I don’t like the Wikipedia definition of Bayesian statistics. The Merriam-Webster definition is much better!

2026-03-19 · Source: Statistical Modeling, Causal Inference, and Social Science · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Advanced, quick

Summary

The provided content critiques Wikipedia's current and past definitions of Bayesian statistics and Bayesian inference, arguing that they inaccurately emphasize "degree of belief" or "updating probability that a hypothesis may be true." The author proposes an alternative definition: "Bayesian statistics is a method for obtaining inferences and predictions by constructing a joint probability distribution over all parameters, observed data, latent quantities, and potential alternative or future data." This proposed definition highlights the use of probability distributions over data, parameters, and unknown quantities, and the necessity of a joint distribution. The author also praises Merriam-Webster's definition as superior, noting its clarity in describing the assignment of prior probabilities and the application of Bayes' theorem for revision.

Key takeaway

For data scientists and researchers evaluating statistical methodologies, recognize that Bayesian statistics is more accurately defined by its use of joint probability distributions over all model components, rather than solely as a "degree of belief." Your understanding should emphasize the mathematical modeling aspect and the construction of comprehensive probabilistic models, aligning with Merriam-Webster's definition for a clearer conceptual foundation.

Key insights

Bayesian statistics is fundamentally about constructing joint probability distributions, not solely about "degrees of belief."

Principles

• Probability is a mathematical model.
• All statistical methods use assumptions.
• Bayesian models require a joint distribution.

Method

Bayesian statistics involves constructing a joint probability distribution across parameters, observed data, latent quantities, and future data to derive inferences and predictions.

In practice

• Apply probability to all model elements.
• Focus on joint distributions for complex models.

Topics

• Bayesian statistics
• Probability theory
• Statistical inference
• Joint probability distribution
• Bayes' theorem

Best for: AI Researcher, Data Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Statistical Modeling, Causal Inference, and Social Science.