Class notes

1. Principles of data reduction

   1.1 The frequentist approach to Statistics

   1.2 The sufficiency principle

   1.3 Ancillary statistics

   1.4 Exponential families of distributions

   1.5 Sufficiency in restricted models

   1.6 Sufficiency and Fisher’s information

   1.7 The likelihood principle

2. Point estimation

   2.1 Estimators and estimates

   2.2 The search for the best estimator

   2.3 Methods of finding estimators

3. Hypothesis testing

   3.1 Tests of hypotheses

   3.2 Uniformly most powerful tests

   3.3 Likelihood ratio tests

4. The Bayesian choice

   4.1 There’s no theorem like Bayes’ theorem

   4.2 Parametric bayesian statistics

   4.3 The main characteristics of Bayesian statistics

   4.4 The prior distribution

5. Bayesian inference

   5.1 Summarizing posterior inference

   5.2 Prediction

   5.3 Computation

Books and stuff

1. Statistical Inference, Casella, G. and Berger, R. L., 2002, 2^nd ed., Duxbury Press, Belmont, CA.

   Selected exercises:

   (Chapter 6) 1-3, 5, 6, 9-13, 17-18, 20-23, 27, 30, 34

   (Chapter 7) 2, 3, 6-13, 19, 21, 37, 38, 40, 46-50, 52, 55, 59, 60

   (Chapter 8) 15, 19, 22-25, 31-33, 3, 5-8

   (Chapter 9) 12-14, 16, 17

2. Estatística Bayesiana, Paulino, C. D., Amaral-Turkman, M. A. e Murteira, B., 2018, 2ª ed., Fundação Calouste Gulbenkian, Lisboa.

   Selected exercises:

   (Chapter 3) 2, 3, 10, 13, 15, 19, 29

3. Bayesian Data Analysis, Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. and Rubin, D.B., 2013, 3^rd ed., CRC Press.

4. Formulae

Past tests

Current semester

First test (8/10/2025)

2022/2023

Exam (7/2/2023)

Fourth test (11/1/2023)

Third test (14/12/2022)

Second test (2/11/2022)

First test (12/10/2022)

2021/2022

Exam (14/2/2022)

Fourth test (1/2/2022)

Third test (14/12/2021)

Second test (9/11/2021)

First test (19/10/2021)

About

What is this?

This is a set of notes written for a one semester course on Mathematical Statistics. These notes are suitable to follow the lectures but they should not be used as the only study material by the students.

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

30/11/2025