Crash Course Statistics: Bayesian Inference

Adriene Hill introduces Bayesian statistics, focusing on Bayes' Theorem and its application in updating beliefs based on new information. The video explains how Bayesian hypothesis testing works, using examples like breast cancer probability and Star Wars fandom. It highlights the subjectivity in Bayesian inference and addresses criticisms. The video concludes with real-life applications, emphasizing how Bayesian methods align with natural thinking processes.

What is an example of a belief that most people share?

• That school uniforms are unnecessary.

• That the sun will rise tomorrow.

• That all snakes are dangerous.

• That vegetarianism is the healthiest diet.

What does Bayes' Theorem help us calculate?

• The probability of A given B.

• The probability of B given A.

• The probability of A or B.

• The probability of A and B.

In the example of Maria's blind date, what initial belief does she have about Star Wars fans?

• That 60% of people are Star Wars fans.

• That 70% of people are Star Wars fans.

• That 40% of people are Star Wars fans.

• That 50% of people are Star Wars fans.

What is a Bayes' Factor?

• A measure of the overall probability of an event.

• A ratio of the probability of our information under one hypothesis compared to another.

• A statistical measure used to determine the likelihood of an event.

• A method to calculate the probability of A given B.

What is the 'posterior belief' in Bayesian statistics?

• The belief before seeing any evidence.

• The measure of how much evidence should change prior beliefs.

• The ratio of two hypotheses.

• The belief after seeing the evidence.

Why is Bayesian statistical inference sometimes criticized?

• Because it does not use prior beliefs.

• Because it is not used in scientific research.

• Because it is too complex to understand.

• Because it includes subjective beliefs in its calculations.

How can you adjust your own beliefs using a researcher's Bayes Factor?

• By multiplying your prior odds by the Bayes Factor.

• By adding the Bayes Factor to your prior odds.

• By dividing your prior odds by the Bayes Factor.

• By subtracting the Bayes Factor from your prior odds.

What happens when there is sufficient evidence in Bayesian hypothesis testing?

• Two people with different prior odds will often come to the same conclusion.

• Two people with different prior odds will always come to different conclusions.

• The prior odds become irrelevant.

• The evidence is ignored.

What is an example of Bayesian inference in everyday life?

• A person ignoring all previous evidence when new evidence is found.

• A doctor updating the odds of a patient having the flu based on symptoms.

• A scientist using only objective data in their calculations.

• A person making decisions without considering any prior beliefs.

What do Bayesians mean by 'yesterday’s posterior is today’s prior'?

• Updated beliefs from yesterday become the prior beliefs for today.

• New evidence is ignored.

• Prior beliefs are always the same.

• Posterior beliefs are not important.