Probability and Statistics 2 (NMAI073)
Instructor: Robert Šámal
- Coordinates
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Lecture: Mon 17:20 in S3.
Tutorial: Tue 12:20 and 14:00 (Czech version for part of the semester) in S10.
Homeworks: in the Postal Owl
- Syllabus
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See info in SIS.
- Last year version
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To get a rough idea about the class, you may see the
last year's version
with all materials. (There will be some changes though.)
- Exam
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Will be organized similarly as in Prob&Stat1: written test from both computing problems and
theoretical understanding. It will be graded 1-5. After that, you will have a possibility to
take oral exam to improve by one grade.
If you solve more homework problems that the required 50 %, you will be getting extra points for
the exam test (up to 10 extra points if you get full score for homework problems).
Credit (Zapocet) is not required for the first attempt to take the exam.
You may bring a "formula sheet" of your own notes on a single sheet of A4 paper (doublesided).
exam from Jan 19
- Literature
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See info in SIS.
Lecture notes (version Jan 29) (final version for this term)
Personal notes of Jonáš Havelka from last year -- in Czech only, no guarantee from me, nor from the author. It looks helpful though, for a review etc.
- Log of lectures
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- Lecture 1 -- Oct 2, 2023
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Definition of a Markov chain, examples. Multistep transition probabilities (Kolmogorov-Chapman recursion formula).
Accesible states.
video
- Lecture 2 -- Oct 9, 2023
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Probability of particular sequence of states. General form of indepednece of future on history.
Communicating states, equivalence relation.
Reduction to smaller Markov chain.
Classification of states: recurrent, transient.
Theorem about convergence to stationary distribution. (just stated)
video
- Lecture 3 -- Oct 16, 2023
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Discussion of the theorem about convergence.
Probability of absorption, time to absorption.
Application: probabilistic algorithm for 2-SAT (to be finished next time).
video
- Lecture 4 -- Oct 23, 2023
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Randomized algo for 2-SAT and 3-SAT.
What is probability?
Intro to Baysian statistics: basic principles of Bayesian inference.
video
youtube video on Bayesian principles
- Lecture 5 -- Oct 30, 2023
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MAP and LMS methods to get point estimates.
Baysian statistics -- example computations using Bayes formula.
video
- Lecture 6 -- Nov 6, 2023
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Bayesian statistics -- Conjugate gradients. Comments on MCMC.
Conditional expectation (as a random variable) -- Law of iterated expectation
video
- Lecture 7 -- Nov 13, 2022
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Conditional expectation (as a random variable) -- proof of Law of iterated expectation,
cond. exp. as an estimator, Eve's rule for variance.
Pdf, joint and conditional pdf revisited.
video
- Lecture 8 -- Nov 20, 2023
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Balls&bins: birthday paradox, upper bound for maxload, applications (hashing and bucketsort).
video
calculator for the birthday paradox
- Lecture 9 -- Nov 27, 2023
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Balls&bins: Poisson approximation.
Simulation shown in the class as python notebook
and as pdf.
Bernoulli processes: very brief introduction.
video
- Lecture 10 -- Dec 4, 2023
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Bernoulli and Poisson process.
video
- Lecture 11 -- Dec 11, 2023
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Permutation test.
Nonparametric statistics: Permutation test, Sign test, Wilcoxon's signed rank test.
video
illustration of the problem
The animation I showed comes from
wiki page on Permutation tests.
A nice visual explanation
- Lecture 12 -- Dec 18, 2023
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Permutation test -- results for the motivational example
Simpson's paradox
Shannon Source Coding theorem & entropy.
video
- Lecture 13 -- Jan 8, 2024
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Central limit theorem -- proof using moment generating functions.
Proof of Chernoff bound and its applications.
video