Bayesian Analysis and P-Values

Dr. Jay explains the differences between p-values and Bayesian posterior probabilities, using an example to illustrate how they can lead to different conclusions. The video discusses the Jeffrey Lindley Paradox, where frequentist and Bayesian methods disagree under certain conditions. It emphasizes understanding the distinct roles of p-values and Bayesian probabilities in hypothesis testing and model adequacy. The video concludes with a summary of the series and a preview of upcoming topics on comparing proportions and normal means.

What is the main topic of Dr. Jay's video?

• The history of statistics

• Advanced algebra techniques

• Introduction to calculus

• P-values and Bayesian posterior probabilities

What is the hypothesis in the binomial model example?

• The probability of success is 0.5

• The probability of success is 0.7

• The probability of success is 0.3

• The probability of success is 0.9

What p-value is obtained from the example with 10,000 observations?

• 0.05

• 0.047

• 0.1

• 0.02

What is the posterior model probability in the Bayesian approach of the example?

• 0.96

• 0.5

• 0.8

• 0.1

What is the Jeffrey Lindley Paradox?

• A situation where Bayesian probabilities are always higher

• A situation where all statistical models are incorrect

• A situation where p-values and Bayesian probabilities disagree

• A situation where p-values and Bayesian probabilities agree

Which condition is NOT part of the Jeffrey Lindley Paradox?

• Small effect size

• Equal prior model probabilities

• Large number of observations

• Precise alternative hypothesis

Why is the Jeffrey Lindley Paradox not considered a real problem?

• Because it only occurs in small datasets

• Because p-values and Bayesian probabilities measure different things

• Because it is a rare occurrence

• Because it only applies to normal distributions

What do p-values measure?

• The likelihood of the alternative hypothesis

• The overall accuracy of a model

• The predictive ability of a model

• The compatibility of data with the null hypothesis

What do Bayesian posterior model probabilities measure?

• The likelihood of the null hypothesis

• The overall accuracy of a model

• The predictive ability of a model relative to others

• The compatibility of data with the null hypothesis

What is required for Bayesian analysis according to the video?

• A large sample size

• At least two well-thought-out models with informative priors

• Only one well-thought-out model

• A precise null hypothesis