**Click on the text like “Week 1: Jan 22 – 25” to expand or collapse the items we covered in that week.**

I will fill in more detail and provide links to lecture notes and labs as we go along. Items for future dates are tentative and subject to change.

- Introduction; review of topics from probability; properties of the sample mean for a simple random sample from a finite populaiton

**In class**, we will work on: Overview and review- Discuss syllabus, overview of course
- Review of prerequisites
- Topics from probability: pdf (also posted on resources page)
- Practice examples for probability: pdf
- Common probability distributions: pdf (also posted on resources page; you don’t need to memorize this material)
- Topics from calculus (not discussed today, please review after class): pdf (also posted on resources page)

**After class**, please do the following:**Register for GitHub**here if you haven’t already; I will ask you to provide your GitHub user name in the questionairre below.**Fill out**a brief questionnairre**Fill out**this brief poll about when my office hours should be held**Sign up**for our class at Piazza (anonymous question and answer forum): https://piazza.com/mtholyoke/spring2019/stat343**Reading**- Review the prerequisite material from probability and calculus. If there are any topics from probability or calculus that you don’t have memorized, please start memorizing them. This will make the rest of this class go much more smoothly for you. If you have any questions on this material, please don’t hesitate to ask me in office hours or on Piazza. I am happy to help with this material.
- Over the next few classes we will cover material from Sections 7.1 - 7.3 of the text. Give those sections in the book a brief skim.

**Homework 0**due Wed, Jan 30

**In class**, we will work on: Sections 7.1, 7.2, 7.3.1, and 7.3.2 (mostly lecture)- Last two probability examples from last class
- Briefly talk through the “common probability distributions” handout
- Motivating example for Chapter 7: pdf
- Definitions from Chapter 7 (some on motivating example handout): population parameter, statistic, estimator, estimate, simple random sample, sampling distribution, bias, variance, mean squared error
- Start on some derivations of the expected value, variance, and MSE of the sample mean based on a simple random sample from a finite population.
- If time (unlikely), start on estimating the population variance based on a simple random sample from a finite population.
- Lecture notes for Sections 7.1, 7.2, 7.3.1, and 7.3.2: pdf
- Set up git on RStudio (if you took Stat 340 with me, you can leave early)

**After class**, please do the following:- Start memorizing any definitions from today’s class that you don’t know yet.
**Problem Set 0**due Wed, Jan 30

Section 7.3.3 (see Stat 344SM, survey sampling, for the rest of Chapter 7 and much more); start on Chapter 8

**In Class**, we will work on: Sections 7.1, 7.2, 7.3.1, and 7.3.2 (mostly lecture, some worked examples)- Finish stuff from Sections 7.2, 7.3.1, and 7.3.2 that we didn’t get to on Friday.

**After class**, please do the following:**Problem Set 0**due Wed, Jan 30

**In Class**, we will work on: Section 5.3 and part of 7.3.3 (mostly lab)- Central Limit Theorem, more on the sampling distribution of the sample mean
- Lab 1 on GitHub
- Topics from R:
`for`

loops: pdf`dplyr::sample_n`

**After class**, please do the following:**Problem Set 0**due Fri, Feb 1

**Problem Set 0 due today!!****In Class**, we will work on: Section 7.3.3- Mean Squared Error = Bias\(^2\) + Variance. Lecture notes: pdf
- Finish lab from last time

**After class**, please do the following:**Problem Set 1**due Fri, Feb 15

**In Class**, we will work on: Section 7.3.3- A first look at confidence intervals for a population mean based on a simple random sample. pdf (not on the lecture notes but discussed in class are the coverage probability and nominal coverage probability of a confidence interval)
- R topics: Logical operations on vectors, mutate and summarize pdf
- Lab 2: confidence intervals for simple random sampling

**After class**, please do the following:**Problem Set 1**due Fri, Feb 15

**In Class**, we will work on: Finish Section 7.3.3- Finish confidence intervals lab from last class
- If you finish early, free time or work on homework

**After class**, please do the following:**Problem Set 1**due Fri, Feb 15

**In Class**, we will work on: Start on Sections 8.1 through 8.5- Introductory worksheet, friend or foe: pdf
- Some plots to go with the introductory worksheet: pdf
- Rmd file in case you want to see code for making the plots: Rmd

- Defined the likelihood function, log-likelihood function, maximum likelihood estimator, maximum likelihood estimate
- Argued that the parameter value that maximizes the log-likelihood also maximizes the likelihood, since log is an increasing function.
- Reviewed some calculus related to finding a maximum of a univariate function

**After class**, please do the following:**Problem Set 1**due Fri, Feb 15

**In Class**, we will work on: Sections 8.1 through 8.5

**In Class**, we will work on: Sections 8.1 through 8.5

**In Class**, we will work on: Sections 8.1 through 8.5- Wrap up examples from last class
- Review of Taylor’s Theorem. See last 2 pages of handout about calculus from first day, also posted on resources page.
- Introduce methods for numerical maximization of functions. Slides: pdf
- Note that on slide 5 I should have had lower case \(\ell\) (for the log-likelihood) rather than upper case \(L\).

- Start Lab 5, on numeric optimization via Newton’s method; posted on GitHub

**In Class**, we will work on:- Finish Lab 5

**In Class**, we will work on:- Numeric maximum likelihood in Stan
- Example pdf
- Lab 6

- Prepare for next class: Lab 7a

- Numeric maximum likelihood in Stan

**In Class**, we will work on:**Before class**, please complete Lab 7a!! Note that in the calls to`qbeta`

, you will need to change the`shape2`

parameter to`b`

. Your revised code will look like this:`qbeta(c(0.25, 0.75), shape1 = a, shape2 = b) qbeta(c(0.05, 0.95), shape1 = a, shape2 = b)`

- Bayesian Estimation: Section 8.6
- Lecture notes: pdf
- Lab 7b

**In Class**, we will work on: Section 8.6

**In Class**, we will work on: Section 8.6- Lab 8

**In Class**, we will work on:- Set up for MCMC: Limits of conjugate priors for handling normal distributions. Notes: pdf

**In Class**, we will work on:- Justification of numerical integration using the law of large numbers. Lecture notes: pdf
- MCMC for Bayesian inference using Stan.
- Handout: pdf
- Lab 9 posted on GitHub

- MCMC for Bayesian inference.
- Reading 1: the discussion of the law of large numbers and its application for numerical integration, discussed in Section 5.2 of Rice.
- Reading 2 (optional?): I’ve posted a chapter from Introduction to Statistical Thought by Michael Lavine. This goes into more depth than we will, but it’s the most readable less-than-book-length introduction to this topic at an undergraduate level that I have found. It is linked to from the resources page: http://www.evanlray.com/stat343_s2019/resources.html

**In Class**, we will work on:- Large-sample normal approximation to the posterior distribution.

**In Class**, we will work on: ideas from Section 8.5.3, borrowed the idea of the likelihood ratio from Section 9.1.

**In Class**, we will work on:- Finish intuition handout from last class
- Lots of lecture about Fisher Information and Observed Fisher Information, large-sample normal approximations to the sampling distribution of the MLE in terms of information; confidence intervals from the large sample normal approximation; Poisson example. Lecture notes: pdf
- Handout to go with Poisson example: pdf

**In Class**, we will work on:**Midterm**on PS1 through PS5

**In Class**, we will work on:- Practice with large sample approximations to sampling distribution of the MLE: pdf
- Start Lab 12

**In Class**, we will work on:- Some large-sample results about maximum likelihood estimators. Consistency, Cramer-Rao Lower Bound, efficiency, shrinkage estimators. Lecture notes: pdf
- Finish Lab 12, Start Lab 11

**In Class**, we will work on:- Shrinkage estimators. No lecture notes, but we talked about how the posterior mean for the mean of a normal distribution and the parameter theta for a binomial distribution can both be viewed as an appropriately weighted average of the prior mean and the data mean.
- Finish old labs
- Start an example about practice with MSE, which will be due for homework: pdf
- Start Lab 13, which will be due for homework.

**In Class**, we will work on:- Bootstrap estimation of a sampling distribution. Handout: pdf
- Lab 14

**In Class**, we will work on:- Bootstrap confidence intervals. Handout (NOTE: the version I distributed in class wasn’t quite right on the last page. Corrected version here.): pdf
- Lab 15

**Class cancelled**

**In Class**, we will work on:- Warm up about likelihood ratio tests: pdf
- Revisit example of tests about mean of a normal distribution with known variance, simple hypotheses from last class
- Wrap up discussion from last class
- A Bayesian approach

- Some things to avoid in hypothesis testing
- Bayesian approach to analysis of normal distributions example: pdf
- Jump into some things to avoid, just so we know about them:
- Type I and Type II errors, Power

**Class cancelled**

**In Class**, we will work on:

**In Class**, we will work on:- Generalized likelihood ratio statistic; inverting tests to obtain confidence intervals. Lecture notes: pdf

**In Class**, we will work on:- Example of inverting likelihood ratio test to get confidence interval
- Start on worksheet about likelihood ratio tests and confidence intervals. pdf

**In Class**, we will work on:- Finish talking through worksheet from last class.
- Introduce permutation tests: pdf
- Lab 17

**In Class**, we will work on:- Sufficient statistics and exponential families. Lecture notes: pdf

**In Class**, we will work on:- Reminder of previous results about shrinkage estimators for a single parameter: pdf

**In Class**, we will work on:

We will have a cumulative final exam.