Bayesian Statistics the Fun Way

Author

Peter Baumgartner

Published

2023-10-06 23:01

Preface

This is work in progress: about 95%.

This Quarto book collects my personal notes, trials and exercises of the Bayesian Statistics the Fun Way: Understanding Statistics and Probability With Star Wars, LEGO, and Rubber Ducks by Will Kurt (Kurt 2019).

About My Motivation for this Quarto Book

I am not an expert in statistics. During my study in sociology back in 1970er I had only rudimentary learned about frequentist statistics. There weren’t computer only via time-sharing and keypunching for card-to-tape converter available. This was painstaking and not motivating because it had not much practical values. 10 years later I worked sometimes with SPSS but used — as many of my colleagues — the “statistics all” option without much understanding. It was no fun and so I dedicated most of my time to theoretical work and later sometimes to qualitative social research via grounded theory.

Only when I heard 2015 about R and began to exerpiment with it, I started my self-directed education in statistics again. Still I was not so intrigued by Null Hypothesis Statistical Testing (NHST) but more from Data Science. I noticed the problems with p-values and was therefore fascinated with Introduction to the New Statistics by Geoff Cumming & Robert Calin-Jageman (Cumming and Calin-Jageman 2017). Instead of concentrating on p-values the book teaches the importance of confidence intervals, (CIs). But at that time I came across some discussion about Bayesian statistics. I read The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne (McGrayne 2011) but didn’t understand at that time how Bayesian statistics works.

The real game changer for me then was Statistical Rethinking by Richard McElreath (McElreath 2020). I immediately started my first Quarto book with notes about the book and the companion bookdown website Statistical rethinking with brms, ggplot2, and the tidyverse: Second edition by A Solomon Kurz. But unfortunately after four chapters I noticed that I am lacking basic knowledge and looked around for other books on Bayesian statistics that are easier to digest for me. I tried A Student’s Guide to Bayesian Statistics by Ben Lambert (Lambert 2018), but I stopped reading it after chapter eight. I has to much theory for me and I was missing the opportunity trying my own hands out with R.

So finally I came around to Will Kurt’s book. I understand that the modern simulation methods like MCMC are not in the focus of the book and also the usage of R code is distributed very sparsely in the book. But I learned (and understood) many Bayesian concepts and could all the graphics in the book — where the R code is missing — replicate with {ggplot2} (Wickham 2016) in tidyverse (Wickham et al. 2019) style. The book was at the time (September/October 2023) a perfect match for my rudimentary knowledge. I have now more trust to continue with Statistical Rethinking or — as a possible alternative — to start with a new Quarto book on Doing Bayesian Data Analysis: A Tutorial With R, JAGS, and Stan (Kruschke 2014) which I have already read and (I believe) mostly understood.

Another motivation to write a Quarto book was to learn how to use Quarto. I already wrote some books with bookdown (Xie 2023) but Quarto was relatively new for me. This book was therefore a good occasion to learn and experiment with the functionality of Quarto.

Content and Goals of this Book

This book collects personal notes during reading of Bayesian Statistics the Fun Way by Will Kurt. Additionally I am using C: Answers to Exercises

Each chapter of the book has three main parts:

Short summaries of the book content

This summarizes my own highlights but gives also the necessary information for my section about “Experiments”. Mostly I quote the text but without page references. Often I made minor editing (e.g., shorting the text) or put sometimes the content in my own wording. As I follow the text section by section reader can easily find the quoted passage.

Almost all of my text of this first part of the Quarto book are not mine, but is coming from the resources mentioned above. There are two exceptions:

Whenever necessary I include personal notes already in this part of the chapter. Most of the time it is combined with a cross reference to the third main part of the book: my experiments.
Sometimes there is also base R Code by the author provided. Whenever possible I convert this base R code by the author in {tidyverse} code.
I copied all figures into the text as a template for my own replication.

Important

Although I have quoted many passages from the original as highlights for me to remember, this Quarto ebook is not meant to stand alone. My summaries are driven by my personal interests and my huge gaps in my statistical knowledge and especially in Bayesian statistics. My notes are therefore in no way a substitute for Will Kurt’s book Bayesian Statistics the Fun Way: Understanding Statistics and Probability With Star Wars, LEGO, and Rubber Ducks by Will Kurt (Kurt 2019). Please buy the book so that you can embed my notes appropriately in the general argumentation of the author.

Exercises

Again I quote the full question text and then try my own solution. If my solution is not correct or I cant find a solution I will note this in a personal callout and will correct the solution. If my solution is correct but with a different method I will also reflect on the result, but will not adapt or change my solution.

Experiments

Here I am trying to make my own exercises. Most of the examples are replications of the book figures because the author has not included the R code. Additionally I cross referenced to the figure from the first part, the author section. If you hover over the cross reference link you will get the authors figure overlaid and can compare it with my replication.

Writing my own R chunks I am using the tidy approach with the collection of the {tidyverse} packages, especially with {ggplot2} for the figures. But instead of using the library() command I always mention the used packages explicitly. Whenever I used another packages I called the function with the package name in front with the syntax <package name>::<function name>(), like ggplot2::gplot(). This is tedious work but it helps me to learn & remember which command “belongs” to which package. Only exception is the {patchwork} package, as I do not know how to call commands like p1 + p2 with the package name.

In graphics I use not only caption for figures but also captions for the R code. There is no easy standardized way to use code listings with captions and to evaluate the code at the same time, but I found a workaround with the following structure of code options in the code chunk:

#| label: fig-name
#| fig-cap: "fig-title"
#| attr-source: '#lst-fig-name lst-cap="list-title"'

This code generates a warning because at the moment the = symbol is not allowed in RStudio when running a R chunks interactively in a Quarto document. See issue 13326. Although I got a warning the code does what I want: It gives the figure and the code listing a heading and evaluates the code at the same time.

Glossary

I started a glossary using the {glossary} package by Lisa DeBruine (DeBruine 2023). A glossary entry is visualized with a double underline. Every chapter has a section where the text of all glossary entries of the chapter are displayed. When you hover with the mouse over the link it opens a pop-up window with the glossary text. You can see example in the section about my motivation for this ebook (See Section 1).

I am using this glossary for all my other Quarto books but it is till work in progress. Please keep in mind that I collected the definition at various places and be attentive because there is no guarantee that the entry is appropriate and correct. I have added the sources where I got the content for the glossary entry.

Session Info

Every chapter ends with a session information printed with the sessionInfo() function.

Warning

I wrote this book as a text for others to read because that forces me to be become explicit and explain all my learning outcomes more carefully. Please keep in mind that this text is not written by an expert but by a learner. In spite of replicating most of the content it may contain many mistakes. All these misapprehensions and errors are my responsibility.

In any case I am the only responsible person for this text, especially if I have used code from the resources wrongly or misunderstood a quoted text passage.

--- engine: knitr --- # Preface {.unnumbered} ::: {.callout-note style="color: blue;"} #### This is work in progress: about 95%. ::: This Quarto book collects my personal notes, trials and exercises of the [Bayesian Statistics the Fun Way: Understanding Statistics and Probability With Star Wars, LEGO, and Rubber Ducks](https://nostarch.com/learnbayes) by Will Kurt [@kurt2019]. ## About My Motivation for this Quarto Book {#sec-book-motivation} I am not an expert in statistics. During my study in sociology back in 1970er I had only rudimentary learned about `r glossary("frequentist statistics")`. There weren't computer only via time-sharing and keypunching for card-to-tape converter available. This was painstaking and not motivating because it had not much practical values. 10 years later I worked sometimes with SPSS but used --- as many of my colleagues --- the "statistics all" option without much understanding. It was no fun and so I dedicated most of my time to theoretical work and later sometimes to qualitative social research via [grounded theory](https://en.wikipedia.org/wiki/Grounded_theory). Only when I heard 2015 about R and began to exerpiment with it, I started my self-directed education in statistics again. Still I was not so intrigued by Null Hypothesis Statistical Testing (NHST) but more from Data Science. I noticed the problems with p-values and was therefore fascinated with [Introduction to the New Statistics](https://thenewstatistics.com/itns/) by Geoff Cumming & Robert Calin-Jageman [@cumming2017]. Instead of concentrating on p-values the book teaches the importance of `r glossary("confidence interval","confidence intervals")`, (CIs). But at that time I came across some discussion about `r glossary("Bayesian statistics")`. I read [The Theory That Would Not Die](https://www.jstor.org/stable/j.ctt1np76s): How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne [@mcgrayne2011] but didn't understand at that time how Bayesian statistics works. The real game changer for me then was [Statistical Rethinking](https://www.routledge.com/Statistical-Rethinking-A-Bayesian-Course-with-Examples-in-R-and-STAN/McElreath/p/book/9780367139919) by Richard McElreath [@mcelreath2020]. I immediately started [my first Quarto book](https://bookdown.org/pbaumgartner/sr2-notes/) with notes about the book and the companion bookdown website [*Statistical rethinking* with brms, ggplot2, and the tidyverse: Second edition](https://bookdown.org/content/4857/) by A Solomon Kurz. But unfortunately after four chapters I noticed that I am lacking basic knowledge and looked around for other books on Bayesian statistics that are easier to digest for me. I tried A Student's Guide to Bayesian Statistics by Ben Lambert [@lambert2018], but I stopped reading it after chapter eight. I has to much theory for me and I was missing the opportunity trying my own hands out with R. So finally I came around to Will Kurt's book. I understand that the modern simulation methods like MCMC are not in the focus of the book and also the usage of R code is distributed very sparsely in the book. But I learned (and understood) many Bayesian concepts and could all the graphics in the book --- where the R code is missing --- replicate with {**ggplot2**} [@ggplot2] in tidyverse [@tidyverse] style. The book was at the time (September/October 2023) a perfect match for my rudimentary knowledge. I have now more trust to continue with Statistical Rethinking or --- as a possible alternative --- to start with a new Quarto book on [Doing Bayesian Data Analysis: A Tutorial With R, JAGS, and Stan](https://sites.google.com/site/doingbayesiandataanalysis/) [@kruschke2014] which I have already read and (I believe) mostly understood. Another motivation to write a Quarto book was to learn how to use [Quarto](https://quarto.org/). I already wrote some books with bookdown [@bookdown] but Quarto was relatively new for me. This book was therefore a good occasion to learn and experiment with the functionality of Quarto. ## Content and Goals of this Book {.unnumbered} This book collects personal notes during reading of [Bayesian Statistics the Fun Way](https://nostarch.com/learnbayes) by Will Kurt. Additionally I am using [C: Answers to Exercises](https://nostarch.com/download/resources/Bayes_exercise_solutions_new.pdf) Each chapter of the book has three main parts: ### Short summaries of the book content {.unnumbered} This summarizes my own highlights but gives also the necessary information for my section about "Experiments". Mostly I quote the text but without page references. Often I made minor editing (e.g., shorting the text) or put sometimes the content in my own wording. As I follow the text section by section reader can easily find the quoted passage. Almost all of my text of this first part of the Quarto book are not mine, but is coming from the resources mentioned above. There are two exceptions: - Whenever necessary I include personal notes already in this part of the chapter. Most of the time it is combined with a cross reference to the third main part of the book: my experiments. - Sometimes there is also base R Code by the author provided. Whenever possible I convert this base R code by the author in {**tidyverse**} code. - I copied all figures into the text as a template for my own replication. ::: callout-important Although I have quoted many passages from the original as highlights for me to remember, this Quarto ebook is not meant to stand alone. My summaries are driven by my personal interests and my huge gaps in my statistical knowledge and especially in Bayesian statistics. My notes are therefore in no way a substitute for Will Kurt's book [Bayesian Statistics the Fun Way: Understanding Statistics and Probability With Star Wars, LEGO, and Rubber Ducks](https://nostarch.com/learnbayes) by Will Kurt [@kurt2019]. Please buy the book so that you can embed my notes appropriately in the general argumentation of the author. ::: ### Exercises {.unnumbered} Again I quote the full question text and then try my own solution. If my solution is not correct or I cant find a solution I will note this in a personal callout and will correct the solution. If my solution is correct but with a different method I will also reflect on the result, but will not adapt or change my solution. ### Experiments {.unnumbered} Here I am trying to make my own exercises. Most of the examples are replications of the book figures because the author has not included the R code. Additionally I cross referenced to the figure from the first part, the author section. If you hover over the cross reference link you will get the authors figure overlaid and can compare it with my replication. Writing my own R chunks I am using the tidy approach with the collection of the {**tidyverse**} packages, especially with {**ggplot2**} for the figures. But instead of using the `library()` command I always mention the used packages explicitly. Whenever I used another packages I called the function with the package name in front with the syntax `<package name>::<function name>()`, like `ggplot2::gplot()`. This is tedious work but it helps me to learn & remember which command "belongs" to which package. Only exception is the {**patchwork**} package, as I do not know how to call commands like `p1 + p2` with the package name. In graphics I use not only caption for figures but also captions for the R code. There is no easy standardized way to use code listings with captions and to evaluate the code at the same time, but I [found a workaround](https://github.com/quarto-dev/quarto-cli/issues/1580#issuecomment-1552673825) with the following structure of code options in the code chunk: ``` #| label: fig-name #| fig-cap: "fig-title" #| attr-source: '#lst-fig-name lst-cap="list-title"' ``` This code generates a warning because at the moment the `=` symbol is not allowed in RStudio when running a R chunks interactively in a Quarto document. [See issue 13326](https://github.com/rstudio/rstudio/issues/13326). Although I got a warning the code does what I want: It gives the figure and the code listing a heading and evaluates the code at the same time. ## Glossary I started a glossary using the {[**glossary**](https://cran.r-project.org/web/packages/glossary/index.html)} package by Lisa DeBruine [@glossary]. A glossary entry is visualized with a double underline. Every chapter has a section where the text of all glossary entries of the chapter are displayed. When you hover with the mouse over the link it opens a pop-up window with the glossary text. You can see example in the section about my motivation for this ebook (See @sec-book-motivation). I am using this glossary for all my other Quarto books but it is till work in progress. Please keep in mind that I collected the definition at various places and be attentive because there is no guarantee that the entry is appropriate and correct. I have added the sources where I got the content for the glossary entry. ## Session Info Every chapter ends with a session information printed with the `sessionInfo()` function. ::: callout-warning ###### Warning I wrote this book as a text for others to read because that forces me to be become explicit and explain all my learning outcomes more carefully. Please keep in mind that this text is not written by an expert but by a learner. In spite of replicating most of the content it may contain many mistakes. All these misapprehensions and errors are my responsibility. In any case I am the only responsible person for this text, especially if I have used code from the resources wrongly or misunderstood a quoted text passage. :::