A First Bayesian Course: Why, What, and How

# A First Bayesian Course: Why, What, and How
## <a href="https://bit.ly/dogucu-talks">bit.ly/dogucu-talks</a> <br> <br>Talk at RSS Teaching Statistics SIG, <i>The past, present and future of statistics teaching </i>
### Mine Dogucu, Ph.D.
### 2022-05-04

---

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---
class: center middle

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

---

<a href="https://arxiv.org/abs/2109.00848" style="font-size: 15px">Dogucu, M., & Hu, J. (2021). The Current State of Undergraduate Bayesian Education and Recommendations for the Future. arXiv preprint arXiv:2109.00848.</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 0 512 512" 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="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></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[Twitter]

[<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="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg>](https://milesott.com/)
[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>](https://github.com/MilesOtt)
[<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)

]
]

---

## 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.

---

.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-7-1.png" title="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" 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

]

---

## 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)

---

## 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
normal_model_sim <- stan_glm(rides ~ temp_feel, 
                             data = bikes, 
                             family = gaussian, 
                             chains = 4, iter = 5000*2,
                             seed = 84735)
```

---

## Pedagogical Approach

- Checking intuition

- Active learning (quizzes and applications)

- Computing & math together

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

- [Accessible and Inclusive](https://arxiv.org/abs/2110.06355)

---

- [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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