ST3457 - Statistical Inference I (Bayesian Statistics)

2017/2018


----

Change of schedule

Two classes are canceled:

- Monday 4/12/17: no class

- Thursday 7/12/17: no class

and replaced by:

- Tuesday 28/11/17, 3pm-4pm, Room LB08

- Tuesday 12/12/17, at 3pm-4pm, Room LB08

----


Module Code: ST3457 

Module Title: Statistical Inference I

Cohorts: Maths 

Week range: 05-10, 12-16 

Semester: S1 (Michaelmas) 

Total hours: 33


Timetable: 

- Monday, h. 12pm-2pm, room LB01

- Thursday, h. 5pm-6pm, room LB107


Labs: 

- Thursday 16/11/17, h. 5pm-6pm, room ICT 1

- Thursday 23/11/17, h. 5pm-6pm, room ICT 1

- Thursday 30/11/17, h. 5pm-6pm, room ICT 1



Textbook:


Hoff, "A First Course in Bayesian Statistical Methods"

Other material and references will be provided when needed


Material:

25/09/17: Slides (pdf)

28/09/17: Slides (pdf)

02/10/17: Slides (pdf)

09/10/17: R script (R)

23/10/17: Slides (pdf)

02/11/17: Slides (pdf), R script (R)

13/11/17: Slides (pdf), R script (R)

16/11/17: Lab 1 (pdf,R), solution (R)

23/11/17: Lab 2 (pdf,R), solution (R)

28/11/17: Slides (pdf)

30/11/17: Lab 3 (pdf,R), solution (R)

11/12/17: Slides (pdf)

12/12/17: Slides (pdf)

14/12/17: Mock exam, with minor edits (pdf)


Doc-cam notes

05/10/17 - 26/10/17: doc-cam notes (encrypted pdf)

02/11/17, 13/11/17: doc-cam notes (encrypted pdf)




Syllabus (lecture by lecture):

25/09/17: Examples to compare Bayesian and frequentist approaches; Bayesian paradigm; A beta-binomial model for proportion estimation.

Textbook: Chapter 1 (with the exclusion of 1.2.2, which is a suggested reading).

---

28/09/17: Belief functions and probability measures; Conditional independence.

Textbook: Chapter 2, pag. 13-17 and pag. 26. (read also Section 2.4 and 2.5 if you need to review these topics).

---

02/10/17: Exchangeability; Comparison of i.i.d. and exchangeability assumption; de Finetti representation theorem (0-1 and general case); Sketch of the proof for the 0-1 case.

Textbook: Chapter 2, pag. 27-30.

---

05/10/17: Binomial model with beta prior; conjugate priors.

Textbook: Chapter 3, pag. 31-38.

---

09/10/17: More on Binomial model; Predictive distribution; Bayesian coverage; Quantile-based posterior credible intervals; Poisson model with gamma prior; Birth rates example (see R script).

Textbook: Chapter 3, pag. 38-50.

---

12/10/17: One-dimensional exponential family; Binomial and Poisson as members of the exponential family; Conjugate prior for the exponential family.

Textbook: Chapter 3, pag. 51-52.

---

19/10/17: Conjugate priors: from the exponential family to Binomial and Poisson;

Textbook: Chapter 3, pag. 51-52.

Assignment: Problem 3.9 pag. 230; Problem on Normal model with variance fixed=1.

---

23/10/17: Monte Carlo method (see slides); Normal model with fixed variance; Normal prior. 

Textbook: Chapter 4, pag. 53-65. Chapter 5, pag. 68-71.

---

26/10/17: Precision; Normal model with fixed variance: interpretation of the posterior distribution, predictive distribution.

Textbook: Chapter 5, pag. 71-73.

---

02/11/17: Normal model with conjugate priors on mean and variance; Point estimation: Bayesian (posterior mean) vs frequentist (empirical mean); Bias.

Textbook: Chapter 5, pag. 73-80 (with the exclusion of "improper priors").

---

13/11/17: Mean squared error for posterior mean and empirical mean; Gibbs sampler.

Textbook: Chapter 5, pag 81-82. Chapter 6, pag. 89-98 (with the exclusion of Section 6.2)

---

16/11/17: Lab 1 - Monte Carlo methods.

---

20/11/17: Multivariate normal model: normal prior for the mean vector.

---

23/11/17: Lab 2 - Normal model: joint inference for mean and variance

---

27/11/17: Multivariate normal model: inverse-Wishart prior for the covariance matrix.

---

28/11/17: Multivariate normal model: an illustration.

---

30/11/17: Lab 3 - Multivariate normal model

---

11/12/17: Bayesian linear regression.

---

12/12/17: Bayesian model selection.

---

14/12/17: Solutions of the mock exam.

---


ċ
021117.R
(2k)
Bernardo N.,
Nov 18, 2017, 10:58 AM
ċ
091017.R
(4k)
Bernardo N.,
Oct 10, 2017, 10:42 AM
ċ
131117.R
(1k)
Bernardo N.,
Nov 18, 2017, 10:58 AM
ċ
LAB_Montecarlo.R
(7k)
Bernardo N.,
Nov 16, 2017, 10:08 AM
ċ
LAB_Montecarlo_solutions.R
(8k)
Bernardo N.,
Nov 16, 2017, 10:08 AM
ċ
LAB_mult_normal.R
(3k)
Bernardo N.,
Nov 30, 2017, 8:54 AM
ċ
LAB_mult_normal_solution.R
(5k)
Bernardo N.,
Nov 30, 2017, 9:33 AM
ċ
LAB_normal.R
(3k)
Bernardo N.,
Nov 23, 2017, 8:31 AM
ċ
LAB_normal_solutions.R
(5k)
Bernardo N.,
Nov 23, 2017, 8:31 AM
Ċ
Bernardo N.,
Oct 8, 2017, 6:30 AM
Ċ
Bernardo N.,
Oct 8, 2017, 6:29 AM
Ċ
Bernardo N.,
Oct 8, 2017, 6:27 AM
Ċ
Bernardo N.,
Oct 23, 2017, 3:56 AM
Ċ
Bernardo N.,
Nov 18, 2017, 11:05 AM
Ċ
Bernardo N.,
Nov 18, 2017, 10:57 AM
Ċ
Bernardo N.,
Dec 2, 2017, 8:38 AM
Ċ
Bernardo N.,
Dec 11, 2017, 3:58 AM
Ċ
Bernardo N.,
Dec 14, 2017, 5:31 AM
Ċ
Bernardo N.,
Nov 16, 2017, 10:08 AM
Ċ
Bernardo N.,
Nov 23, 2017, 8:30 AM
Ċ
Bernardo N.,
Nov 30, 2017, 8:54 AM
Ċ
Bernardo N.,
Dec 14, 2017, 7:01 AM
Ċ
Bernardo N.,
Nov 18, 2017, 11:06 AM
Ċ
Bernardo N.,
Nov 18, 2017, 11:06 AM