Bayesian Statistics Exam Questions with 100% Correct Answers

Bayesian statistics is about Correct Answer - Quantified belief - Common sense expressed in numbers - Updating belief in light of new evidence Bayes theorem Correct Answer The probability of an event occurring based upon other event probabilities. Posterior = prior + likelihood Posterior probability Correct Answer Probability of the hypothesis given the data. The updated belief in the hypothesis after assessing the data. Posterior distribution can be used to quantify the plausible values of a parameter. Likelihood Correct Answer Probability of the data, given the hypothesis, divided by the probability of the data. The support the data provides for the hypothesis. Prior probability Correct Answer Initial subjective belief in the probability of the hypothesis. Can be informative or uninformative. Informative prior distribution Correct Answer The peak is the value with the highest probability and the tails represent the values with low probability. When you are confident in your belief in a specific value of theta. Highly informative - data will influence posterior distribution less. Uninformative prior distribution Correct Answer A flat line which means that you are prepared to believe all possible outcomes with equal probability. Bayesian hypothesis testing Correct Answer Comparing different beliefs, and getting a Bayes factor that favors one or the other. Bayes factor Correct Answer The ratio of the likelihood of the data under the alternative and the null.