Math204
Introduction to Statistics
Faculty
Evgeniya Korneva
Data Scientist at BOLD
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
We will start from descriptive statistics and consider methods of summarizing, describing and visualizing data. Then, we will move to statistical inference. Topics covered in this part of the course include a brief overview of standard probability distributions, point estimates, confidence intervals and hypothesis testing. In the last part of the course, we will learn to model the relationship between several variables with linear and logistic regression.
Since statistical analysis is typically done on the computer, homework will include not only pen-and-paper exercises, but also practical assignments with Python.
Learning highlights
- Learn basic concepts of theory and application for statistical inference.
- Get an introduction to statistical and critical thinking, including descriptive statistics, probability, sampling distributions, interval estimation, hypothesis testing and regression.
Course outline
15 classes
Descriptive statistics
Statistics, data and statistical thinking. Descriptive vs inferential statistics.
Methods for describing sets of data: sample mean and variance, median, mode, etc.
Association of two variables. Contingency tables. Sample correlation. Correlation vs causation. Examples of spurious correlations.
Graphical representation of data: histogram, boxplot, scatterplot (if time permits)
Random variables
Probability recap: probability, conditional probability.
Discrete and continuous random variables. Cumulative distribution function. Density function.
Expectation and variance. Covariance and correlation.
Standard distributions and their properties
Standard discrete distributions: Bernoulli distribution, Binomial distribution
Standard continuous distributions: uniform distribution, normal distribution.
Chi-squared distribution, t-distribution
Inferential statistics. Point estimation
Sampling distributions. The goal of inferential statistics.
Estimators. Properties of estimators
Maximum Likelihood estimators.
Method of moments (if time permits)
Interval estimation
Confidence interval.
Examples of constructing confidence intervals for parameters of various distributions.
Hypothesis testing
Introduction to hypothesis testing. Type I and II errors. alpha-level, p-value.
Tests for the mean with known and unknown variances: one-sample Gauss test, one-sample t-test.
One-Sample Binomial test
Likelihood Ratio Test.
Two-sample tests
Comparing the means of two independent samples with known and unknown variances: two-sample Gauss test, two-sample t-test, Welch test
Comparing the means of two dependent samples: paired t-test
More on hypothesis testing
Testing the goodness of fit of the observed data to a distribution: Chi-squared goodness of fit test, Kolmogorov-Smirnov test.
Chi-squared independence test.
Midterm Exam
In Class midterm exam
Non-Parametric tests
Parametric vs non-parametric tests.
Non-parametric test for population mean, comparing two populations paired test, sign test, non-parametric test for correlation.
Linear Regression
- Linear model.
- Method of Least Squares.
- Properties of the Linear Regression line.
- Goodness of fit.
More on regression
- Multiple regression.
- Binary covariates.
- Modelling interactions.
- Interpretation of a linear regression model. Bias and confounding.
Overview (Final Exam preparation).
Recap of all studied material
Final Exam
Final Exam
Class 15
Logistic regression
Prerequisites
Basic Calculus, Linear Algebra and Probability, familiarity with Python is a plus.
Methodology
This course relies on lectures as the primary delivery mechanism for the material. Pen-and-paper examples will be worked out during the class to highlight the main theoretical concepts.
Grading
Evgeniya was born in Moscow and got a bachelor’s degree in Applied Mathematics and Informatics from the Higher School of Economics in 2015. She then moved to Belgium to continue her education at KU Leuven, where she got a master's degree in Artificial Intelligence. In October 2016, Evgeniya joined the DTAI research group as a researcher. Evgeniya was also teaching master’s courses on Fundamentals of AI and Data Mining. For three years in a row, she won The Best Teaching Assistant prize.
Apart from that, Evgeniya volunteers as an instructor at summer schools and workshops, as well as creates educational content on programming and Machine Learning for several online learning platforms.
See full profileApply for this course
Introduction to Statistics
by Evgeniya Korneva
Total hours
45 Hours
Dates
Nov 30 - Dec 18, 2020
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.