decibans (1.6 bits of evidence) as “beyond a reasonable doubt”, whereas Jeffreys would merely describe such a degree of evidence as “substantial”. “Strong” evidence requires more than 3.3 bits, or 10 decibans.
Decibans, deciHartleys, and decidits are, indeed, close to being the ‘official’ names for this unit, insofar as any exist.
As for the ‘beyond a reasonable doubt’ line, some time ago, I went looking for numbers, and the best I found was a specialized survey which asked how certain people would have to be in order to convict someone as being guilty ‘beyond a reasonable doubt’. The answers varied depending on the crime, from 75% for petty larceny to 95% for murder; so I assumed that the higher numbers were because of the significant punishments involved, and that people wanted to be extra sure that if they voted to convict, that the person really deserved it; and thus that the ‘real’ meaning of ‘beyond a reasonable doubt’ was the lower number, 75%.
Though… are there other examples of where we have a unit that mathematically is unitless and just represents a multiplication factor, other than Decibels?
Though… are there other examples of where we have a unit that mathematically is unitless and just represents a multiplication factor, other than Decibels?
Radians and degrees (measures of angle) are common dimensionless units.
I calculated a similar table for my own purposes, one version of which can be seen at http://www.orionsarm.com/eg-article/4d5bf17b86585 , another at http://www.lojban.org/tiki/bei%27e .
Isn’t this unit actually called the deciban, with the base unit being known as either the Ban or the Hartley? The WP article on Bayes factors also gives a table of qualitative interpretations, sourced from Harold Jeffreys. Note that your tables seem to give five decibans (1.6 bits of evidence) as “beyond a reasonable doubt”, whereas Jeffreys would merely describe such a degree of evidence as “substantial”. “Strong” evidence requires more than 3.3 bits, or 10 decibans.
Decibans, deciHartleys, and decidits are, indeed, close to being the ‘official’ names for this unit, insofar as any exist.
As for the ‘beyond a reasonable doubt’ line, some time ago, I went looking for numbers, and the best I found was a specialized survey which asked how certain people would have to be in order to convict someone as being guilty ‘beyond a reasonable doubt’. The answers varied depending on the crime, from 75% for petty larceny to 95% for murder; so I assumed that the higher numbers were because of the significant punishments involved, and that people wanted to be extra sure that if they voted to convict, that the person really deserved it; and thus that the ‘real’ meaning of ‘beyond a reasonable doubt’ was the lower number, 75%.
A bit of Googling turns up http://www.law.northwestern.edu/faculty/fulltime/diamond/papers/conflictBetweenPrecisionAndFlexibility.pdf , which appears to be what I was looking at.
It certainly does get called that, but I don’t know how common it is.
I do like “Jaynes” as the name of the unit.
Though… are there other examples of where we have a unit that mathematically is unitless and just represents a multiplication factor, other than Decibels?
Radians and degrees (measures of angle) are common dimensionless units.