Introduction to Statistics

We're excited to host lectures on Statistics. These lectures may be thought of as a continuation of previous lectures "A Rigorous Introduction to Probability Theory".

 

They are a part of a 2022 lecture series that aims to build a solid foundation of statistics knowledge for the participants. The first 2 lectures by Michal Fabinger focus on crucial and often misunderstood properties of probability distributions that influence the behavior of statistical models. The concepts are introduced in an intuitive yet rigorous way. The material should later help the participants understand scientific articles that use probability theory and statistics. Such knowledge is useful both for machine learning and data science practitioners and for those on an academic path (undergraduates, graduate students, postdocs, or faculty members). The content is similar to the corresponding course at the Acalonia school.

📌 To sign up for the whole lecture series, please fill out this form.

Statistics: Shapes and Moments of Probability Distributions 1

Expectation, variance, skewness, kurtosis, and higher moments of distributions. Fat-tailed distributions. Properties of distributions that are often wrongly neglected.


Statistics: Shapes and Moments of Probability Distributions 2

Expectation, variance, skewness, kurtosis, and higher moments of distributions. Fat-tailed distributions. Properties of distributions that are often wrongly neglected.


Statistics: Dependence of random variables and conditional distributions 1

The topics include expectations, independence of random variables, joint distributions, marginal distributions, conditional distributions, and Bayesian reasoning, as well as covariance and correlation.


Statistics: Dependence of random variables and conditional distributions 2

Expectation, variance, skewness, kurtosis, and higher moments of distributions. Fat-tailed distributions. Properties of distributions that are often wrongly neglected.

Statistics: Dependence of random variables and conditional distributions 3

The topics include expectations, independence of random variables, joint distributions, marginal distributions, conditional distributions, and Bayesian reasoning, as well as covariance and correlation.

Statistics: Estimators asymptotic theory and random variable convergence 1

The topics include the convergence of sequences of random variables in distribution, in probability, in r-th mean, and almost sure convergence, estimators, consistency of estimators, asymptotic distributions of estimators, and bias of estimators, the law of large numbers, and the central limit theorem.

Statistics: Estimators asymptotic theory and random variable convergence 2

The topics include the convergence of sequences of random variables in distribution, in probability, in r-th mean, and almost sure convergence, estimators, consistency of estimators, asymptotic distributions of estimators, and bias of estimators, the law of large numbers, and the central limit theorem.

Lectures by: Michal Fabinger
Twitter: https://twitter.com/fabinger


Bio: Michal is the founder of the Acalonia school (acalonia.com,
formerly tokyodatascience.com), which aims to build an education
system for a world where location does not matter. The school provides a straightforward way for talented people from developed and developing countries to improve their skills for their current jobs,
get new knowledge-demanding jobs, or get admitted to graduate schools. The Fair Play Tuition system (acalonia.com/fair-play) makes this possible even for those who currently lack finances. Michal's research is in physics and economics, with the corresponding PhD training completed at Stanford and Harvard. At the University of Tokyo and the Pennsylvania State University, Michal taught courses on Deep Learning, Data Science, Statistics, Asset Pricing, International Trade,
International Finance, and Development Economics.