Baysian Statistics
A quick recap
Made by @jgarcia621
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1: What is the range of Bayesian probability?
20s
-1 to 1
0 to ∞
-∞ to ∞
0 to 1
2: What is the core formula for the Bayesian Posterior distribution?
35s
Posterior ∝ Likelihood + Prior
Posterior ∝ Likelihood / Prior
Posterior ∝ Prior - Likelihood
Posterior ∝ Likelihood × Prior
3: What is the formula for the Bayesian probability?
20s
P(B|A) = (P(A) * P(B)) / P(A|B)
P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (P(B) * P(A)) / P(B|A)
P(B|A) = (P(A|B) * P(B)) / P(A)
4: he pink line represents the posterior mode. Which Loss Function does this estimator minimize?
20s
Zero-One Loss
Quadratic Loss
Absolute Loss
Infinite Loss
5: What does the likelihood function in Bayesian probability do?
27s
It calculates the probability of prior knowledge
It updates the prior probability based on new evidence
It eliminates uncertainties completely
It determines the absolute probability of an event
6: Both analyses estimated the same mean (𝜇=5), but Analysis B (Green) is much narrower/sharper. What is the most likely cause?
20s
Analysis B used a "flat" prior
Analysis B had a higher variance in the data.
Analysis B had a higher variance in the data.
Analysis B had a much larger sample size ( 𝑛 )
7: What is the posterior probability?
20s
Probability based on prior knowledge
Probability calculated after observing new evidence
Probability calculated without considering any evidence
Probability based on frequentist principles
8: The pink line marks the highest point of the posterior density. Which Bayesian estimator is this?
20s
Posterior Mean
Posterior Mode (MAP)
Posterior Median
Standard Deviation
9: Why is posterior distribution (green) narrower and taller than the prior distribution (pink)?
35s
Because the Posterior has less information than the Prior
Because the data added information, reducing uncertainty.c
Because the Prior was ignored completely.
Because the standard deviation increased.
10: The pink posterior curve shifted to the right (towards 1.0) after observing the data. What does this tell us about the data?
20s