Lecture 1: Introduction

Applied Statistics: From Data to Decisions

Professor Madeleine Udell

Monday, March 30, 2026

2,217 hospitals penalized for excess readmissions. which ones actually have a quality problem — and which just serve sicker patients?

source: CMS Hospital Readmissions Reduction Program

NBA shot locations, 2003 vs 2024. why did players eliminate the mid-range jumper?

source: Kirk Goldsberry / NBA shot chart data

Wealthfront manages $50B. which clients should harvest losses today to save on taxes?

source: Wealthfront blog, “10 Years of Tax-Loss Harvesting”

World Food Programme, 2018. how to reallocate food baskets in Yemen to feed 2M more people at the same cost?

source: WFP HungerMap LIVE / Zero Hunger Lab

NextEra is siting 4.5 GW of new solar across four states. which parcels maximize energy per dollar?

source: NREL Solar Resource Data (public domain)

Pfizer, November 2020. do 8 vs 162 cases in 43,000 patients prove 95% efficacy — enough for emergency authorization?

source: Polack et al., NEJM 2020

North Carolina, 2016. was a 10–3 Republican sweep from 53% of votes gerrymandering — or geographic luck?

source: Mattingly et al., Duke University

Zillow’s algorithm bought 9,790 homes in Q3 2021. why did it overpay on nearly all of them?

source: Yahoo Finance

Broward County uses COMPAS scores to set bail. why is the false positive rate 45% for Black defendants vs 23% for white?

source: ProPublica Machine Bias analysis

80% of Netflix viewing comes from recommendations. can a $1M algorithm improve predictions enough to save $1B/yr in churn?

source: Netflix Prize / matrix factorization

data, model, decision

who am I?

academic

• math and physics at Yale
• PhD in computational math, Stanford
• postdoc at Caltech
• professor of OR at Cornell
• professor of MS&E at Stanford

applied

• finance: Goldman, Two Sigma, Tau Balance
• tech: Google
• energy: Aurora Solar
• health: Apixio, epidemiology research
• politics: Obama 2012
• logistics: World Food Program

Spend ~2 minutes. The point: statistics touches every domain. Tie back to the montage — “I’ve worked on problems like the ones I just showed you.” Emphasize the diversity: this is what MS&E graduates do.

every one required: data, model, decision

who are you?

poll: PollEv.com/madeleineudell824

• what’s your major?
• what year are you?
• dream industry?

Live poll, ~3 minutes. Show results. “Look at this room — finance, tech, healthcare, policy. The same tools work in every backyard.”

what kinds of consequential decisions do you expect to make in your career? what data will you have? what uncertainties will you face?

2 min think. 3 min share with a neighbor. 2 min class discussion.

DISCUSSION: Think-pair-share (7 min) This is a warm-up. Students should connect the montage to their own future. They should realize: whatever domain they care about, the structure is the same — data, uncertainty, decision.

AI can build the analysis

can you trust it?

• building analyses is getting easier every year
• evaluating whether it’s trustworthy — that’s getting harder
• MS&E graduates are in an extremely strong position here

This is the philosophical core of the course. Pause after “can you trust it?” Let it land. These three bullets should feel weighty, not rushed.

the deal

• we use AI to arrive at the best decisions we can

• then we defend these conclusions, real-time, in-person
• your writing should represent your authentic opinion and voice

• we’re even. we’re going into this future together.

This frames the grading philosophy. Quizzes test understanding, not memorized syntax. Review sessions test whether you can explain your homework. The project presentation tests whether you can sell your analysis authentically. The skills that matter: tell a good decision from a bad one, identify the right framework, present the result.

an AI hands you an analysis that says Hospital X should be fined. what questions do you ask before signing off?

2 min think. 3 min share with a neighbor. 2 min class discussion.

DISCUSSION: Think-pair-share (7 min) If stuck: “How was the data collected? What assumptions did the model make? Could there be confounders? What’s the cost of being wrong?” Key insight: This is “critical evaluation” — the central skill of the course. The answer isn’t “don’t use AI” — it’s “know what to check.”

let’s dig into this one

Demo: hospital readmissions

open in Colab

readmissions = pd.read_csv(
    'https://github.com/stanford-mse-125/book/raw/main/data/hospital-readmissions/hrrp_full.csv')
readmissions.head()

Switch to the pre-filled Jupyter notebook. Clear outputs before class. Walk through: load CMS data, df.head(), .shape, ERR histogram. Fiddle with histogram bins. Show the dirty data first — let students see what real data looks like before any cleaning.

Excess Readmission Ratio

ERR = predicted readmissions / expected readmissions

above 1.0 → more readmissions than expected → penalty

Show this AFTER students have seen the histogram in the notebook. They’ve already formed intuitions about the distribution. Now the definition lands.

your hospital’s ERR is 1.05. why might your readmissions be so high? what questions would you ask, or what data would you gather, to understand why — and to figure out what you might do to lower them?

2 min think. 3 min share. 2 min class.

DISCUSSION: Think-pair-share (7 min) If stuck: “What kinds of patients does your hospital serve? What happens after they’re discharged? Is the expected rate adjusted for your patient population?” Key insight: Reducing ERR requires prediction (which patients are at risk?) and intervention (what can we change?). This is not just inference — it’s a decision problem.

missing data: who disappears?

back to the notebook — .isna().sum()

• “Too Few to Report” → data suppressed for small samples
• small/rural hospitals disproportionately affected

Show in notebook: readmissions.isna().sum(). Point out the “Too Few to Report” pattern. This is missingness not at random — a concept we’ll formalize later.

which patients are most likely to be in the “too few” category? what does that mean for fairness?

2 min think. 3 min share. 2 min class.

DISCUSSION: Think-pair-share (7 min) If stuck: “Think about which hospitals have small sample sizes. Rural? Specialty? Serving underrepresented populations?” Key insight: Data that’s missing is not random — it’s systematically missing for the most vulnerable patients. Any analysis that ignores this is biased.

four ways to reason with data

same dataset, four different questions:

	question	decision
summary	what does the ERR distribution look like?	which hospitals are outliers?
prediction	given a hospital’s traits, what ERR to expect?	should CMS flag this hospital?
inference	is an ERR of 1.05 real or noise?	should the hospital be fined?
causation	do fines actually reduce readmissions?	should CMS continue the program?

This is the intellectual core of the restructured lecture. Walk through each row. “Same data — completely different questions. Summary tells you what happened. Prediction tells you what to expect. Inference tells you whether to believe it. Causation tells you what to do about it.” Connect to the acts: “Act 1 teaches summary and prediction. Act 2 teaches inference. Act 3 teaches causation.”

Three acts of applied statistics

I

build models

explore, clean, predict

regression, trees, features

Lec 1–7

II

trust models

sample, test, infer

bootstrap, hypothesis tests

Lec 8–12

III

see further

classify, cluster, cause

PCA, causal inference

Lec 13–19

the montage → the course

question	topic	act
hospital readmission penalties	EDA, hypothesis testing	I → II
NBA shot selection	EDA, conditional expected value	I
Wealthfront tax-loss harvesting	optimization, regression	I
WFP food allocation	linear algebra, optimization	I
NextEra solar farm siting	feature engineering, regression	I
Pfizer vaccine efficacy	hypothesis testing, multiple testing	II
NC gerrymandering	permutation tests	II
Zillow’s iBuying algorithm	regression, backtesting	II
COMPAS bail scores	classification, fairness	III
Netflix recommendations	PCA, SVD	III

logistics

• website: stanford-mse-125.github.io/web
• Ed Discussion: Q&A and announcements
• grading: HW 10%, review sessions 15%, quizzes 25%, project 30%, final 20%
• AI policy: use it. then defend your conclusions in person.

Keep this under 3 minutes. Point to the website for details. Emphasize: the review sessions are where you prove you understand your homework. That’s 15% of your grade — take them seriously.

quizzes and exam

• you may skip either quizzes or the final exam, but not both
• take both? your grade = max of standardized scores
• quizzes: 8 Wednesdays, closed book, 10 minutes
• final exam: Fri Jun 5, 3:30–5:00 PM

Emphasize the reward: if you take all quizzes AND the exam, we use whichever is higher. So there’s no risk to trying. You can also drop one quiz.

device policy

• laptops: back row only
• iPads and phones: note-taking only

Be matter-of-fact about this. Not punitive — just practical. “Research shows that laptop screens distract people sitting behind you. I want you focused on the discussion, not your inbox.” why? - your screen distracts those behind you. - focus helps you identify what doesn’t make sense (yet), and draw connections between the material and your own goals.

data, model, decisions

many fields study the how to make consequential decisions with data:

• operations research
• management science
• AI
• machine learning
• applied statistics
• data science . . .

each has its own methods, tools, and culture. they overlap significantly!

These are all overlapping fields. The course draws from all of them. “Consequential decisions” is the throughline — not the methods, not the tools.

what makes a decision consequential?

• financial — $881M loss (Zillow), $50B managed (Wealthfront)
• human — who gets bail, who gets the vaccine
• irreversible — can’t un-sentence, can’t un-approve, can’t un-elect
• scale — 2M people fed, 200M recommendations served

every example in the montage is a consequential decision

This is the throughline. Connect each bullet back to a montage example. “Consequential” doesn’t just mean “big” — it means the cost of being wrong is high, and someone has to live with the outcome.

• Financial: Zillow lost $881M because its pricing model was wrong. Wealthfront manages $50B — a bug in tax-loss harvesting costs real people real money.
• Human: COMPAS scores determine bail — wrong score, someone sits in jail who shouldn’t. Pfizer vaccine — wrong call on efficacy, millions don’t get vaccinated (or get a bad vaccine). Hospital penalties — wrong readmission estimate, a hospital serving vulnerable patients loses funding.
• Irreversible: You can’t un-sentence someone. You can’t un-approve a drug. Surgical decisions, infrastructure investments — some choices are one-way doors.
• Scale: WFP feeds 2M people — reallocation affects every one of them. Netflix serves 200M users — a recommendation algorithm shapes what the whole world watches.

by the end of the quarter

you’ll have the tools to answer all of these

Callback to the opening montage. The grid of small thumbnails reminds students of the breadth. “We started with 10 questions. By June, you’ll be able to answer every one.”

before next class

• read Chapter 1 in the course notes
• install Python (Anaconda or Colab)
• sign up for Ed Discussion
• browse the course website

one-minute feedback

1. what was the most useful thing you learned today?
2. what was the most confusing?

give feedback

Show for the last 1-2 minutes. Remind students this is anonymous and helps improve the course in real time. QR code goes to the same form.