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Welcome to the course TMA4295 Statistical Inference. The first lecture will be on Monday, August 21 at 12.15 in room R4.
The exercise hours in week 34 and 35 will be used for lecturing. These lectures will be on Wednesday from 8:15-9.00 in B3.
20.08: Chapter 1. Probability and distributions.
21.08: Chapter 1 and 2: Distributions, combinatorics, transformations and expectation. Slides week 34
22.08: Momentgenerating function.
27.08: Momentgenerating function, differentiation under an Integral sign. Chapter 2.4. Chapter 3.1-3.2. Commmon families of distributions
28.08: Chapter 3.2-3. Negative binomial, gamma, exponential and Chi-square distributions.
29.08: Beta distribution and Chapter 3.4 Exponential family of distributions. Slides week 35
03.09: Inga førelesing
04.09: Inga førelesing. Om nokon har lyst til å bli med i eit forskningsprosjekt så følgjer det ein kinobillett på kjøpet. Informasjon om forskningsprosjekt.
10.09: Chapter 3.4 Exponential family of distributions. Chapter 3.5. Location and scale families.
11.09: Chapter 3.6 Inequalities. Chapter 4.2 and 4.3 Bivariate distributions Slides week 37
17.09: Chapter 4.3 and 4.4: Bivariate transformations, hierarchical models and mixture distributions.
18.09: Chapter 4.4-4.7: Hierarchical models, mixture distributions and covariance and correlations, inequalities. Slides week 38
24.09: Chapter 4.7: Inequalities. Random samples 5.1-2
25.09: Chapter 5.3: Nomally Distributed random sample, Chisquare distribution and t-distribution Slides week 39
01.10: Chapter 5.3 and 5.5 F-distribution and convergence in probability and distribution
02.10: Chapter 5.5.3 and 5.5.4; Convergence in distribution and the Delta Method Slides week 40
08.10: Chapter 5.5.4 and 6.2.1 The Delta Method and sufficiency.
09.10: Chapter 6.2.1 and 6.2.2 Sufficient and minimal sufficient estimators. Slides week 41
15.10: Chapter 6.2.2 Minimal sufficient and Complete statistics
16.10: Chapter 6.2.2, 7.2.1-7.2.3: Complete statistics and Maximum likelihood. Slides week 42
22.10: Chapter 7.2.1-7.2.3: Maximum likelihood, invariance and Bayes estimator.
23.10: Chapter 7.2.2 and 7.2.3 Bayes estimator, MSE Slides week 43
29.10: Chapter 7.3.2 Cramer-Rao Inequality and Equality. Cramer-Rao in the multiparameter case
30.10: Chapter 7.3.3 Sufficiency and Unbiasedness. Slides week 44
05.11: Chapter 8.2.1 Likelihood ratio test.Chapter 8.3. Methods of Evaluating tests.
06.11: Chapter 8.3.2 Most powerful tests, Neymann-Pearson. Chapter 9.1. Confidence intervals.Slides week 45
12.11: Chapter 9.2.1 and 9.2.2: Methods of finding confidence intervals. Inverting the LRT and Pivotal quantities
13.11: Chapter 9.2.3 and 9.2.4: Pivoting the cdf and Bayesian Interval
19.11: Chapter 9.2.4: Bayesian Intervals. Chapter 10.1.1-10.1.2. Point estimation and efficiency. Confidence interval in the Poisson distribution
20.11: Chapter 10.3.1: Asymptotic distribution of the LRT. Repetition

Lectures

Mondays: 12.15 - 14.00 in room R4.
Tuesdays: 08:15-10:00 in room B3.

Meeting hour

Fridays: 14-15

Exercises

Wednesdays 08:15-09:00 in room B3. First time 05.09. Note that the exercises are not compulsory in the sense
that they will be collected and approved, but they are extemely important for the exam.
Exercise 1, 05.09: 2.33ac, 2.35, 2.38, 3.28abd, 3.39. lf
Exercise 2, 12.09: Exercise 2 lf
Exercise 3, 19.09: 3,46, 3.47 (hard), 4.1, 4.4, 4.10, 4.34. lf
Exercise 4: 26.09: 4.15, 4.30, 4.31, 4.32, 4.35, 4.36, 4.58 lf
Exercise 5: 03.10: 5.6, 5.17, 5.31, 5.35 lf
Exercise 6: 10.10: 5.36, 5.43a), 5.44, 6.1. lf
Exercise 7: Exercise 7 lf
Exercise 8: Exercise 8 Note of Rue and Skaflestad Bayes and the normal distribution in details lf
Exercise 9: Exercise 9. lf
Exercise 10: Exercise 10. lf
Exercise 11: Exercise 11. lf
Exercise 12: Exercise 12 lf

Teacher

John Tyssedal, room 1132, SII. Email: John [dot] tyssedal [at] ntnu [dot] no

Teaching assistant

Jacopo Paglia, room 1001, SII. Email: jacopo [dot] paglia [at] ntnu [dot] no

Reference group

Curriculum

The curriculum is defined to be all that is covered in lectures and exercises, as described on the course homepage under "Lecture plan and progress" and "Exercises".

The following list gives references to the planned topics covered from the course book: Statistical Inference by George Casella and Roger Berger (Second Edition)
Chapter 1: Probability theory. Assumed known
Chapter 2: Transformations and expectations. 2.1 (assumed known); 2.2-2.4
Chapter 3: Common families of distributions. 3.1-3.3 (assumed known); 3.4, 3.5, 3.6.1
Chapter 4: Multiple random variables. 4.1-4.6 (4.5 only partly); 4.7 (only Cauchy-Schwarz and Jensen's inequality)
Chapter 5: Properties of a random sample. 5.1-5.3 (not all in detail),5.5.1, 5.5.3, 5.5.4.
Chapter 6: Principles of data reduction. 6.1, 6.2.1, 6.2.2, Def. 6.2.21, Examples 6.22.22-23, Theorem 6.2.25
Chapter 7: Point estimation. 7.1, 7.2.1, 7.2.2, 7.2.3, 7.3.1 (except from "In certain situations…" on p. 333), 7.3.2, 7.3.3 (from beginning to Example 7.3.18, then from top of page 347 and rest of section 7.3.3; Theorem 7.5.1.
Chapter 8: Hypothesis testing. 8.1, 8.2.1, 8.3.1 (except page 387), 8.3.2 until Def. 8.3.16 (only part a in Theorem 8.3.12).
Chapter 9: Interval estimation. 9.1, 9.2
Chapter 10: Asymptotic evaluations. 10.1.1, 10.1.2, 10.1.3, 10.3.1 to theorem 10.3.3, Score statistic on page 494.

Exam

The exam will be on December 5., 9.00-13.00. It will be a written exam. You are allowed to bring with you:
Tabeller og formler i statistikk
NTNU certified calculator
Personal, handwritten, stamped yellow sheet, A5-format. You get the sheet in the Department office, 7. floor
The exam text will contain a collections of results from the text-book as given here
Earlier exams with solutions can be found here:earlier exams
The exam 2017 with suggested solution
The exam 2018 with suggested solution
The curriculum should make you able to solve the problems in most of the earlier exams, but you will meet questions about ARE or Square Loss function in a Bayesian setting in some of them. That is not covered by our curriculum, and you will not meet such questions on the exam.

Meeting hours before the exam in my offfice
Friday 30. November 14-16
Monday 3. December 13-15
Tuesday 4. December 13-15

2019-01-15, Hallvard Norheim Bø