DS-GA 1002: Statistical and Mathematical Methods

Instructor: Carlos Fernandez-Granda (cfgranda@cims.nyu.edu)

Teaching assistants:

This course introduces fundamental concepts in probability and statistics from a data-science perspective. The aim is to become familiarized with probabilistic models and statistical methods that are widely used in data analysis.

Announcements

Final

The final will be open notes and books. You may use a computer or a tablet, but only to access your notes, any other use will be considered cheating. The time and location are Tuesday December 13 from 5pm to 7pm in Warren Weaver Hall room 109 for both sections

Syllabus

  • Probability: probability spaces, conditional probability, independence, univariate random variables, multivariate random variables, random vectors, expectation, random processes, law of large numbers, central limit theorem, simulation.

  • Statistics: descriptive statistics, statistical estimation, confidence intervals, parametric models, nonparametric models, hypothesis testing (parametric, nonparametric, multiple testing), Bayesian statistics, regression

Prerequisites

Calculus and linear algebra at the undergraduate level. The first recitation will cover some of the necessary material.

General Information

Lecture

  • Section 1: Monday 5:10-7 pm, SILV 405

  • Section 3: Tuesday 6:20-8:20 pm, MEYR 121

Recitation

  • Section 2 (for students attending Section 1): Thursday 6:20-7:10 pm, GCASL C95

  • Section 4 (for students attending Section 3): Thursday 8:20-9:10 pm, SILV 405

Office hours

  • Section 1 and 3 (Carlos): Wednesday 4:00-6:00 pm, CDS (60 5th Av.) room 606

  • Section 2 (Vlad): Monday 9:30-11:00 am, CDS (60 5th Av.) room 609 or 663

  • Section 4 (Levent): Thursday 6:30-8:00 pm, CDS (60 5th Av.) room 650

Grading policy

Homework (40%) + Midterm (20%) + Final (40%)

Homework

Homework will be posted on Wednesday and is due a week later on Friday at 11 pm. We will not take into account the assignment with the worst grade.

The homework assignments should be submitted as a pdf through NYU classes. The solutions and the grades will be available also on NYU classes.

Feel free to collaborate and discuss in person or on Piazza, but do not share specific answers and make sure that you write your assignment yourself. Always explain your thought process and if you use results from the notes or a book reference them adequately.

Piazza

We will be using Piazza to answer questions and post announcements about the course. Please sign up here.

Books

We will provide self-contained notes and no other texts are required. However, here are some additional references that could be useful:

  • Probability:

    • A First Course in Probability by Ross

    • Introduction to Probability by Bertsekas and Tsitsiklis

  • Statistics:

    • Introduction to Mathematical Statistics by Hogg, McKean and Craig

    • Statistical Inference by Casella and Berger

    • All of Statistics by Wasserman

    • Probability and Statistics by DeGroot and Schervish

    • Statistics by Freedman, Pisani and Purves