Teaching Bayesian modeling with
Bayes Rules!

bit.ly/isba-rules

Talk at International Society for Bayesian Analysis World Meeting

Mine Dogucu, Ph.D.
University of California Irvine

2022-07-01

A headshot of a woman with curly, short, ear-length hair with green eyes and red lipstick.

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.

Dogucu, M., & Hu, J. (2022). The Current State of Undergraduate Bayesian Education and Recommendations for the Future. The American Statistician.

A table with list of majors that include Bayesian courses as part of the major. There are two majors that require a Bayesian course.

Dogucu, M., & Hu, J. (2022). The Current State of Undergraduate Bayesian Education and Recommendations for the Future. The American Statistician.

Introduction to Bayesian Data Analysis

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.

a hex shaped logo with shiny green-pink disco ball and purple starry background. There is text that says Bayes Rules!

Bayes Rules! An Introduction to Applied Bayesian Modeling

{bayesrules}

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Alicia Johnson
Macalester College

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

Miles Ott
Twitter

Bayesian Foundations

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

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

Posterior Simulation & Analysis

A traceplot with no axis labels. Traceplots have thin vertical lines with varying lengths.

Grid Approximation
The Metropolis-Hastings Algorithm
Posterior Estimation
Posterior Hypothesis Testing
Posterior Prediction

Regression and Classification

A scatterplot with multiple regression lines passing through points. These regression lines are not all over the place, they are clustered with similar but varyin intercepts and slopes.

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

Hierarchical Models

a figure showing hierarchy with a rectangle on top. With a set of arrows pointing downwards leading to a set of rectangles below which also have a set of arrows pointing downwards leading to a different set of rectangles.

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

Background of students taking the coursePrerequisite: 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)
10

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):

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.

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):

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. $\pi \in [0,1]$ ).

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:

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

Plotting Beta Prior

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))
}

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))
}

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

library(rstan)# 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);
  }
"

# 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)

22

`library(rstanarm)`

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)`

mcmc_trace(bike_model, size = 0.1)

mcmc_dens_overlay(bike_model)

Pedagogical Approach

Learning Bayesian Modeling is Fun

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

vs.

What is probability?

Checking Intuition

There are two ellipses at the top of the image. The first ellipse reads 'Prior: Only 40% of articles are fake'. The second ellipse reads 'Data: Exclamation points are more common among fake news'. There are two arrows each from the upper two ellipses leading to a third ellipse in the lower part of the image. The third ellipse reads 'Posterior: Is the article fake or not?'

Active Learning

Quizzes

Quiz Yourself: Bayesian vs. Frequentist

An icon with a question mark and for choices labeled as A, B, C, and D.

Hands-on Programming

Metropolis-Hastings Algorithm

An icon of a student sitting on a chair and in front a desk with a computer typing.

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

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

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. (2021). Framework for Accessible and Inclusive Teaching Materials for Statistics and Data Science Courses. arXiv preprint arXiv:2110.06355.

Undergraduate Bayesian Education Resources

THANK YOU

bit.ly/isba-rules

minedogucu.com
mdogucu
MineDogucu

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Teaching Bayesian modeling with Bayes Rules!

bit.ly/isba-rules Talk at International Society for Bayesian Analysis World Meeting

Mine Dogucu, Ph.D. University of California Irvine

2022-07-01

Southern California Data Science Program

Bayesian Foundations

Posterior Simulation & Analysis

Regression and Classification

Hierarchical Models

Background of students taking the course

Big Picture

Context

Context

Plotting Beta Prior with bayesrules package

Plotting Beta Prior

library(rstan)

library(rstanarm)

library(bayesplot)

Learning Bayesian Modeling is Fun

Checking Intuition

Active Learning

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

Accessible and Inclusive

THANK YOU

Help

Teaching Bayesian modeling with
Bayes Rules!

bit.ly/isba-rules

Talk at International Society for Bayesian Analysis World Meeting

Mine Dogucu, Ph.D.
University of California Irvine

Plotting Beta Prior with `bayesrules` package

`library(rstan)`

`library(rstanarm)`

`library(bayesplot)`