29\(^\text{th}\) of September 2022

Introduction

Admin aspects

  • Lecturer: Dr. Daniela Castro-Camilo

  • Tutor: Toby Kettlewell

  • Lectures (20, from 29/09/2022 until 02/12/2022):

    • Thursday 10:00-11:00 (ADAM SMITH 718 LT)
    • Friday 12:00-13:00 (BOYD ORR 407 LT A)

  • Tutorials (4): there will be four tutorials at 9:00 on the following days: 10/10/22, 24/10/22, 07/11/22, and 28/11/22.

  • Office Hours: Send me an email to arrange day and time

  • Announcements & Feedback: All official announcements will be posted in the Moodle news forum.

Lectures setup

  • The lecture material is divided by topic and will become available one week in advance.

  • A printable version of the lecture notes is available (with all the information contained in a single slide displayed at once).

  • Students can (and are encouraged to) use the Moodle Discussion forum to discuss any topic.

  • Note: The first topic will go a bit fast. This is because it is a recap! 😊

Lecture goals

  • Probability: Given a data generating process, what are the properties of the outcomes?
    • \(\to\) Probability is the formal language of uncertainty.
  • Statistics: Given the outcomes, what can we say about the process that generated the data?
    • \(\to\) Statistics has to do with prediction, estimation, classification, clustering, pattern recognition, inference.

Lecture goals: Probability

By the end of the course you will be able to:

  • State, use and prove various probabilistic inequalities.

  • Describe and contrast convergence in probability, convergence in distribution, convergence in quadratic mean and almost sure convergence.

  • State, prove and use the Weak Law of Large Numbers and the Central Limit Theorem.

Lecture goals: Statistics

By the end of the course you will be able to:

  • State and discuss optimal properties of point estimators.

  • State, prove and use the Rao-Blackwell-Lehmann-Scheffe theorem and the Cramer-Rao lower bound.

  • State, prove and apply general asymptotic properties of maximum-likelihood estimators.

  • Construct an EM algorithm for various missing data problems.

Lecture content

  • Course schedule (tentative):
    • Topic 1 (~ week 1): Recap of previously learned topics: Probability, Random variables, Expectation.
    • Topic 2 (~ week 2): Probability Inequalities.
    • Topic 3 (~ week 3): Inequalities for expectations.
    • Topic 4 (~ Weeks 4-7): Convergence of random variables.
    • Topic 5 (~ week 7): Introduction to the estimation problem.
    • Topic 6 (~ week 8-9): Minimum variance unbiased estimation.
    • Topic 7 (~ week 9-10): Maximum likelihood estimation.


  • M level students will receive additional reading material that will be evaluated during the exam.

Tutorials

  • The goal of the tutorials is for students to get practical experience in solving examinable problems related to the lecture topics.
  • A sheet of exercises will be made available one week before the tutorials take place.
  • It is advisable and strongly recommended that students work on these exercises before the tutorial, and use the tutorials to solve doubts.

Additional lecture material

  • Summaries: summary sheets highlighting the most important concepts and results are available from the start of the semester.


  • Additional exercises: In preparation for the exam, a document with 34 additional exercises is available. No solutions will be provided at any point.


  • Past exam papers: Four past papers and their solutions are available under the block “Preparation for the exam”. Note that the 2018 and 2019 exam papers were carried out in a classroom while the 2020 and 2021 papers were carried out online. This explains why there are no bookwork questions in the 2020 and 2021 papers.

Assessment and revision lecture

  • The module assessment is 100% based on an end-of-course examination. The exam will be held in the April/May diet.


  • A revision lecture will be held during semester 2 (usually late March).

Advise: abouth the level of difficulty of the course

  • This course is historically harder than other. The percentage of A and B grades is smaller than in other courses.

  • The course deals with definitions and results that need to be “digested” properly. In order to do that, you need time.

  • So plan ahead, and do not leave everything to the last minute (even if that has worked for you in the past).

  • As long as you consistently work throughout the semester by reading the lecture notes, reviewing past papers, solving the tutorial and the additional list of exercises, you should be fine 😊

Consequences of online teaching: I need to show you a pic of my cat