ABSTRACT
This chapter describes various statistical distributions used in Bayesian Statistics. Although scalar and vector distributions can be found as special cases of their corresponding matrix distribution, they are treated individually for clarity. A Bernoulli trial or experiment is an experiment in which there are two possible outcomes, one labeled “success” with probability ϱ, the other labeled “failure” with probability 1 - ϱ. The Binomial distribution gives the probability of x successes out of n independent Bernoulli trials, where the probability of success in each trial is ϱ. A Bernoulli trial is an experiment such as flipping a coin where there are only two possible outcomes. The Beta distribution gives the probability of a random variable ϱ having a particular value between zero and one. The Beta distribution is often used as the prior distribution for the probability of success ϱ in a Binomial experiment.
