Multioutcome

Multioutcome refers to a random outcome that can take one of several discrete categories, as opposed to a binary outcome which has only two possibilities. In probabilistic modeling, the set of all possible results is called the sample space or outcome space. A multioutcome scenario is typically described by a probability distribution over its categories.

For a single trial with k possible outcomes, the categorical distribution assigns probabilities p1, ..., pk with sum 1. When many independent trials are performed, the counts of each category follow a multinomial distribution characterized by the same category probabilities and the number of trials n. If the probabilities are unknown, they can be estimated by maximum likelihood or Bayesian methods. In some contexts, a Dirichlet prior leads to the Dirichlet-multinomial model for overdispersed counts.

Data about multioutcome processes are commonly encoded as labels or integers corresponding to categories. Inference aims to determine the probability of each outcome, compare categories, or predict the most probable outcome for a new trial.

Applications include quality control with multiple defect types, opinion polling with several response categories, genetics with genotype classes, language processing with word classes, and A/B testing with more than two variants.

See also: categorical distribution, multinomial distribution, probability mass function, sample space, discrete random variable.

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