Teaching Bayesian Modeling with Bayes Rules!

.title[
# Teaching Bayesian Modeling with <br> Bayes Rules!
]
.subtitle[
## <a href="https://mdogucu.github.io/bayes-lund-2023">mdogucu.github.io/bayes-lund-2023</a> <br> <br>Talk at Bayes @ Lund </i>
]
.author[
### Mine Dogucu, Ph.D. <br> University College London <br>University of California Irvine
]
.date[
### 2023-01-23
]

---

<img src="img/headshot.jpeg"
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.large[<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M433 179.11c0-97.2-63.71-125.7-63.71-125.7-62.52-28.7-228.56-28.4-290.48 0 0 0-63.72 28.5-63.72 125.7 0 115.7-6.6 259.4 105.63 289.1 40.51 10.7 75.32 13 103.33 11.4 50.81-2.8 79.32-18.1 79.32-18.1l-1.7-36.9s-36.31 11.4-77.12 10.1c-40.41-1.4-83-4.4-89.63-54a102.54 102.54 0 0 1-.9-13.9c85.63 20.9 158.65 9.1 178.75 6.7 56.12-6.7 105-41.3 111.23-72.9 9.8-49.8 9-121.5 9-121.5zm-75.12 125.2h-46.63v-114.2c0-49.7-64-51.6-64 6.9v62.5h-46.33V197c0-58.5-64-56.6-64-6.9v114.2H90.19c0-122.1-5.2-147.9 18.41-175 25.9-28.9 79.82-30.8 103.83 6.1l11.6 19.5 11.6-19.5c24.11-37.1 78.12-34.8 103.83-6.1 23.71 27.3 18.4 53 18.4 175z"/></svg>] <a href = "https://mastodon.social/@MineDogucu">mastodon.social/@MineDogucu</a>

---

We have reviewed curricula of **152 high ranking universities and colleges** in the United States and identified **51 Bayesian courses** at the undergraduate level.

We have examined **prerequisites, majors, and course content** through catalog and syllabus analysis.

<a href="https://www.tandfonline.com/doi/abs/10.1080/00031305.2022.2089232" style="font-size: 22px">Dogucu, M., & Hu, J. (2022). The Current State of Undergraduate Bayesian Education and Recommendations for the Future. The American Statistician. 76:4, 405-413, DOI: 10.1080/00031305.2022.2089232</a>

---

---

class:center

.pull-left[
<script src="https://use.fontawesome.com/releases/v5.15.1/js/all.js" data-auto-replace-svg="nest"></script>

[Bayes Rules! An Introduction to Applied Bayesian Modeling](https://bayesrulesbook.com)

]

[{bayesrules}](https://www.github.com/bayes-rules/bayesrules)
]

---

Alicia Johnson          
.font-20[Macalester College]
        
[<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M579.8 267.7c56.5-56.5 56.5-148 0-204.5c-50-50-128.8-56.5-186.3-15.4l-1.6 1.1c-14.4 10.3-17.7 30.3-7.4 44.6s30.3 17.7 44.6 7.4l1.6-1.1c32.1-22.9 76-19.3 103.8 8.6c31.5 31.5 31.5 82.5 0 114L422.3 334.8c-31.5 31.5-82.5 31.5-114 0c-27.9-27.9-31.5-71.8-8.6-103.8l1.1-1.6c10.3-14.4 6.9-34.4-7.4-44.6s-34.4-6.9-44.6 7.4l-1.1 1.6C206.5 251.2 213 330 263 380c56.5 56.5 148 56.5 204.5 0L579.8 267.7zM60.2 244.3c-56.5 56.5-56.5 148 0 204.5c50 50 128.8 56.5 186.3 15.4l1.6-1.1c14.4-10.3 17.7-30.3 7.4-44.6s-30.3-17.7-44.6-7.4l-1.6 1.1c-32.1 22.9-76 19.3-103.8-8.6C74 372 74 321 105.5 289.5L217.7 177.2c31.5-31.5 82.5-31.5 114 0c27.9 27.9 31.5 71.8 8.6 103.9l-1.1 1.6c-10.3 14.4-6.9 34.4 7.4 44.6s34.4 6.9 44.6-7.4l1.1-1.6C433.5 260.8 427 182 377 132c-56.5-56.5-148-56.5-204.5 0L60.2 244.3z"/></svg>](https://ajohns24.github.io/portfolio)
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]
]

.pull-right[
.center[
<img src="img/miles.png"
        alt="A headshot of a man with short dark hair, and a dark moustache. He is wearing a blue button up shirt and dark gray jacket"
        style="width:165px; margin-top:20px; border: 3px solid whitesmoke; padding: 10px;">

Miles Ott  
.font-20[Tubi]

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[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>](https://twitter.com/Miles_Ott)
[<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M433 179.11c0-97.2-63.71-125.7-63.71-125.7-62.52-28.7-228.56-28.4-290.48 0 0 0-63.72 28.5-63.72 125.7 0 115.7-6.6 259.4 105.63 289.1 40.51 10.7 75.32 13 103.33 11.4 50.81-2.8 79.32-18.1 79.32-18.1l-1.7-36.9s-36.31 11.4-77.12 10.1c-40.41-1.4-83-4.4-89.63-54a102.54 102.54 0 0 1-.9-13.9c85.63 20.9 158.65 9.1 178.75 6.7 56.12-6.7 105-41.3 111.23-72.9 9.8-49.8 9-121.5 9-121.5zm-75.12 125.2h-46.63v-114.2c0-49.7-64-51.6-64 6.9v62.5h-46.33V197c0-58.5-64-56.6-64-6.9v114.2H90.19c0-122.1-5.2-147.9 18.41-175 25.9-28.9 79.82-30.8 103.83 6.1l11.6 19.5 11.6-19.5c24.11-37.1 78.12-34.8 103.83-6.1 23.71 27.3 18.4 53 18.4 175z"/></svg>](https://mastodon.social/@Miles_Ott@aus.social)
]
]

---

[Introduction to Bayesian Data Analysis](https://www.stats115.com)

---

## Background of students taking the course

- Prerequisite: STATS 120C. Introduction to Probability and Statistics III
- Recommended: STATS 110. Statistical Methods for Data Analysis I
- Students: Data Science major (required), Statistics minor (elective)

---

.panelset.sideways[
.panel[.panel-name[Unit 1]

### Bayesian Foundations

- Bayes' Rule
- The Beta-Binomial Bayesian Model
- Balance and Sequentiality in Bayesian Analysis
- Conjugate Families

]

<img src="index_files/figure-html/unnamed-chunk-6-1.png" alt="three curves on a single plot with no axis labeled. It is coloring scheme indicates its similarity to the previous plot with prior, scaled likelihood and posterior" style="display: block; margin: auto;" />
]

]

### Posterior Simulation & Analysis

]

- Grid Approximation

- The Metropolis-Hastings Algorithm

- Posterior Estimation

- Posterior Hypothesis Testing

- Posterior Prediction

]

### Regression and Classification

]

- Normal Regression
- Poisson and Negative Binomial Regression
- Logistic Regression
- Naive Bayes Classification

]
]

### Hierarchical Models

]

- Normal hierarchical models without predictors
- Normal hierarchical models with predictors
- Non-Normal Hierarchical Regression & Classification

]

---

---

## Big Picture

---

## Context

In Alison Bechdel’s 1985 comic strip The Rule, a character states that they only see a movie if it satisfies the following three rules ([Bechdel 1986](https://dykestowatchoutfor.com/the-essential-dtwof/)):

- the movie has to have at least two women in it;
- these two women talk to each other; and
- they talk about something besides a man.

Let `$\pi$`, a random value between 0 and 1, denote the unknown proportion of  movies that pass the Bechdel test (i.e. `$\pi \in [0,1]$`).

---

]

.pull-right2[
- **Feminist** thinks that women are not represented in movies often. 
- **Clueless** is unsure. 
- **Optimist** thinks that Bechdel is a low bar for representation of women in movies and thinks almost all movies pass the test.
- Can you match the plots with the personas?]

---

## Plotting Beta Prior with `bayesrules` package

One can use the `plot_beta()` function in the `bayesrules` package to try different shape parameters. Example:

```r
library(bayesrules)
plot_beta(alpha = 2, beta = 10) 
```

---

## Plotting Beta Prior

---

---

```r
one_mh_iteration <- function(w, current){
 # STEP 1: Propose the next chain location
 proposal <- runif(1, min = current - w, max = current + w)
  
 # STEP 2: Decide whether or not to go there
 proposal_plaus <- dnorm(proposal, 0, 1) * dnorm(6.25, proposal, 0.75)
 current_plaus  <- dnorm(current, 0, 1) * dnorm(6.25, current, 0.75)
 alpha <- min(1, proposal_plaus / current_plaus)
 next_stop <- sample(c(proposal, current), 
  size = 1, prob = c(alpha, 1-alpha))
  
 # Return the results
 return(data.frame(proposal, alpha, next_stop))
}
```

---

```r
mh_tour <- function(N, w){
  # 1. Start the chain at location 3
  current <- 3
  # 2. Initialize the simulation
  mu <- rep(0, N)
  # 3. Simulate N Markov chain stops
  for(i in 1:N){    
    # Simulate one iteration
    sim <- one_mh_iteration(w = w, current = current)
    
    # Record next location
    mu[i] <- sim$next_stop
    
    # Reset the current location
    current <- sim$next_stop
  }
  
  # 4. Return the chain locations
  return(data.frame(iteration = c(1:N), mu))
}
```

---

```r
set.seed(84735)
mh_simulation_1 <- mh_tour(N = 5000, w = 1)
```

---

## `library(rstan)`

```r
# STEP 1: DEFINE the model
stan_bike_model <- "
  data {
    int<lower=0> n;
    vector[n] Y;
    vector[n] X;
  }
  parameters {
    real beta0;
    real beta1;
    real<lower=0> sigma;
  }
  model {
    Y ~ normal(beta0 + beta1 * X, sigma);
  }
"
```

]

```r
# STEP 2: SIMULATE the posterior
stan_bike_sim <- 
  stan(model_code = stan_bike_model, 
  data = list(n = nrow(bikes), 
              Y = bikes$rides, X = bikes$temp_feel), 
  chains = 4, iter = 5000*2, seed = 84735)
```

]

---

## `library(rstanarm)`

```r
bike_model <- stan_glm(rides ~ temp_feel, data = bikes,
                       family = gaussian,
                       prior_intercept = normal(5000, 1000),
                       prior = normal(100, 40), 
                       prior_aux = exponential(0.0008),
                       chains = 4, iter = 5000*2, seed = 84735)
```

---

### `library(bayesplot)`

```r
mcmc_trace(bike_model, size = 0.1)
```

]

```r
mcmc_dens_overlay(bike_model)
```

<img src="index_files/figure-html/unnamed-chunk-26-1.png" width="80%" style="display: block; margin: auto;" />
]

---

---

### Learning Bayesian Modeling is Fun

> How can we live if we don’t change?
—Beyoncé. Lyric from “Satellites.”

> What is probability?

---

### Checking Intuition

---

## Active Learning

Quizzes

[Quiz Yourself: Bayesian vs. Frequentist](https://www.bayesrulesbook.com/chapter-1.html#quiz-yourself-1)

]

Hands-on Programming

[Metropolis-Hastings Algorithm](https://www.bayesrulesbook.com/chapter-7.html#the-metropolis-hastings-algorithm)

]

---

### Compute for a single case, then use built-in functions

```r
predictions <- rstanarm::posterior_predict(bike_model, newdata = bikes)
```

```r
bayesplot::ppc_intervals(bikes$rides, yrep = predictions, 
                         x = bikes$temp_feel, prob = 0.5, prob_outer = 0.95)
```

---

### Accessible and Inclusive

[Dogucu, M., Johnson, A. A., & Ott, M. (In Press). Framework for Accessible and Inclusive Teaching Materials for Statistics and Data Science Courses. Journal of Statistics and Data Science Education](https://www.tandfonline.com/doi/full/10.1080/26939169.2023.2165988)

---

### Accessibility and Inclusion

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Accessibility and Inclusion Criteria </th>
   <th style="text-align:left;"> Questions </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Accessibility </td>
   <td style="text-align:left;"> Is the cost affordable for learners from diverse socioeconomic backgrounds? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Are plots distinguishable to color blind learners? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Is alt text provided for images? </td>
  </tr>
</tbody>
</table>

---

---

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Accessibility and Inclusion Criteria </th>
   <th style="text-align:left;"> Questions </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Inclusivity of students </td>
   <td style="text-align:left;"> Do examples avoid the necessity of specialized knowledge? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Do names and pronouns reflect diverse cultural and personal identities? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Are there examples that could potentially speak to younger as well as older students? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Does the delivery embrace mistakes and critical thinking? </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> Are efforts made to accommodate different academic experiences and create a shared foundation? </td>
  </tr>
</tbody>
</table>

---

---

## Southern California Data Science Program

HDR DSC awards: \#2123366 \#2123380 \#2123384

Through this collaborative grant between University of California Irvine, California State University Fullerton, and Cypress College, a Bayesian course will be adopted at California State University Fullerton.

---

## Bayes BATS

w/ [Monika Hu](https://pages.vassar.edu/jihu/) and [Amy Herring](https://sta198f2021.github.io/website/authors/amy/)

NSF DUE awards: #2215879, #2215920, and #2215709.

---

Dogucu, M., Kazak, S. & Rosenberg J. (forthcoming) **The Design and Implementation of a Bayesian Data Analysis Lesson for Pre-Service Mathematics and Science Teachers**

---

## Resources

- [Bayes Rules! resources](https://bayes-rules.github.io/)

- [Undergraduate Bayesian Education Resources](https://undergrad-bayes.netlify.app/)

- [Undergraduate Bayesian Education Network](https://undergrad-bayes.netlify.app/network.html)

---

# THANK YOU

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