Thursday 25 August
- There will be no exercises this introductory week
Thursday 1 September
- Exercise 1 in 'Course Notes and Exercises by Nils Lid Hjort'. For b): 'y' is a scalar, single observation
- Exercises 1 and 6 in Chapter 1 of the textbook
Thursday 8 September
- Exercise 9 in Chapter 1 of the textbook
- Exercise 1 in 'Supplemental exercises'
Thursday 15 September
- Exercises 1 and 5 in Chapter 2 of the textbook
- Exercise 2 in 'Supplemental exercises'
Thursday 22 September
- Exercises 8, 9 and 18 in Chapter 2 of the textbook
- Exercise 12 in 'Course Notes and Exercises by Nils Lid Hjort'
- Giovanni's presentation of solutions and R-scriptwhich we have posterior samples for using e.g. MCMC
Thursday 29 September
- Exercise 3 in 'Supplemental exercises'
- Exercise 10 a)-b) in Chapter 2
- Extend exercise 10 in Chapter 2 by redoing a)-b) when you in addition to the previous observation y1 = 203, also observe y2 = 157 and y3 = 222
- Exercises 7 and 15 in Chapter 3
- Boris' solutions
Thursday 6 October
- Exercises 11 and 12 in Chapter 2 of the textbook
- Exercise 3 and 9 in Chapter 3 of the textbook
- Jariek's solutions
Thursday 13 October
- Exercise session cancelled
Thursday 20 October
- Exercises 1 and 2 from Chapter 3 of the textbook
- Read section 3.7 "Example: analysis of a bioassay experiment" and do Exercise 2 from Chapter 4 of the textbook
- Ahmed's solutions
- Ida's solution to exercise 2, Ch. 4, is in the examples note
Thursday 27 October
- Read section 5.3: "Fully Bayesian analysis of conjugate hierarchical models"
- Then do Exercise 13 from Chapter 5 of the textbook
- Mohib's presentation, R-script and bicycle data file
Thursday 3 November
- Exercises 5, 10 and 15 a)-d) from Chapter 5. For 15: First read ch 5.6 to get familiar with the application and data. You can use a slightly altered version of the one-way random effects model from the lectures (with yj being the estimate of the effect \(\theta_j \), and replace the random standard deviation \(\sigma\) of the data by the fixed, estimated standard error \(\sigma_j\)), and simulate using Gibbs
- Exercises 6 and 7 from Chapter 10
- Ida's Smartboard-solutions
- Ida's R-scripts: ex.15-ch5, ex.6-ch10, ex.7-ch10
- The meta-analysis data can be found on the textbook webpage here (I saved it as a .txt-file).
Thursday 10 November
- Exercise 11, Chapter 5.
- Exercise 4 a.-b. in 'Supplemental exercises'. Solution
- Exercise 3, Chapter 11. For the hierachical model the only MCMC algorithm you need is Gibbs sampling, which we have talked about. Solution and R-script
- Ida will go through the exercises
Thursday 17 November
- Exercise 1, Chapter 11
- Exercise 4 c.-d. in 'Supplemental exercises'
- Exercises 3 and 4, ch 14
- Exrecise 3, Chapter 16
- Ida's Smartboard notes on exercises 3 and 4, ch 14 and exercise 3, Chapter 16
- Ida's Smartboard notes on exercise 4 in 'Supplemental exercises'. NB: There was an error in the mean of the full conditional distribution for mu, this is corrected in the notes
- R-script to the MCMC for the full Bayesian analysis of the metaanalysis example
Thursday 24 November
- Exercise 2a, Ch 16, where posterior simulations are obtained by using Gibbs combined with Metropolis steps. In particular report the approximate posterior mean and 95% interval of the parameter LD50=-alpha/beta. LD50 is the dose level x at which the probability of death is 50%, which means that logit-1(alpha+beta*x)=0.5, hence LD50=-alpha/beta. This is straightforward using the posterior samples of alpha and beta, but an important concept to get into the fingertips: how to find the posterior samples of functions of the parameters in the model
- Exercises 17 and 18 in 'Course Notes and Exercises by Nils Lid Hjort'. NB: There is a misprint in Exercise 18 for cM, the correct is that cM=M(M+1)/2
- Knut's solutions