DS302BKK
Statistical Data Analysis
Faculty
Sasha Shapoval
Professor of Applied Mathematics at the University of Lodz, Poland
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This is a “practical” course that covers selected concepts and tools that are most needed for working with the data arising in economics, finance, sociology, and physics. Although students may be familiar with the introductory concepts from the course, we will soon jump into topics that do not get enough attention in the curriculum of any undergraduate math program, including the best ones. In this course, we will rarely discuss proofs. Methods and results will be described in a loose manner, with the goal of starting to think like practitioners do and getting the statistical intuition required to choose appropriate methods to solve actual problems. This will lead us to important insights about the world around us.
Learning highlights
- Emphasise statistical literacy and develop statistical thinking.
- Use real data in teaching statistics
- Stress conceptual understanding
- Foster active learning
- Use technology to develop conceptual understanding
- Deeply understand statistical methods, be able to choose an appropriate test, and construct reliable mathematical models.
Course outline
15 classes
Session 1
Foundations of statistics: basic probability distributions: exponential, Poisson, normal, Cauchy, gamma, and beta. Central limit theorem. The sum of exponential distributions and the gamma distribution. Waiting time paradox. (PROB)
Session 2
Bayesian approach. Example of the problem: probability of success in the Bernoulli trials. Bayes rule. Application to the above example. Expected value and the deviation of the estimate. Practical example: Estimate of the centre of the Cauchy distribution. (Bayesian)
Session 3
Bayesian approach II. Metropolis algorithm (Bayesian) Practical example: detection of spam. (PYTHON)
Session 4
Hypothesis testing. Motivating examples. General framework. Significance level and quantiles. P-values. One-sided and two-sided tests. Statistical errors. Size and power of the tests. Neyman-Pearson lemma. (CDA)
Exercises: examples of the tests: mean of normal sampling; the equality of the means of two samples; is the fraction larger than a given leve.l (PSE)
Session 5
Hypothesis testing II. Kolmogorov-Smirnov statistics. Independence on the true distribution. Comparison between a sample and a continuous probability distribution. Are two samples from the same distribution? Pearson’s test. (PSE) Practical example: does the first baby come late? (ThinkStats)
Session 6
Bootstrap and jackknife. Manual reconstruction of the inverse pdf. Approximation of the bootstrapped distribution with a continuous one: percentile and kernel approximation. Bootstrapped estimates and bias reduction.
Session 7
Point estimates. Bias and mean square error of the estimators. Natural estimates of the mean, sample variance, covariance, higher moments. Variance of the estimator. Non-parametric estimates. Method of moments. Application to basic distributions. (PSE)
Session 8
Maximum likelihood estimates. Examples: exponential and normal distributions. Variance of MLE. Rao-Cramer Inequality and Fisher Information. MLE and Goodness-of-the-fit: Likelihood Ratio. Pearson test to estimate the parameter as an alternative to the likelihood ratio. MLE and Bayesian estimators. (CDA)
Session 9
The method of least squares. Connection with maximum likelihood. Testing goodness-of-fit with chi-squared. (CDA)
Session 10
Confidence intervals. Examples: the probability of the Bernoulli trials, parameter of the exponential distribution, Gaussian distributed estimator. MLE for the uniform distribution. (CDA)
Session 11
Consistency of data. Testa about standard deviations. A/B testing: usage of Mann–Whitney test under unknown distribution. Practical. Computation of the mean trend of the sea-level rise rates at the locations where the rise is observed.
Session 12
Linear regression I. Simple linear regression. Unbiasedness of the regression coefficients. The variance and the confidence interval of the slope of the response variable. Discussion on an appropriate model choice. (ECON)
Session 13
Linear regression II. Hypothesis: the slope is zero. Instrumental variables. Multiple linear regression. Basic equations. Qualitative issues (ECON). Practical example: Description of the bitcoin dynamics.
Session 14
Causal inference. Treatment variable, treatment group, control group, outcome. Measurement problem. Average treatment effect. Average treatment effect for treated. Independence of the choice of the individuals to be treated with respect to the outcomes. Practical computation with the sample quantities. Alternative computation with the regression. (CAUSAL)
Session 15
Exam.
Course materials
Books
Prerequisites
A good understanding of calculus and probability theory
Preliminary knowledge of Python helps, as my calculations are performed in Python. Nevertheless, you may acquire the necessary knowledge of Python during our course.
The knowledge of Linear Algebra is a plus, as rare references to this discipline are expected.
Methodology
Lectures
Labs
Homework
Brainstorming
Question and answer sessions
Final exam
Grading
The area of expertise of Dr. Shapoval is complex systems. In interdisciplinary research, he applies modern mathematical, computational, machine learning, and statistical tools to analyze data, construct predictions, detect anomalies, and assess scenarios of real-life processes. His papers are published in Scientific Reports, Physical Review, Astrophysical Journal, Chaos, Journal of Mathematical Economics, and other professional first-tier outlets. Dr. Shapoval joined the Department of Mathematics and Computer Science at the University of Lodz in 2021. Prior to coming to Lodz, he was a Professor at HSE University. As a visiting researcher he worked a month per year in the Paris Institute of Earth Physics from 2011 till 2019.
Dr. Shapoval obtained his PhD from Lomonosov Moscow State University and was a postdoctoral research fellow at the International Center of Theoretical Physics in Italy, as well as an invited lecturer at New Economic School.
See full profileApply for this course
Statistical Data Analysis
by Sasha Shapoval
Total hours
45 Hours
Dates
Sep 11 - Sep 29, 2023
Fee for single course
€1500
Fee for degree students
€750
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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.
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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.