Sergey Nikolenko

Main page

Books
Research papers
Talks and posters
Students
Popular science
Other stuff

   Research
CS and crypto
Bioinformatics
Machine learning
Algebraic geometry
Algebra
Bayesian networks
Earth sciences

   Teaching
 2014
ML, KFU
Game Theory, HSE
Mech. Design, HSE
ML, CSClub Kazan
Game theory, HSE
Math. logic, AU
Machine learning, STC
Machine learning, AU
 2013
Discrete math, HSE
Machine learning, STC
Math. logic, AU
Cryptography, AU
 2012
Machine learning, STC
Math. logic, AU
Machine learning II, AU
Machine learning, AU
Machine learning, EMC
 2011
Cryptography, AU
Math. logic, AU
Machine learning, AU
 2010
Math. logic, AU
Machine learning, AU
Cryptography, AU
 2009
Crypto in CS Club
Statistics
Machine learning, AU
Cryptography
 2008
Speech recognition
MD for CS Club
ML for CS Club
Mechanism design
 2007
Machine Learning
Probabilistic learning

  External links
Google Scholar profile
DBLP profile
LiveJournal account
nikolenko (in Russian)

Teaching activities

Fundamentals of mathematical statistics

This course is presented in the «Academic University of Physics and Technology» as part of the recently established Chair of Mathematics and Computer Science.

The course itself:

1. Introduction. Probability distributions: binomial, normal, exponential, Poisson. Law of large numbers and the central limit theorem.

2. Maximum likelihood estimators. Properties. Method of moments. Biased and unbiased estimators. Asymptotic normality.

3. Fischer information. Convergence and asymptotic normality of the MLE. Examples.

4. The Rao-Cramer inequality. Efficient estimators.

5. Prior and posterior distributions. Conjugate priors. Examples: Bernoulli trials, Poisson distribution. Equivalent sample size.

6. Sufficient statistics. The Neyman-Fischer factorization criterion.

7. Hypotheses testing. Simple hypotheses. False positives and false negatives. Bayesian decision rules. Examples.

8. The most powerful test for simple hypotheses. Likelihood ratios. One-sided hypotheses. Most powerful test for a one-sided hypothesis.

9. The Pearson theorem. Covariance.

10. Chi-square tests. Examples. Composite hypotheses and chi-square tests for them. Independence and homogeneity tests.

11. Fischer distribution. Student's t-distribution. Confidence intervals for the normal distribution parameters.

12. The Kolmogorov-Smirnov test.

13. Linear regression. Least squares, statistical justification. Confidence intervals on the linear regression parameters.