• Pre-recorded and available at all time (20-25 minutes videos divided by topics).

• The lecture material is divided into 10 weeks.

• Within each week, lecture notes and videos have been divided into sessions to help you navigate the POPS topics more easily.

• A printable version of the lecture notes is also available for each week (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.

• Video recording have automatic transcripts, so they need to be taken with caution. Apologies in advance for any mistake.

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

• Note: the lecture videos were recorded last year when I was still getting used to the whole online environment. That explains why you won’t see my face in the videos until week 4!

• 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.

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.

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.

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

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

• Live tutorials will run using Zoom.
• 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.
• A poll will be made available twenty minutes before the end of the tutorial to allow students to vote for a problem they struggled with or want the answer to. I will solve the most voted problem live.
• The tutorials Zoom link will be available in due course.
• Tutorial will be held from 9 am until 10 am (UK time) on the following dates: 11th October, 25th October, 8th November, 29 November.

• 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 exam paper and their solutions are available. Note that the 2018 and 2019 exam papers were carried out in a classroom (i.e., under “normal” exam conditions) while the 2020 and 2021 papers were carried out online (i.e., the same conditions you will sit the exam). This explains why there are no bookwork questions in the 2020 and 2021 papers.

• 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. The revision lecture is scheduled for Wednesday, March 23rd, from 4:00 PM until 5:00 PM.

• 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 watching the videos, reading the lecture notes, reviewing past papers, solving the tutorial and the additional list of exercises, you should be fine 😊

• During Tutorial, mics should be off unless you want to discuss something with your peers or with me (to avoid backgroun noise).

• Videos might be on or off, it’s up to you (although it will be nice to see some faces from time to time!)

• When exchanging one-to-one messages (such as emails), it’s good to acknowledge you receive them.

• We are aware of the special circumstances and extra pressures students are working under this year. Remember that you are not alone on this.

• Specialist advice is available through the University’s central services to help students under different situations. Should you need any guidance, you might contact your academic advisers, tutors or lectures.

• We won’t necessarily know the answer but we’ll be able to point you in the direction of further support, or help you to find out where you can get the support that you need.

• Random pet visits are allowed and welcomed.

• This is mine; her name is Lili. She might show up during Tutorials, especially if I ask her not to, because, you know, cats.