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.

Wed, Jan 22

  • 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

Fri, Jan 24

  • 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

Mon, Jan 27

  • In class, we will work on:
    • Start on maximum likelihood estimation.
      • Warm up example/worksheet: pdf
      • Plots to go with the example above: pdf
      • Lecture notes for maximum likelihood estimation for this example: pdf
      • We had a few extra minutes so we also defined an estimator (a random variable) and estimate (realized value of an estimator based on a sample, a number).
  • 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

Wed, Jan 29

  • 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:
      • Example about seedlings: pdf Solutions: pdf
      • Lab 2. Solutions: GitHub
  • 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

Fri, Jan 31

  • In class, we will work on:
    • More on maximum likelihood estimation:
      • Example about bird hops: pdf
      • Example about normal distribution.
  • After class, please:
    • Homework 1 due 5 pm Wed, Feb 5
    • Reading: Read Section 8.4.

Mon, Feb 03

  • In class, we will work on:
    • Example where analytically maximizing the likelihood doesn’t work: pdf
    • Method of moments. Lecture notes: pdf
    • Reminder about Taylor’s theorem, from calculus review handout (linked on resources page)
    • Intro to Newton’s method for optimization. Slides: pdf
  • 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:

Wed, Feb 05

  • 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
  • After class, please:
    • Homework 1 due 5 pm today Wed, Feb 5

Fri, Feb 07

  • 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:

Mon, Feb 10

  • In class, we will work on:
    • Numerical maximum likelihood using Stan
      • Handout: pdf
      • Lab 3
  • After class, please:
    • Homework 2 due 5pm Friday Feb 14

Wed, Feb 12

  • 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

Fri, Feb 14

  • In class, we will work on:
    • Example of bias, variance, MSE for estimators of the variance of a normal distribution. Lecture notes: pdf
    • We didn’t have time to get to Lab 4, but maybe you could take a quick look at it on your own?
    • Motivation for subjective probability intervals: pdf
  • After class, please:
    • Homework 2 due 5pm today Friday Feb 14

Mon, Feb 17

  • In class, we will work on:
    • Wrap up lab on bias, variance, and MSE
    • Wrap up subjective probability intervals/subjective interpretation of probability
    • Intro to Bayesian inference
      • Lecture notes on Binomial example: pdf
      • We also did the first example on this worksheet: pdf
  • After class, please:

Wed, Feb 19

  • In class, we will work on:
    • More on Bayesian inference:
      • Lab 6
      • Finish examples from practice worksheet last class.
  • After class, please:
    • Homework 3 due Wed. Feb 26

Fri, Feb 21

  • 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.
      • Lecture notes: pdf. Note that for case 1 (unknown mean, known variance) I mixed up the notation a little towards the end of page 1 of these notes. The stuff I wrote in class was correct.
      • Plots illustrating MSE for Bayesian estimator of the mean when the variance is known: pdf
    • Another practice example we didn’t have time for: pdf. Solutions: pdf
  • After class, please:
    • Homework 3 due Wed. Feb 26

Mon, Feb 24

  • In class, we will work on:
    • Finish examples of estimation for normal distribution from last class.
    • Introduce Monte Carlo integration:
      • Lecture notes: pdf
      • Examples: pdf
  • After class, please:
    • Homework 3 due Wed. Feb 26

Wed, Feb 26

  • In class, we will work on:
    • Finish examples from last class
  • After class, please:
    • Homework 3 due Thursday Feb. 27

Fri, Feb 28

  • In class, we will work on:
    • Some additional Monte Carlo integration examples: pdf
    • Introduce MCMC
  • After class, please:

Mon, Mar 02

  • 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:

Wed, Mar 04

Fri, Mar 06

  • In class, we will work on:
    • Large-sample approximation to sampling distribution of MLE
      • Hand out with proof: pdf
      • Hand out with conditions: pdf
  • After class, please:

Mon, Mar 09

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

Wed, Mar 11

  • In class, we will work on:
    • Consistency and Efficiency
      • Notes: pdf
      • Set up for lab 10: pdf
  • After class, please:

Fri, Mar 13

  • In class, we will work on:
    • No new material.
  • After class, please:

Mon, Mar 16

  • No Class: Midsemester Break. Safe travels!

Wed, Mar 18

  • No Class: Midsemester Break. Safe travels!

Fri, Mar 20

  • No Class: Midsemester Break. Safe travels!

Mon, Mar 23

  • No Class: Midsemester Break. Safe travels!

Wed, Mar 25

  • No Class: Midsemester Break. Safe travels!

Fri, Mar 27

  • No Class: Midsemester Break. Safe travels!

Mon, Mar 30

  • 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:
    • Proof Part 2: 2nd order Taylor approximation:
  • After class, please:

Wed, Apr 01

  • In class, we will work on:
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Fri, Apr 03

  • In class, we will work on:
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Mon, Apr 06

  • In class, we will work on:
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Wed, Apr 08

  • In class, we will work on:
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Fri, Apr 10

  • In class, we will work on:
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Mon, Apr 13

  • In class, we will work on:
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Wed, Apr 15

  • In class, we will work on:
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Fri, Apr 17

  • In class, we will work on:
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Mon, Apr 20

  • In class, we will work on:
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Wed, Apr 22

  • In class, we will work on:
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Fri, Apr 24

  • In class, we will work on:
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Mon, Apr 27

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

We will not have a final exam in this class.