Winter 2022 focus is on Richard McElreath 2022 course on Bayesian statistics. Pdf of first two chapters of his Statistical_Rethinkng gives foundational philosophy. Course ends on the subject of state-space representation of time-series data. Calendar is from McElreath's site.
There are 10 weeks of instruction. Links to lecture recordings will appear in this table. Weekly problem sets are assigned on Fridays and due the next Friday, when we discuss the solutions in the weekly online meeting.
Lecture playlist on Youtube: <Statistical Rethinking 2022>
| Week ## | Meeting date | Reading | Lectures |
|---|---|---|---|
| Week 01 | 07 January | Chapters 1, 2 and 3 | The Golem of Prague, Bayesian Inference |
| Week 02 | 14 January | Chapter 4 | Basic Regression, Categories & Curves |
| Week 03 | 21 January | Chapters 5 and 6 | Confounding, Even Worse Confounding |
| Week 04 | 28 January | Chapters 7 and 8 | Overfitting, Interactions |
| Week 05 | 04 February | Chapters 9, 10 and 11 | Markov chain Monte Carlo, Binomial GLMs |
| Week 06 | 11 February | Chapters 11 and 12 | Poisson GLMs, Ordered Categories |
| Week 07 | 18 February | Chapter 13 | Multilevel Models, Multi-Multilevel Models |
| Week 08 | 25 February | Chapter 14 | Varying Slopes, Gaussian Processes |
| Week 09 | 04 March | Chapter 15 | Measurement Error, Missing Data |
| Week 10 | 11 March | Chapters 16 and 17 | Beyond GLMs: State-space Models, ODEs, Horoscopes |
Devised around in 1763 by Thomas Bayes, Bayesian Statistics addresses conditional probability in terms of the ratio between an event A happening simultaneously with another event, B written: P(A given B) = P( A and B ) / P( only A ).
Bayes described conditional probability- not how to update priors or measure probability beyond counting.
In 1814, Laplace presents the classical interpretation of probability which treats probability as a measure of a ratio between a favorable interpretation of an event and all those events not deeemed favorable. In this way, more experimental data leads to tighter confidence intervals — e.g. 90% of the experiments (confidence level) fall between θlow and θhigh (confidence interval). This is the language of classic statistical hypothesis testing.
In 1857 logicians Venn and Boole introduce the frequentist interpretation of probability which treats probability as the measure of likelihood after attempting a large number of trials.
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A Student's Guide to Bayesian Statistics: by Ben Lambert. This course aims to provide a core understanding of Bayesian statistics that is grounded in mathematical theory, yet friendly to the less mathematically-minded of persons. It aims to focus on the intuitive results of Bayesian theory rather than dwell on the mathematical minutiae.
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Statistical Rethinking: by Richard McElreath. The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.
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Learning Bayesian Statistics Podcast: A very well produced podcast interviewing big thinkers in Bayesian statistics by Alexandre Andorra.
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Statistical Thinking: Frank Harrell is a Professor of Biostatistics in the School of Medicine at Vanderbilt University. This blog is devoted to statistical thinking and its impact on science and everyday life.
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Modeling Emotions Associated With Novelty at Variable Uncertainty Levels: A Bayesian Approach by Hideyoshi Yanagisawa. Good, simple example of using Bayesian statistics to model human behaviour based on prior beliefs about states of excitement before (prior distribution), during (ikelihood) and after the event (posterior distribution).
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Bayesian modeling of time series From Introduction to biological time series data by Kyrre Lekve from Department of Biology, University of Oslo. Masterpiece of a lecture. See also: State-space representation of time-series data.