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MCQ On Descriptive Statistics

The document contains 5 multiple choice questions about Bayesian statistics and Markov chain Monte Carlo methods. The questions cover topics like conditional probability, posterior distributions, MCMC sampling, and Gibbs sampling.

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Dr. JOYDEB BHATTACHARYYA
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287 views1 page

MCQ On Descriptive Statistics

The document contains 5 multiple choice questions about Bayesian statistics and Markov chain Monte Carlo methods. The questions cover topics like conditional probability, posterior distributions, MCMC sampling, and Gibbs sampling.

Uploaded by

Dr. JOYDEB BHATTACHARYYA
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

In the colour-fading example from the video suppose that P (is Y |was Y ) =
0.5 (instead of 1, as in the video). Then what is P (was Y |is Y )?
(A) 0.5
(B) 0.2
(C) 0.8
(D) 0.1
2. If X has uniform distribution over the finite set {1, 2, ..., θ}, where θ is
a parameter with prior that is uniform on {6, 8, 10}, then what is the
posterior distribution of θ given the data 3, 2, 9, 2, 1?
(A) Same as the prior.
(B) Constant at the value 10.
(C) Undefined.
(D) Takes the values 6,8,10 with probabilities 0.1, 0.2 and 0.7, respec-
tively.
3. If an MCMC is run with burn-in 10000 and gap 100, then how many steps
would be needed to generate a sample of size 50?
(A) ≥ 13000 but ≤ 16000.
(B) ≥ 17000.
(C) 10150.
(D) 500.
4. A Gibbs sampler is being used to generate samples from the joint posterior
distribtion of two parameter (θ, φ). If at the 100-th step we have the values
θ = 0.12, φ = 0.43, and at the 102-nd step we have θ = 0.20, φ = 0.34, then
which of the following is a possible value after the 101-st step? Assume
that the parameter space is (0, ∞) × (0, ∞).
(A) θ = 0.20, φ = 0.31,
(B) θ = 0.34, φ = 0.12,
(C) θ = 0.23, φ = 0.16,
(D) θ = 0.20, φ = 0.24.
5. The joint posterior density of two parameters (θ, φ) is proportional to
θ3 (1 − θ)4 e−φ . Then the full conditional distribtions for θ and φ are, re-
spectively,
(A) normal and gamma
(B) beta and exponential
(C) beta and beta
(D) binomial and geometric

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