Chapter 6 Bayesian Methods Flashcards
(8 cards)
Q: When do you use a Student’s t-distribution?
A: Use it when the sample size is small (n < 30), the population standard deviation is unknown, and the data is approximately normal.
Q: What is a Student’s t-distribution?
A: It is a probability distribution used for small sample sizes, with a mean of 0 and standard deviation greater than 1, depending on the degrees of freedom.
Q: How is the Student’s t-distribution defined?
A: It has a mean of 0 and a standard deviation that depends on the degrees of freedom. The PDF is defined by a specific formula involving the Gamma function.
Q: How to approach answering questions on Bayes’ Theorem?
A: Identify the prior probabilities, likelihoods, and evidence. Then apply Bayes’ Theorem formula to update the belief about a parameter based on observed data.
Q: What is Bayes’ Theorem?
A: Bayes’ Theorem is a way to update the probability of a hypothesis based on new evidence. It is given by P(B|A) = [P(A|B) * P(B)] / P(A).
Q: How to calculate a posterior distribution in Bayesian statistics?
A: Use the formula: Posterior ∝ Likelihood × Prior. Integrate the joint distribution over the parameter space to normalize the posterior.
Q: What is a conjugate family of distributions?
A: A conjugate family of distributions allows the posterior distribution to belong to the same family as the prior, making computations easier.
Q: What is the role of loss functions in Bayes’ estimators?
A: A loss function quantifies the cost of estimation errors, and Bayes’ estimators minimize the expected loss.
