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Bayesian Inference Practice

Test your understanding of Bayesian statistical inference with 12 comprehensive questions covering prior specification, posterior analysis, credible intervals, and modern computational methods

12
Total Questions
0
Correct Answers
0
Questions Attempted
Prior Distribution Construction
1 questions
Question 1: Beta Distribution Moments Method
An expert believes a success probability has mean 0.3 and variance 0.05. Using the moments method, w...
Not attempted
Conjugate Priors
1 questions
Question 2: Beta-Binomial Updating
Starting with Beta(3,7) prior for success probability θ, after observing 8 successes in 15 trials, w...
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Posterior Mean Estimation
1 questions
Question 3: Gamma-Poisson Estimation
With Gamma(4,2) prior for Poisson rate λ and observing sum of 20 events in 5 observations, what is t...
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Bayes' Theorem Application
1 questions
Question 4: Diagnostic Testing
A disease has 1% prevalence. A test has 95% sensitivity and 90% specificity. If someone tests positi...
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Credible Intervals
1 questions
Question 5: Beta Distribution Intervals
For Beta(12,8) posterior distribution, which statement about the 95% credible interval is correct?...
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Prior Sensitivity
1 questions
Question 6: Informative vs Non-informative Priors
With n=100 observations and x=60 successes, how do Beta(1,1) and Beta(10,10) priors compare in their...
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Bayesian Prediction
1 questions
Question 7: Beta-Binomial Prediction
With Beta(8,4) posterior for success probability, what is the probability of success in the next tri...
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Normal-Normal Model
1 questions
Question 8: Precision-Weighted Average
Normal prior N(0,4) and sample mean 2.0 from n=16 observations with known variance 1. What is the po...
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Hierarchical Models
1 questions
Question 9: Empirical Bayes
In empirical Bayes, what distinguishes it from full Bayes?...
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Model Comparison
1 questions
Question 10: Bayes Factors
A Bayes factor of 5 in favor of Model A over Model B means:...
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Computational Methods
1 questions
Question 11: MCMC Diagnostics
In MCMC sampling, what does an R-hat (potential scale reduction factor) value of 1.1 indicate?...
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Decision Theory
1 questions
Question 12: Loss Functions and Optimal Estimators
Under squared loss, the optimal Bayesian point estimator is:...
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