Question 1: Data For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose ß so that the prior probability P(q≤ 0.4) is 0.9. (a) Find the value of 3 that satisfies this requirement. (b) Use R to simulate a large sample from this beta distribution, and so check your calculation.
Question 1: Data For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose ß so that the prior probability P(q≤ 0.4) is 0.9. (a) Find the value of 3 that satisfies this requirement. (b) Use R to simulate a large sample from this beta distribution, and so check your calculation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please answer asap using r code and showing the method. you need to refer to the bottom question and the dataset on the side but no need to answer question 2, just question 1a and 1b. thanks!
Transcribed Image Text:Question 1:
Dataset:
3.807
For the geometric model of exercise sheet 5, question 2, suppose that for a
prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose B so 2.264
that the prior probability P(q ≤ 0.4) is 0.9.
2.971
2.617
1.852
(a) Find the value of 3 that satisfies this requirement.
2.253
3.572
2.017
(b) Use R to simulate a large sample from this beta distribution, and so check your 1.991
calculation.
1.261
Question 2 Exercise Sheet 5:
The column in the exercise sheet 5 dataset, labelled x, contains the observed data data
be ₁,...,n. Suppose that each data-point x; is normally distributed, with unknown
mean and standard deviation assumed to be equal to 1.
As a prior distribution for 0, we assign a normal distribution with mean 5 and standard
deviation 10.
(a) What is the posterior distribution for 8?
(b) What is the posterior mean for ?
(c) What is the posterior median for 0?
(d) What is a 95% equal tail credible interval for ?
1.925
2.539
1.122
2.788
2.356
3.508
2.541
2.317
2.021
3.177
1.163
1.775
2.006
2.604
2.553
2.65
4.313
1.478
2.41
2.683
3.563
2.413
2.692
3.055
1.778
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