A prior distribution where the probability of every outcome is the same. For discrete data, this is a probability of 1/N for each value, where N is the number of values. If the data is unbounded there is no meaningful uniform prior, and the Cauchy distribution is often used as a best alternative, but for this you need to decide a midpoint and spread, either of which may introduce unintentional bias. You also have to be careful about the perspective from which data is measured. For example, with sound do you choose a prior that is uniform over power or decibels? Because the latter is the logarithm of the former, the uniform prior of one is not uniform for the other. This is particularly important in Bayesian statistics as the choice of prior can make a big difference to the results. See also uniform distribution.

Used on pages 77, 85