Bayesian Inference Quiz

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Questions and Answers

What is the initial prior distribution over θ denoted as?

  • p(α | θ)
  • p(θ | α) (correct)
  • p(θ)
  • p(α)

What is the probability of observing evidence E given hypothesis H?

  • P(E)
  • P(H)
  • P(E|H) (correct)
  • P(H|E)

What is the term used for the probability of a hypothesis given the observed evidence?

  • Posterior probability (correct)
  • Model evidence
  • Marginal likelihood
  • Prior probability

Which factor is the same for all possible hypotheses being considered?

<p>P(H) (A)</p> Signup and view all the answers

What is the posterior probability of a hypothesis proportional to?

<p>The prior probability and the likelihood (B)</p> Signup and view all the answers

Bayesian inference is a method of statistical inference that uses Bayes' theorem to update the probability for a hypothesis as more evidence becomes available.

<p>Bayesian inference is a method of mathematical inference that uses Bayes' theorem to update the probability for a hypothesis as more evidence becomes available. (A)</p> Signup and view all the answers

What is the posterior probability?

<p>The probability of a hypothesis after new evidence is observed. (B)</p> Signup and view all the answers

What does the prior probability represent in Bayesian inference?

<p>The probability of a hypothesis before new evidence is observed. (C)</p> Signup and view all the answers

Flashcards

Prior distribution p(θ | α)

The initial probability distribution over the parameter θ, influenced by the hyperparameter α.

Likelihood P(E|H)

This is the likelihood of seeing the evidence E, assuming that the hypothesis H is true.

Posterior probability

The probability of a hypothesis being true after considering the evidence. It combines prior knowledge with new data.

Constant factor P(H)

Prior probability P(H) is constant across all hypotheses being evaluated, ensuring each starts with a fair assessment.

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Posterior proportionality

The posterior probability reflects both the prior belief and how well the hypothesis predicts the observed data (likelihood).

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Bayesian inference

A statistical method that uses Bayes' theorem to revise probabilities as new data emerges.

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Posterior probability

The probability of a hypothesis being true after considering the new evidence, reflecting an update from the prior.

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Prior probability

The initial probability of a hypothesis before any new evidence is considered, representing a baseline belief.

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Study Notes

Bayesian Inference Basics

  • The initial prior distribution over θ is denoted as P(θ).
  • The probability of observing evidence E given hypothesis H is denoted as P(E|H).
  • The term used for the probability of a hypothesis given the observed evidence is posterior probability.
  • The likelihood P(E|H) is the same for all possible hypotheses being considered.
  • The posterior probability of a hypothesis is proportional to the product of the prior probability and likelihood.

Bayesian Inference Concepts

  • Bayesian inference is a method of statistical inference that uses Bayes' theorem to update the probability for a hypothesis as more evidence becomes available.
  • The posterior probability represents the updated probability of a hypothesis given the observed evidence.
  • The prior probability represents the probability of a hypothesis before observing the evidence.

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