Topic outline

  • Lectures

    The course has 12 lectures during 6 weeks (Mon and Wed 10–12).  Each lecture is preceded by an online quiz which helps you to identify preliminaries from earlier courses and lectures that you may need to review independently before a lecture. Points from quizzes amount to up to 10% of the course grade, see the course syllabus for details. The deadline for completing a quiz is the start of the corresponding lecture.

    In the schedule below [Kyt19] refers to lectures notes


    Schedule
    # Topics [Kyt19]
    1 Measures and sigma-algebras [Kyt19, I, II]
    2 Measurable functions and random variables [Kyt19, III.1–III.3]
    3 Integration of positive functions [Kyt19, III.4, VII.1–2, VII.6]
    4 Almost everywhere, almost surely, Markov's inequality, change of variables formula, integration of signed functions. [Kyt19, VII.2–3, VIII.1]
    5 Stochastic independence [Kyt19, V, IX]
    6 Product measures, infinite product measures (IID sequences) [Kyt19, IX, X]
    7 Weighted measures and probability densities. Materials / 'Densities'
    8 Kernels, conditional densities, Markov chains, Bayesian likelihood functions [www.randomservices.org/random/,  2.6, 3.13] 
    9 Probability metrics: Total variation distance, Wasserstein distances Materials / 'Probability metrics'
    10 L1 and L2 spaces, Chebyshev's inequality, weak law of large numbers [Kyt19, X, XI]
    11 Moment generating and characteristic functions, weak convergence, central limit theorem [Kyt19, XII]
    12 Optional topics (feel free to vote): Questions and answers, model solutions, etc. -


    Before the first lecture, please look through Appendix A and Appendix B of Kytölä's lecture notes. This will also help you significantly with the first quiz.

    Old lecture videos from the course in Spring 2021 are available at https://youtube.com/playlist?list=PLLUr70a-tqjf5htSOg4qeFCx-jqM2jlO5.


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Materials