Credence is a statistical term that expresses how much a person believes that a proposition is true. As an example, a reasonable person will believe with 50% credence that a

fair coin In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In th ...

will land on heads the next time it is flipped. If the prize for correctly predicting the coin flip is $100, then a reasonable

risk-neutral In economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indif ...

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 closely related to

odds Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have ...

, 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 Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...

. 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 Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

of drawing a red marble is 80%. Credence values can be based entirely on subjective feelings. 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

for conversion equations.

References

{{reflist Bayesian statistics