# ST3457_17_18

**ST3457 - Statistical Inference I (Bayesian Statistics)**

**2017/2018**

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**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

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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)

12/04/18: Examinable material (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)

27/11/17: doc-cam notes (encrypted pdf)

14/12/17: 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).

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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).

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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.

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

Textbook: Chapter 3, pag. 31-38.

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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.

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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.

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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.

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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.

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

Textbook: Chapter 5, pag. 71-73.

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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").

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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)

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

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

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

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

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28/11/17: Multivariate normal model: an illustration (see slides)

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

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11/12/17: Bayesian linear regression.

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12/12/17: Bayesian model selection.

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

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