M.petrishchev: Created page with "= Statistical Techniques for Data Science = * '''Course name:''' Statistical Techniques for Data Science * '''Course number:''' BS-STDS == Course c..."

2022-06-15T13:51:42Z

Created page with "= Statistical Techniques for Data Science = * '''Course name:''' Statistical Techniques for Data Science * '''Course number:''' BS-STDS == Course c..."

New page

= Statistical Techniques for Data Science =

* '''Course name:''' Statistical Techniques for Data Science
* '''Course number:''' BS-STDS

== Course characteristics ==

=== Key concepts of the class ===

* Statistical Hypothesis Testing
* Resampling
* Statistical ML
* MCMC

=== What is the purpose of this course? ===

The course covers non-standard statistics, applicable in a wide set of contexts, including non-parametric statistics, simulation methods, and time series analysis.

This course will provide an opportunity for participants to learn: random variables, elementary probability, and distributions; relevant probabilistic inequalities; random vectors, marginal and joint distributions; sequences of random variables and concepts of convergences; Markov chains; processes in continuous time; univariate and multivariate simulation methods; non-parametric and parametric resampling methods.

=== Course Objectives Based on Bloom’s Taxonomy ===

=== - What should a student remember at the end of the course? ===

By the end of the course, the students should be able to recognize and define

* Estimation methods: point estimates, MLE
* Confidence interval, p-value
* Estimation and Non-parametric Tests. Kolmogorov-Smirnov Test
* Sampling. Metropolis-Hastings. Markov Chains. MCMC

=== - What should a student be able to understand at the end of the course? ===

By the end of the course, the students should be able to describe and explain (with examples)

* Describe the Statistical Hypothesis Testing, p-value, Power of a test and Sample size
* Explain ANOVA, Chi-square tests
* Smoothing methods with examples

=== - What should a student be able to apply at the end of the course? ===

By the end of the course, the students should be able to apply

* Apply Non-parametric Tests, such as KS-test
* Apply resampling methods (jackknife, bootstrap)
* Apply Markov chain Monte-Carlo methods

=== Course evaluation ===

{|
|+ Course grade breakdown
!
!
!align="center"| '''Proposed points'''
|-
| Labs/seminar classes
| 20
|align="center"| 40
|-
| Interim performance assessment
| 30
|align="center"| 30
|-
| Exams
| 50
|align="center"| 30
|}

If necessary, please indicate freely your course’s features in terms of students’ performance assessment: None

=== Grades range ===

<div id="tab:ModelsCourseGradingRange">

{|
|+ Course grading range
!
!
!align="center"| '''Proposed range'''
|-
| A. Excellent
| 90-100
|align="center"| 80-100
|-
| B. Good
| 75-89
|align="center"| 65-79
|-
| C. Satisfactory
| 60-74
|align="center"| 50-64
|-
| D. Poor
| 0-59
|align="center"| 0-49
|}

</div>
If necessary, please indicate freely your course’s grading features: The semester starts with the default range as proposed in the Table [[#tab:ModelsCourseGradingRange|1]], but it may change slightly (usually reduced) depending on how the semester progresses.

=== Resources and reference material ===

* Murphy K.P. Machine Learning: A Probabilistic Perspective. Massachusetts Institute of Technology, 2012. — 1067 p.
* Bishop Christopher. Pattern Recognition and Machine Learning. Springer, 2006. — 738 p.
* M. Ross. Introduction to Statistics. Prentice Hall. 1989
* Efron, R. J. Tibshirani. An introduction to the bootstrap. Springer. 1993
* G. Casella, R. L. Berger. Statistical Inference. Thomson Press. 2006
* S. Hojsgaard, D. Edwards, S. Lauritzen. Graphical Models with R. Springer. 2012
* Hastie, T. Tibshirani, R. and Friedman, J. (2008) The Elements of Statistical Learning 2ed. Springer
* Steven M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory (v. 1). Prentice Hall. 1993

== Course Sections ==

The main sections of the course and approximate hour distribution between them is as follows:

{|
|+ Course Sections
!align="center"| '''Section'''
! '''Section Title'''
!align="center"| '''Teaching Hours'''
|-
|align="center"| 1
| Parametric Statistics
|align="center"| 42
|-
|align="center"| 2
| Non-parametric Statistics
|align="center"| 24
|-
|align="center"| 3
| Sampling and Simulation
|align="center"| 24
|}

=== Section 1 ===

=== Section title: ===

Parametric Statistics

=== Topics covered in this section: ===

* Review of Probability Theory. Random variables. Density. Distributions. Expected value
* Exploring the Data Distributions. Multivariate distributions. Plots
* Data and Sampling Distributions. Standard error. CLT
* Experiment Design. Confidence intervals. Introduction to Hypotheses Testing
* A/B Testing, T-test, ANOVA, Chi-square.

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 1 
Homework and group projects & 1 
Midterm evaluation & 1 
Testing (written or computer based) & 1 
Reports & 1 
Essays & 0 
Oral polls & 0 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# What is the Central Limit Theorem?
# What is statistic?
# What is sampling distribution?
# What is standard error?
# What are Type I and Type II errors?
# What is t-statistic error? T-test?

=== Typical questions for seminar classes (labs) within this section ===

# Create a bi-modal dataset, which has the mean less than the median, draw a histogram.
# Poisson Distribution in practice: seatching patterns of palindromes in DNA.
# Experiments and A/B testing.
# A researcher claims that Democrats will win the next election. 4300 voters were polled; 2200 said they would vote Democrat. Decide if you should support or reject null hypothesis. Is there enough evidence at ''alpha'' = 0.05 to support this claim?

=== Test questions for final assessment in this section ===

# Prove Chebyshov inequality
# Prove Markov inequality
# What is ANOVA, what is the difference with Chi-square test?

=== Section 2 ===

=== Section title: ===

Non-parametric Statistics

=== Topics covered in this section: ===

* Empirical CDF. Resampling. Jackknife and Bootstrap
* Density Estimation
* Estimation and Non-parametric Tests. KS Test
* Non-parametric Tests. Kruskal-Wallis Test. Multi-arm Bandits

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 0 
Midterm evaluation & 1 
Testing (written or computer based) & 0 
Reports & 1 
Essays & 0 
Oral polls & 0 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# What is Empirical CDF?
# How to apply resampling? Jackknife and Bootstrap?
# What is Kernel Density Estimation?
# What is Smoothing?

=== Typical questions for seminar classes (labs) within this section ===

# Implement Kernel Density Estimation.
# Apply KS-test.
# Apply Kruskal-Wallis Test
# Implement Multi-arm Bandits

=== Test questions for final assessment in this section ===

# What is epsilon-greedy algorithm?
# Perform 1 sample KS test in Python and Scipy. Compare KS test to visual approaches for checking normality assumptions
# Plot CDF and ECDF to visualize parametric and empirical cumulative distribution functions

=== Section 3 ===

=== Section title: ===

Sampling and Simulation

=== Topics covered in this section: ===

* Sampling. Metropolis-Hastings.
* Rejection Sampling. Gibbs Sampling
* Thompson Sampling. Upper confidence bound
* Markov Chains. MCMC
* Time Series: Tools and Applications

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 1 
Midterm evaluation & 0 
Testing (written or computer based) & 0 
Reports & 0 
Essays & 0 
Oral polls & 0 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# What is Thompson Sampling?
# What Upper confidence bound algorithm?
# What is stationary distribution?

=== Typical questions for seminar classes (labs) within this section ===

# Given density function, implement Accept-Reject sampling
# Run Metropolis Hastings and Accept-Reject (on the same f(x)) (n=1000, 10000, 100000). Compare results
# Apply Gibbs Sampling
# Apply tools for time series analysis and prediction

=== Test questions for final assessment in this section ===

# Consider a transition matrix of a Markov Chain (MC).
#* Show that this is a regular MC (A MC is called regular if for some integer n all entries of transition matrix after n steps are strictly positive).
#* Find the limiting probability vector w
# Compare Gibbs Sampling to Metropolis Hastings.

BSc:StatisticalTechniquesForDataScience.previous version - Revision history

M.petrishchev: Created page with "= Statistical Techniques for Data Science = * '''Course name:''' Statistical Techniques for Data Science * '''Course number:''' BS-STDS == Course c..."