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Questions and Answers
What is the initial prior distribution over θ denoted as?
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?
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?
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?
Which factor is the same for all possible hypotheses being considered?
What is the posterior probability of a hypothesis proportional to?
What is the posterior probability of a hypothesis proportional to?
Bayesian inference is a method of statistical inference that uses Bayes' theorem to update the probability for a hypothesis as more evidence becomes available.
Bayesian inference is a method of statistical inference that uses Bayes' theorem to update the probability for a hypothesis as more evidence becomes available.
What is the posterior probability?
What is the posterior probability?
What does the prior probability represent in Bayesian inference?
What does the prior probability represent in Bayesian inference?
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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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