**Click on the text like “Week 1: Jan 20 – 24” 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.

**In class**, we will work on:- Discuss syllabus, overview of course
- Review of prerequisites
- Topics from probability: pdf (also posted on resources page)
- Practice examples for probability: pdf Solutions: 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 (if you are taking two classes with me, you only need to fill out this questionairre once)**Fill out**this brief poll about when my office hours should be held (if you are taking two classes with me, you only need to fill out this poll once)**Sign up**for our class at Piazza (anonymous question and answer forum): https://piazza.com/mtholyoke/spring2020/stat343**Reading**- Review the prerequisite material from probability and calculus. If there are any topics from probability 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 1 or 2 classes we will cover material from Chapter 6 of the text. Give those sections in the book a brief skim.

**Homework 0**due 5 pm Mon, Jan 27

**In class**, we will work on:- Wrap up any remaining probability examples from last class
- Define the \(t\), \(F\), and \(\chi^2\) distributions; this material is in Chapter 6 of Rice. Lecture notes: pdf
**Note that there is a minor error in the lecture notes that we did not make in class:**on page 5, the denominator should be the square root of a chi squared random variable divided by its degrees of freedom. Basically, we need to take the square root of the square of the denominator to see that we have a t-distributed random variable. - Lab 01. See labs page for solutions.

**After class**, please:**Reading:**Over the next few classes we will cover material from Sections 8.1, 8.2, 8.3, and 8.5 of the text. Give those sections in the book a brief skim.**Homework 0**due 5 pm Mon, Jan 27

**In class**, we will work on:- Start on maximum likelihood estimation.

**After class**, please:**Reading:**Over the next few classes we will cover material from Sections 8.1, 8.2, 8.3, and 8.5 of the text. Give those sections in the book a brief skim.**Homework 0**due 5 pm**today**, Mon, Jan 27

**In class**, we will work on:**Quiz**on probability background. This will be very similar to the examples from Wednesday Jan 22 and HW 0. Please memorize everything on the “Topics from probability” document linked on the Resources page, and know how to use it. You only need to know the informal statement of the Central Limit Theorem.- More on maximum likelihood estimation:

**After class**, please:**Reading:**Continue working through Section 8.5. Also give Section 8.4 a brief skim.**Homework 1**due 5 pm Wed, Feb 5

**In class**, we will work on:**After class**, please:**Homework 1**due 5 pm Wed, Feb 5**Reading**: Over the next few days, we’ll explore using Newton’s method to numerically optimize the log-likelihood function. Wikipedia is a reasonably good source; you could give the following a skim:- Remind yourself about how Taylor’s theorem works by skimming the [Wikipedia article] and/or looking at the last page of the review of topics from calculus posted on the Resources page of the course website. We’ll review this at the beginning of class on Wednesday too.
- Newton’s method for root finding
- Newton’s method for optimization

**In class**, we will work on:- Newton’s method for numerical maximization of the log-likelihood function
- Slides posted Monday
- Start Zero-inflated Poisson example: html

- Newton’s method for numerical maximization of the log-likelihood function
**After class**, please:**Homework 1**due 5 pm**today**Wed, Feb 5

**In class**, we will work on:**Quiz**on maximum likelihood. I’ll ask you to find the maximum likelihood estimator for a model with 1 unknown parameter.- Newton’s method for numerical maximization of the log-likelihood function
- Finish Zero-inflated Poisson example we started last class.

**After class**, please:

**In class**, we will work on:- Numerical maximum likelihood using Stan
- Handout: pdf
- Lab 3

- Numerical maximum likelihood using Stan
**After class**, please:**Homework 2**due 5pm Friday Feb 14

**In class**, we will work on:- Sampling distributions, bias, variance, and mean squared error. Lecture notes: pdf

**After class**, please:**Homework 2**due 5pm Friday Feb 14

**In class**, we will work on:**After class**, please:**Homework 2**due 5pm**today**Friday Feb 14

**In class**, we will work on:**After class**, please:

**In class**, we will work on:- More on Bayesian inference:
- Lab 6
- Finish examples from practice worksheet last class.

- More on Bayesian inference:
**After class**, please:**Homework 3**due Wed. Feb 26

**In class**, we will work on:- Bayesian credible intervals: posterior percentiles, highest posterior density. Partial lecture notes are here, but I also discussed highest posterior density: pdf
- Start on analysis of normal distribution from a Bayesian perspective.
- Another practice example we didn’t have time for: pdf. Solutions: pdf

**After class**, please:**Homework 3**due Wed. Feb 26

**In class**, we will work on:**After class**, please:**Homework 3**due Wed. Feb 26

**In class**, we will work on:- Finish examples from last class

**After class**, please:**Homework 3**due**Thursday Feb. 27**

**In class**, we will work on:- Finish MCMC (correction to last pages of handout from last class) and lab on MCMC:
- Quiz 3

**After class**, please:

**In class**, we will work on:**After class**, please:- If you want reading for the material we’ll cover in the next few days, you can refer to the following sources (in order of how useful I think they are):

**In class**, we will work on:- Large-sample normal approximation to sampling distribution of MLE (Continuing handouts from last class)

**After class**, please:

**In class**, we will work on:**After class**, please:

**In class**, we will work on:- No new material.

**After class**, please:

**No Class**: Midsemester Break. Safe travels!

**No Class**: Midsemester Break. Safe travels!

**No Class**: Midsemester Break. Safe travels!

**No Class**: Midsemester Break. Safe travels!

**No Class**: Midsemester Break. Safe travels!

**No Class**: Midsemester Break. Safe travels!

**In class**, we will work on:- Reminder/overview of recent topics:
- Notes: pdf
- Errors:
- At about 16:50 in the video, I should have written \(\hat{\Theta}^{MLE}\)

- Statement of Theorem: Normal approximation to posterior distribution for large \(n\).
- Notes: pdf
- Errors:
- At about minute 4:00 in the video, I incorrectly state that the marginal posterior distribution for the mean in a Bayesian analysis of a normal distribution with unknown variance is normal.

- Proof Part 1: Prior doesn’t matter:
- Notes: pdf

- Proof Part 2: 2nd order Taylor approximation:
- Notes: pdf

- Reminder/overview of recent topics:
**After class**, please:

**In class**, we will work on:- Example of finding a normal approximation to the posterior distribution and using that approximation to find a credible interval:
- Notes: pdf

- Worksheet and lab:

- Example of finding a normal approximation to the posterior distribution and using that approximation to find a credible interval:
**After class**, please:- Finish worksheet and lab from today.

**In class**, we will work on:- Taking stock of where we are in the class:
- Motivating example for confidence intervals:
- Notes: pdf

- Defining confidence intervals, and an example of a confidence interval derivation:
- Notes: pdf
- Errors:
- At about minute 36 I wrote down the wrong formula for the confidence interval. The formula should be \([\bar{x} - t_{n-1}(1 - \frac{\alpha}{2}) \frac{s}{\sqrt{n}}, \bar{x} - t_{n-1}(\frac{\alpha}{2}) \frac{s}{\sqrt{n}}]\)

- The videos were longer than I originally planned, so we’ll do the example/lab next class.

- Taking stock of where we are in the class:

**In class**, we will work on:**After class**, please:

**In class**, we will work on:- Motivation for getting confidence intervals based on a large-sample normal approximation to a sampling distribution:
- Notes: pdf

- Example of getting confidence intervals based on a large-sample normal approximation to a sampling distribution:
- Example for you to do: Rayleigh distribution

- Motivation for getting confidence intervals based on a large-sample normal approximation to a sampling distribution:

**In class**, we will work on:- There is a little more content here than would fit into one class day. I’ll do a little less on Monday.
- Introduction to bootstrap for estimating a sampling distribution
- Annotated notes: pdf

- Example of bootstrap for estimating the distribution of the mean for a Poisson distribution

**In class**, we will work on bootstrap confidence intervals- Materials used throughout all videos today and next class
- Introduction and set up:
- Errors and Notes:
- At about 6:40, I gave an incorrect formula for the estimated standard error of the sample mean. The correct formula is \(\widehat{SE}(\bar{X}) = S/\sqrt{n} = \left[ \frac{\sum_{i=1}^n (X_i - \bar{X})^2}{n - 1} \right]^{0.5} / \sqrt{n}\)
- As I made this video, I claimed we really needed a bootstrap for this case. As I looked at the example more, I decided that although I’m most comfortable with a bootstrap based interval in this example, probably other approaches would also work OK.

- Errors and Notes:
- Percentile bootstrap confidence intervals:
- Bootstrap t confidence intervals when a formula is available to calculate the estimated standard error.

**In class**, we will work on:- Continuing with handout from April 13
- Bootstrap t confidence intervals when no formula is available to calculate the estimated standard error. Part 1: concepts
- Bootstrap t confidence intervals when no formula is available to calculate the estimated standard error. Part 2: code walk-through
- Lab on bootstrap confidence intervals

**After class**, please:

**In class**, we will work on:- Warm up example for likelihood ratio tests.
**I suggest giving the problem a try before watching the solutions video or looking at the solutions pdf.** - Example of likelihood ratio tests for a normal distribution.
**I suggest giving the problem a try before watching the solutions video or looking at the solutions pdf.** - Lab 15, which follows up on the second example above.

- Warm up example for likelihood ratio tests.

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

**In class**, we will work on:- Warm Up about Power Functions
**I suggest giving the problem a try before watching the solutions video or looking at the solutions pdf.** - Motivation for Neyman Pearson Lemma
- Set up for Neyman Pearson Lemma: reminder and more detail about likelihood ratios
- Annotated pdf: pdf

- Statement and proof of Neyman Pearson Lemma
- Notes: pdf

- Warm Up about Power Functions

**In class**, we will work on:- Composite likelihood ratio tests; derivation of t tests
- Notes: pdf

- Composite likelihood ratio tests; derivation of t tests

We **will** have a final exam in this class.