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A probability distribution representing beliefs about parameters before observing data.
DESCRIPTION
A prior distribution encodes assumptions and beliefs about parameters before data is observed. In Bayesian inference, the prior combines with the likelihood to yield the posterior. Priors can be informative, weakly informative, or noninformative depending on available knowledge. Conjugate priors simplify calculations by producing posteriors in the same family. Choice of prior affects results notably with limited data, making sensitivity analysis important.
ALTERNATIVE DEFINITIONS
Wikipedia
In Bayesian statistics, a prior probability is the probability assigned to an event or parameter before new data is taken into account.
Defines prior as probability before seeing data.
Encyclopaedia Britannica
Prior probability is the probability of an event before new evidence is considered.
Emphasizes pre-evidence assignment of probability.
StatLect
A prior distribution is the probability distribution that expresses one’s beliefs about a parameter before any data are observed.
Explicitly focuses on parameters and beliefs.
RELATED TERMS
Posterior Probability Bayes’ Theorem Likelihood Conjugate Prior Hyperprior Subjective Prior Empirical Bayes Noninformative Prior Jeffreys Prior Bayesian Inference
COMPETING TERMS
KNOWLEDGE AREAS
TARGET AUDIENCE
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EXTERNAL SOURCES
- Wikipedia - Prior probability
- Forecasting: Principles and Practice - Bayesian methods and priors explained
- StatLect - Bayesian inference with priors
- CRAN Task View - Bayesian packages and resources
TOP QUESTIONS
What is a Prior in Bayesian analysis?
It’s a probability distribution representing beliefs about parameters before observing data. Priors combine with likelihoods to form posteriors.
Category: Overview
How does the choice of Prior affect results?
With limited data, priors can strongly influence the posterior. Sensitivity analysis tests robustness to different priors.
Category: Opinion
What’s a conjugate Prior?
It’s a prior that, when combined with a likelihood, yields a posterior in the same distribution family, simplifying computation.
Category: Example
What is a noninformative Prior?
A prior intended to have minimal influence on the posterior, often reflecting ignorance. Use with care to avoid improper posteriors.
Category: Misunderstanding
How do Empirical Bayes priors work?
They estimate prior parameters from data, blending frequentist estimation with Bayesian updating.
Category: Topic
What are common mistakes when selecting Priors?
Using overly strong priors without justification, ignoring domain knowledge, and failing to test sensitivity.
Category: Mistakes
What risks arise from poorly chosen Priors?
Biased estimates and misleading inferences. Stakeholders may lose trust if priors seem arbitrary.
Category: Risks
How do you elicit Priors from experts?
Use structured interviews, quantile assessments, and calibration exercises. Translate beliefs into parameterized distributions.
Category: Requirements
What’s a competing approach to Priors?
Frequentist inference avoids priors, focusing on sampling distributions and estimators.
Category: Alternatives