Credence (statistics)

Credence is a statistical term that expresses how much a person believes that a proposition is true.^[1] As an example, a reasonable person will believe with 50% credence that a fair coin will land on heads the next time it is flipped. If the prize for correctly predicting the coin flip is $100, then a reasonable person will wager $49 on heads, but they will not wager $51 on heads.

Credence is a measure of belief strength, expressed as a percentage. Credence values range from 0% to 100%. Credence is deeply related to odds, and a person's level of credence is directly related to the odds at which they will place a bet. Credence is especially important in Bayesian statistics.

If a bag contains 4 red marbles and 1 blue marble, and a person withdraws one marble at random, then they should believe with 80% credence that the random marble will be red. In this example, the probability of drawing a red marble is 80%.

Credence values can be based entirely on subjective feelings.^[1][2] For example, if Alice is fairly certain that she saw Bob at the grocery store on Monday, then she might say, "I believe with 90% credence that Bob was at the grocery store on Monday." If the prize for being correct is $100, then Alice will wager $89 that her memory is accurate, but she would not be willing to wager $91 or more. Given that Alice is 90% credent, this level of belief can be expressed as gambling odds in the following ways:

• 90% credence
• 1 / 9 fractional odds (1 to 9)
• 1.11 decimal odds
• -900 moneyline odds
• The return on a $100 wager is $11.11 (plus the $100 initial wager).

See the article odds for conversion equations.

References