other methods - bayesian Flashcards
(16 cards)
What is the main idea behind Bayesian statistics?
Bayesian statistics is about updating your beliefs based on new evidence.
What are the three components of Bayes’ Theorem?
Prior (initial belief), Likelihood (evidence from data), Posterior (updated belief).
What is the formula for Bayes’ Theorem in words?
Posterior = Likelihood × Prior.
Give a real-world example of Bayesian reasoning.
You think it won’t rain (prior), but see grey clouds (evidence), so you now think rain is more likely (posterior).
How does Bayesian inference differ from NHST?
Bayesian inference compares the probability of H₁ vs. H₀ given the data, while NHST calculates how likely the data is if H₀ is true.
What is a Bayes Factor (BF)?
A ratio that compares how likely the data is under H₁ vs. H₀.
What does a Bayes Factor of 3 mean?
H₁ is 3 times more likely than H₀ given the data.
What does a Bayes Factor of 1/3 mean?
H₀ is 3 times more likely than H₁ given the data.
What does a Bayes Factor close to 1 indicate?
There is not much evidence in favor of either hypothesis.
What is a credible interval?
A Bayesian interval that shows the range where the true value likely lies, interpreted directly as probability.
How is a credible interval different from a confidence interval?
Credible intervals reflect the probability that the parameter lies within the interval, while confidence intervals do not.
Why do people prefer Bayesian methods?
They allow prior knowledge, provide probabilities about hypotheses, are intuitive, and flexible.
Can Bayesian methods provide evidence for the null hypothesis?
Yes, unlike NHST, Bayesian methods can support the null when BF < 1.
What is the philosophical appeal of Bayesian statistics?
It matches how people naturally think—adjusting beliefs based on new evidence.
What are ‘frequentists’ in statistics?
Statisticians who use traditional NHST methods focusing on p-values.
What does the Bayesian approach allow that NHST doesn’t?
It allows testing any hypothesis, not just the ‘no difference’ null hypothesis.
