Lectures and code demonstrations will be given live over Zoom at 1:00pm Eastern on Monday, Wednesday, and Friday. They will also be recorded and shared on this page within an hour of the live session. You are highly encouraged to attend the live Zoom sessions, but I understand that it might not be possible with our current circumstances and your other commitments.

Links to Zoom meetings will be distributed through announcements in Canvas before the lecture time.

Course Introduction
June 26

Motivation for course, overview of course logistics, and discussion of Bayesian and frequentist philosophies.

Video Notes
Discrete Probability Distributions
June 29

Introduction to probability theory and discrete probability distributions.

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Introduction to Bayesian Inference
July 1

Conditional distributions and Bayes' rule in the discrete setting.

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Continuous probability distributions
July 6

Introduction to continuous random variables and distributions.

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Continuous distributions and Bayes' rule
July 8

Discussion of Bayes' rule, sequential updates, and mixed discrete-continuous formulations.

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Demo: Probabilistic Robotics
July 10

Application of Bayesian ideas to the localization (i.e., Where am I?) problem in robotics.

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Expectations and Conjugate Bayesian analysis
July 13

Expected values and more analytic applications of Bayes' rule.

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Scalar Gaussian inference
July 15

The scalar Gaussian distribution and applications in regression.

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Demo: Federalist Papers
July 17

Conjugate inference with the Poisson-Gamma conjugate pair.

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Sequential Gaussian Filtering
July 20

Application of the univariate Gaussian distribution to sequential inference problems.

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Midterm Review
July 22

Review material for stay-at-home midterm exam.

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Demo: Numpy and Least Squares
July 24

Some python building blocks that will be useful for working with multivariate Gaussian distributions.

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Multivariate Gaussian inference
July 27

Introduction to the multivariate Gaussian distribution and inference problems with affine models.

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Linear Bayesian Regression
July 29

Multivariate Gaussian models for regression.

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Demo: Solving linear Gaussian problems with Numpy.
July 31

Constructing functions in python for computing Gaussian posterior distributions.

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Non-Conjugate Inference: The need for sampling.
August 3

Introduction to sampling, the law of large numbers, and central limit theorem.

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Markov chain Monte Carlo.
August 5

Overview of Markov chains and the Metropolis-Hastings rule.

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Demo: Estimating sea ice thickness with electromagnetic measurements.
August 7

Use of MCMC to solve Bayesian inference problem based on the EM31 ground conductivity meter.

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Assessing the quality of MCMC samples.
August 10

Use of central limit theorem and autocorrelation function to assess sampling quality.

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Bayesian Model Selection.
August 12

Model comparison and selection in the Bayesian setting.

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Demo: MCMC, autocorrelation, and aquifer pump tests.
August 14

Application of Bayesian inference and MCMC for estimating aquifer properties.

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Posterior checks and hierarchical modeling.
August 17

Provides an introduction to posterior predictive checks and motivation for the use of hierarchical modeling.

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Hierarchical modeling.
August 19

Discuss the use of hierarchical techniques for characterizing hyperparameters.

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Demo: Batting Averages.
August 21

More robust estimates of batting averages in baseball using a hierarchical model.

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Description of COVID-19 Model.
August 24

See recorded video in Canvas Media Gallery.

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Course summary.
August 26

A brief overview of the course and an outline of more advanced topics.

Video Notes

 (1) Consent to recording of course and group office hours

  a) I affirm my understanding that this course and any associated group meetings involving students and the instructor, including but not limited to scheduled and ad hoc office hours and other consultations, may be recorded within any digital platform used to offer remote instruction for this course;

  b) I further affirm that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part, and distribution of any of these recordings in whole or in part without prior written consent of the instructor may be subject to discipline by Dartmouth up to and including expulsion;

  c) I authorize Dartmouth and anyone acting on behalf of Dartmouth to record my participation and appearance in any medium, and to use my name, likeness, and voice in connection with such recording; and

  d) I authorize Dartmouth and anyone acting on behalf of Dartmouth to use, reproduce, or distribute such recording without restrictions or limitation for any educational purpose deemed appropriate by Dartmouth and anyone acting on behalf of Dartmouth.

  (2) Requirement of consent to one-on-one recordings

By enrolling in this course, I hereby affirm that I will not under any circumstance make a recording in any medium of any one-on-one meeting with the instructor without obtaining the prior written consent of all those participating, and I understand that if I violate this prohibition, I will be subject to discipline by Dartmouth up to and including expulsion, as well as any other civil or criminal penalties under applicable law.