Spring 2027

Introduction to Probability and Mathematical Statistics II

Covers likelihood-based statistical inference, estimation, hypothesis testing, and theoretical properties using mathematical statistics and computers.

offering recorded3 credits
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 6

Past student reviews · Cecile Ane

Homework assignments can be challenging and may rely heavily on statistical software like R, which some students found difficult without prior experience. The course material itself is generally not considered overly difficult conceptually.

What you’ll be able to do

  • Construct point estimators including maximum likelihood estimators, understand the theoretical properties of point estimation methods, and evaluate their performance

  • Construct hypothesis tests including likelihood ratio tests, interpret their results, evaluate their performance, and understand the theoretical properties of hypothesis testing methods

  • Construct interval estimators to quantify uncertainty, understand the theoretical properties of interval estimation methods, and interpret their results

  • Mathematically derive key quantities required for statistical inference methods and be familiar with simulation-based techniques for obtaining those quantities

  • Describe the Bayesian approach to inference and contrast it with the frequentist approach

  • Identify and describe the assumptions underlying methods of statistical inference and explain their importance

Source: UW Guide 1 UW Guide 2

Grade history

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average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

(STAT/​MATH 309,STAT 311,STAT/​MATH 431, or MATH 531) and (STAT 240,STAT 301, STAT 302,STAT 324,STAT 371, or ECON 310), or graduate/professional standing

MATH/STAT 310 used by

“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

BO YANG is recorded teaching in Fall 2020, Fall 2021, Spring 2022, Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

BRET HANLON is recorded teaching in Fall 2013, Spring 2014, Fall 2014, Spring 2015, Spring 2016, Fall 2016, Spring 2017. Recorded history may be incomplete and does not establish a future schedule.

BRET LARGET is recorded teaching in Spring 2009. Recorded history may be incomplete and does not establish a future schedule.

CECILE ANE is recorded teaching in Spring 2013. Recorded history may be incomplete and does not establish a future schedule.

GARVESH RASKUTTI is recorded teaching in Spring 2019, Fall 2020. Recorded history may be incomplete and does not establish a future schedule.

HYUNSEUNG KANG is recorded teaching in Spring 2018. Recorded history may be incomplete and does not establish a future schedule.

KEITH LEVIN is recorded teaching in Fall 2023, Fall 2024, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

PANDUAN AN is recorded teaching in Spring 2020, Spring 2025. Recorded history may be incomplete and does not establish a future schedule.

PIXU SHI is recorded teaching in Fall 2018, Fall 2019. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction0 / 660
DIS 311Classroom Instruction0 / 220
DIS 312Classroom Instruction0 / 220
DIS 313Classroom Instruction0 / 220
LEC 001Classroom Instruction0 / 660
DIS 311Classroom Instruction0 / 220
DIS 312Classroom Instruction0 / 220
DIS 313Classroom Instruction0 / 220

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.

Meeting source records
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Student experience

the class

Past student reviews · Panduan An

The course is exam-heavy, with the midterm counting for 30% and the final for 50% of the grade. Instructors typically provide practice problems before exams, and actual test questions often mirror these examples.

Recent recorded grades — Spring 2025: 3.32 GPA, 56.3% A/AB (n=71 letter grades); Fall 2025: 3.26 GPA, 54.7% A/AB (n=53 letter grades); Spring 2026: 2.96 GPA, 42.6% A/AB (n=68 letter grades).

difficulty & workload

Past student reviews · Cecile Ane

Homework assignments can be challenging and may rely heavily on statistical software like R, which some students found difficult without prior experience. The course material itself is generally not considered overly difficult conceptually.

Past student reviews · Panduan An

Grading has been described as generous, with frequent bonus points available to help balance the course difficulty. Students noted that taking the provided practice problems seriously was key to success.

Topics

  • Likelihood's central role in statistical inference
  • Samples, populations, estimation, and hypothesis testing
  • Theoretical properties of statistical inference
  • Bayesian versus frequentist inference

Skills

  • Construct and evaluate point estimators, including maximum likelihood estimators.
  • Construct and interpret hypothesis tests, including likelihood ratio tests.
  • Construct and interpret interval estimators to quantify uncertainty.
  • Derive key inference quantities mathematically and apply simulation-based techniques.
  • Contrast Bayesian and frequentist approaches to statistical inference.
  • Identify and explain assumptions underlying statistical inference methods.

Grades

Historical instructor

Spring 2027 · Projected

Before grades are released

– average GPA

Approximate 80% prediction interval

About this estimate

The course’s semester-average GPA, not an individual student’s grade. The center uses 5 same-season terms, weighted toward recent results.

The range uses the finite-sample 80th-percentile rank of absolute errors from earlier same-season forecasts. Each forecast uses only records from earlier terms. At least four forecasts are required; bounds are rounded outward and limited to 0–4. This is an empirical estimate: changing instructors or grading policies can reduce its coverage.

8 earlier forecasts · 0.32 GPA average error.

Grades over time

Through Spring 2027

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Spring 2026 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1280 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records
MATH/STAT 310 · Spring 2027

Introduction to Probability and Mathematical Statistics II

Recorded 2026-10-14
MATH/STAT 310 · Spring 2027

Introduction to Probability and Mathematical Statistics II

Recorded 2026-10-14
Raw records 
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Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

Explore recorded grades
Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
Download part 1
Full model traces

Recorded model configuration, reasoning, and tool conversations.

Download part 1Download part 2Download part 3
Model & dataset provenance 
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  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
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  "output_id": "90ac2094e00345f2f1b390bc7674a36811da31679b9b7116df1d67edc012e0c6",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
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}