Prior probability

A prior probability is the probability assigned to a hypothesis or outcome before new evidence is incorporated. It represents uncertainty based on existing information or assumptions.

Bayes' theorem: A rule for updating probabilities using new evidence and the probability of that evidence under competing hypotheses. It combines a prior with a likelihood to calculate a posterior.
Probability distribution: A mathematical description assigning probabilities to possible values of a random variable. A prior is often a distribution over possible parameter or hypothesis values.
Frequentist inference: A statistical approach that evaluates procedures through their long-run behavior under repeated sampling. It generally avoids assigning probabilities to fixed hypotheses before observing data.
Beta distribution: A continuous probability distribution on the interval from zero to one, commonly used for unknown probabilities. A beta prior conveniently represents uncertainty about a Bernoulli success probability.
Prior sensitivity analysis: An assessment of how statistical conclusions change under different plausible prior distributions. It tests whether a conclusion is robust to reasonable choices of prior.
Likelihood function: A function measuring how probable observed data are under different parameter values or hypotheses. The likelihood weights each hypothesis against the prior when evidence arrives.
Conditional probability: The probability of an event given that another event is known to have occurred. Bayesian updating relates evidence-conditioned probabilities to prior probabilities.
Maximum likelihood estimation: A method that selects parameter values maximizing the probability of observed data. Unlike Bayesian estimation, it does not combine a likelihood with a prior distribution.
Dirichlet distribution: A probability distribution over vectors of nonnegative values that sum to one. It serves as a prior for categorical probabilities and multinomial models.
Subjective probability: An interpretation of probability as a rational degree of belief held by an agent. It provides one account of what prior probabilities represent.

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