Arcadia AI — Master's Program
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Program  /  Semester 1 — AI Foundations
Course

Probability Theory and Statistics for ML: Bayesian Inference, Estimation, Bootstrap

Probabilistic reasoning and statistical inference as the foundation for sound conclusions in ML

DI
Dilya

About the course

This course builds a rigorous understanding of probability theory and mathematical statistics in the context of machine learning. The focus is on Bayesian inference, parameter estimation, and hypothesis testing; students learn methods that ensure reproducibility and correct interpretation of results. The course feeds directly into the Reliable ML and Bayesian ML modules in the third semester.

What you'll learn

✓Build Bayesian models by choosing meaningful priors and deriving posterior distributions
✓Apply bootstrap methods and confidence intervals to quantify uncertainty
✓Correctly interpret statistical significance and avoid common p-value pitfalls
✓Estimate model parameters via MLE and compare models using information criteria

Key topics

•Kolmogorov axioms, conditional probability, and independence
•Core distributions and their properties
•The Central Limit Theorem and the law of large numbers
•Maximum likelihood estimation (MLE) and the method of moments
•Bayesian inference: priors, posteriors, MAP
•Confidence intervals and bootstrap
•Hypothesis testing: p-values, FDR, multiple testing
•Information criteria (AIC, BIC) and the Bayesian information criterion
•Concentration inequalities (Hoeffding, Bernstein)
This description was generated automatically and has not yet been reviewed by an instructor — it's a draft for discussion.