Bayesian stats Flashcards
(15 cards)
Formula for Bayes’ Theorem
Belief (posterior) = evidence (likelihood) x expectation (prior)
This formula highlights the relationship between prior beliefs, evidence, and updated beliefs.
‘Prior’ in Bayes’ Theorem
What we believe before seeing data
The prior represents initial beliefs or assumptions prior to obtaining new evidence.
‘Likelihood’ in Bayes’ Theorem
Probability of data given the hypothesis
Likelihood assesses how probable the observed data is under a specific hypothesis.
‘Posterior’ in Bayes’ Theorem
Updates belief after seeing data
The posterior is the revised belief that incorporates the new evidence.
Key Bayesian concepts
-Bayesian reasoning
-Surprising claims require stronger evidence
-Incorporates prior beliefs in analysis
Bayesian Reasoning
We naturally update beliefs based on new evidence
This concept emphasizes the dynamic nature of belief adjustment in light of new data.
Bayesian approach to hypothesis testing
Compare how likely data is under both H₀ and H₁
This approach assesses both null and alternative hypotheses simultaneously.
Bayes Factor (BF)
BF = P(data|H₁)/P(data|H₀)
The Bayes Factor quantifies the strength of evidence in favor of one hypothesis over another.
Bayes Factor greater than 1 (BF>1)
Evidence for H₁
A BF greater than 1 suggests that the data is more likely under the alternative hypothesis.
Bayes Factor less than 1 (BF<1)
Evidence for H₀
A BF less than 1 suggests that the data is more likely under the null hypothesis.
Bayes Factor around 1 (BF~1)
No strong evidence either way
A BF close to 1 indicates a lack of decisive evidence for either hypothesis.
Can NHST provide evidence for H₀?
No
NHST can only fail to reject H₀ but cannot confirm its validity.
Difference between Bayesian and Frequentist approaches
Frequentists interpret p-values as frequency under H₀; Bayesians assess which hypothesis is more likely
This distinction illustrates the fundamental philosophical differences between the two statistical paradigms.
Credible Interval
95% chance true value lies within intervals
Unlike confidence intervals, credible intervals provide a probability-based interpretation.
Credible Interval vs Confidence Interval
CI: in repeated samples, 95% of intervals will contain the mean; Credible interval: 95% chance true value lies within intervals
This emphasizes the difference in interpretation between the two types of intervals.
