# 15-260 Statistics and Computing (SnC), Spring 2022, 3 Units

This is a "micro" class, which allows you to get credit for having covered the Statistics you need to receive an ML minor or do an ML concentration. You will not be able to register for 15-260 until a month AFTER PnC starts. The registrar insists on this because they want to make sure that only people who are in PnC get into 15-260. Everyone who is in PnC will be eligible for 15-260. People who are not in PnC are ineligible to take 15-260.

## Lectures: Mondays 7:00 pm - 8:20 pm in GHC 4307.

• Weekly homework (~2 problems/homework) -- 60%
• Three quizzes -- 40%
• We will drop your 1 lowest homework score and 1 lowest quiz score
• Usual grade breakdowns: A (90-100%); B (80-90%); C (70 - 80%); D (60 - 70%); R (<60%)

## Syllabus:

### March 21: Statistical Estimation and Inference

• Basics of statistics: data generating models, common problem formulations and goals
• Point estimation of parameters
• Likelihood function, log likelihood
• Maximum likelihood estimator (MLE)

### March 28: Bayesian estimation

• Priors
• Bayes update, maximum a posteriori (MAP) estimator
• Error metrics, minimum mean square error (MMSE) estimator

### April 4: Hypothesis testing

• Hypotheses, samples
• Type I and type II errors
• ML decision rule, MAP decision rule
• Minimum cost testing

### April 11: Confidence intervals

• Point estimation vs interval estimation
• Sampling theory
• Connection with hypothesis testing
• Prediction

### April 18: Classification

• Problem formulation, classifiers
• Error rate, empirical/training error
• Bayes classfier, regression functions
• Plug-in classifier
• Classifiers used in practice

### April 25: Regression

• Linear regression, least squared error
• Linear regression of a random variable on a random variable
• Least squared error (LSE) estimator
• Linear regression with Gaussian noise