Statistics for Data Science: Lecture Notes

Typeset lecture notes for Statistics for Data Science, University of Pisa, academic year 2024/25. The notes run from probability to statistical inference: probability, independence and Bayes, a calculus recall, discrete and continuous random variables, power laws and Zipf's law; expectation, variance and moments, distances between distributions; simulation, the limit theorems, data summaries and condensed observations; estimation theory (unbiasedness and MSE, maximum likelihood, confidence intervals, bootstrap); linear, non-linear and logistic regression and statistical decision theory; hypothesis testing, classifier- performance tests, two-sample tests, the multiple-comparisons problem, and distribution fitting with independence tests. Two seminar sections on causal reasoning and the do-calculus close the notes.

⚠️ Disclaimer. Derived from the Statistics for Data Science course materials (Academic Year 2024/2025), MSc in Data Science & Business Informatics, University of Pisa.

These notes are open educational content created by a student. They are not an academic source and may contain inaccuracies. You may freely share, modify, and reuse this material for educational and non-commercial purposes with appropriate attribution. The content is my personal interpretation of the professor's course materials and should not replace official teaching resources. I assume no responsibility for any errors or misinterpretations.

These notes were produced with an AI-in-the-middle workflow: a first human pass, then Claude Code to support formulation, understanding, and rewriting, followed by a final human review.

If you find errors, have suggestions, or spot unintentionally included copyrighted material (which I will promptly remove on notification), contact me at sclfnc@proton.me.

This course is part of the MSc Data Science lecture notes collection (University of Pisa), one repository per course. Clone the whole set with git clone --recursive.

Layout

• main.tex: entry point, in the folder root; identical across the whole notes collection (it only loads the shared preamble and the course file).
• src/housestyle.tex, shared house style: geometry, colors, section and ToC formatting, running heads, and the math environments (theorem, definition, …).
• src/common-preamble.tex: the shared package set, identical across courses.
• src/course.tex, everything specific to this course: title metadata, the subfiles setup, hyperref, the img/ graphics path, and the \coursebody that \subfile{sec/...}s the sections in reading order (no \part groupings).
• sec/NN.tex: section files (the body of the notes), pulled in by course.tex; file numbering is non-contiguous and does not match reading order, so \coursebody lists the files in the order they are read. Two sec/_seminary*.tex files hold the closing seminar sections and are compiled with the rest.
• img/: the PNG figures (power-law and Zipf plots, a decision boundary, a risk-coverage curve, a forward/backward-pass sketch); most other figures are native TikZ.
• References.bib, present but unused: no \cite in the notes, so the build runs no bibliography pass.
• sds-notes.pdf: the compiled notes, in the folder root.

Build

Build from the folder root:

latexmk main.tex

latexmk runs pdflatex as many times as needed (a second pass resolves the table of contents and cross-references) and produces sds-notes.pdf. The auxiliary files (.aux, .log, .toc, .bcf, .bbl, …) land in the folder root alongside it and are git-ignored (listed in .gitignore). A .latexmkrc in the folder sets the output name via $jobname. To do it by hand instead:

pdflatex -jobname=sds-notes main && pdflatex -jobname=sds-notes main

The second pass fills in the ToC and references. There is no bibliography pass: the notes use no \cite. Requires a standard TeX Live installation. Alternatively, upload the folder to Overleaf (New Project → Upload Project), set main.tex as the main document, and compile.

Credits

Written by Francesco Secoli, revised with the help of Claude Code: the course slides and lectures were transcribed and refined into LaTeX, then reworked into standalone notes. Based on the Statistics for Data Science course (a.y. 2024/25), University of Pisa. Contributions welcome: open an issue or a pull request.

Contents

Twenty-eight sections in reading order (the last two are seminar sections):

#	Section
1	Probabilities, independence and Bayes
2	Correction under shift
3	Recalls on Calculus
4	Discrete random variables
5	Continuous Random Variables
6	Power Laws and Zipf's Law
7	Expectation and Variance
8	Moments and functions
9	Distances between distributions
10	Simulation
11	Large Numbers and Central Limit
12	Summaries in Statistics for Data Science
13	Condensed Observations
14	Unbiased Estimators, Efficiency and MSE
15	Maximum Likelihood Estimation
16	Confidence Intervals
17	Bootstrap and Resampling Methods
18	Linear Regression and Least Squares Estimation
19	Non-linear and Multiple Linear Regression
20	Issues with Linear Regression and Logistic Regression
21	Statistical Decision Theory
22	Hypothesis Testing
23	Tests and Confidence Intervals for Classifier Performance
24	Two-Sample Tests of the Mean and Applications to Classifier Comparison
25	The Multiple Comparisons Problem
26	Fitting Distributions and Testing Independence/Association
27	Bias in Statistics and Causal Reasoning
28	Seminar: Causal Models and the Do-Calculus