Bayesian model

As explained in Bayesian Optimization in Action

A Bayesian model represents uncertain quantities with probability distributions and updates beliefs using observed data and Bayes' theorem.

A Bayesian model represents uncertain beliefs with probability distributions and updates them when new observations arrive. The same evidence can produce different conclusions because people begin with different prior probabilities. section 3.1

The carnival psychic

Imagine a person correctly guessing a number from 0 to 9 one hundred times. For a true psychic, the likelihood of a correct guess is 1; without psychic ability, it is 1 out of 10. Each observer combines these likelihoods with a personal prior belief and updates to a posterior probability. A skeptical observer’s belief rises slowly, while someone who assigns a prior of 0 remains at 0. section 3.1

Figure 3.3 How each person’s prior belief is updated by the same data. Compared to Bob’s, your prior is much lower and increases more slowly. Alice’s prior is 0 and stays at 0 throughout.

Compare how identical observations produce different posterior beliefs when the initial priors differ. section 3.1

How Bayesian Optimization in Action covers it

How deep it goes

Defines prior, likelihood, and posterior through a toy example while treating Bayes’ theorem only at a high level.

Examples

Uses a carnival psychic guessing secret digits one hundred times and compares three observers’ reactions.

What you can do after

Evaluate how prior beliefs influence posterior conclusions when multiple observers receive identical evidence.

How it connects

Connects prior probability, likelihood, posterior probability, and Bayes’ theorem.

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Also explained in

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  Causal AIBayesian modeling is the construction and analysis of probabilistic models using prior distributions, likelihoods, and posterior distributions.

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Related concepts

• language modelcontrasts with · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.
• prior probabilityhas part · A prior probability distribution represents beliefs or assumptions about an unknown quantity before relevant observations or evidence are incorporated.
• likelihoodhas part · A likelihood is the probability of observed data under a specified probabilistic model, regarded as a function of candidate hypotheses or parameter values.
• posterior probabilityproduces · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
• datasethas part · A dataset is an organized collection of related data items, records, or observations treated as a unit for storage, processing, analysis, or computation.
• prior knowledgeuses · Prior knowledge is information, beliefs, skills, or assumptions available to an agent before it encounters a task or incorporates new observations.

This explainer was generated by Manning's knowledge graph from the text of Bayesian Optimization in Action. The section links point to the parts of the book it draws on.