• Bayes Rules! Book Club
  • Welcome
    • Book club meetings
    • Pace
  • Preface
    • 0.1 Bayesian statistics?
    • 0.2 Tips and tricks from the authors
    • 0.3 Set up
    • 0.4 The authors:
  • 1 The Big (Bayesian) Picture
    • 1.1 Thinking like a Bayesian 1/4
    • 1.2 Quiz time!
    • 1.3 Thinking like a Bayesian 2/4
      • 1.3.1 Interpreting probability:
    • 1.4 Thinking like a Bayesian 3/4
      • 1.4.1 Bayesian balancing act
    • 1.5 Thinking like a Bayesian 4/4
      • 1.5.1 Asking question
    • 1.6 Quick history lesson
    • 1.7 Look ahead
      • 1.7.1 4 units
    • 1.8 Summary
    • 1.9 Resources mentioned
      • 1.9.1 Other Bayesian books:
      • 1.9.2 Drawing DAG (Directed Acyclic Graph)
      • 1.9.3 Podcast
    • 1.10 Meeting Videos
      • 1.10.1 Cohort 1
      • 1.10.2 Cohort 2
      • 1.10.3 Cohort 3
      • 1.10.4 Cohort 4
  • 2 Bayes’ Rule
    • 2.1 Building a Bayesian model for events
      • 2.1.1 Workflow:
    • 2.2 Prior probability model
    • 2.3 Model for interpreting the data
    • 2.4 Posterior probability model
    • 2.5 Posterior simulation
    • 2.6 Example Pop vs Soda vs Coke
    • 2.7 Building a Bayesian model for random variables
      • 2.7.1 Prior probability model
      • 2.7.2 Data model
      • 2.7.3 Posterior probability model
      • 2.7.4 Posterior simulation
    • 2.8 Links shared in the second meeting
    • 2.9 Meeting Videos
      • 2.9.1 Cohort 1
      • 2.9.2 Cohort 2
      • 2.9.3 Cohort 3
      • 2.9.4 Cohort 4
  • 3 The Beta-Binomial Bayesian Model
    • 3.1 What is a Beta Binomial model for ?
    • 3.2 The Beta Prior Model
    • 3.3 Are we good so far ?
    • 3.4 How has the model changed from last week ?
    • 3.5 What quality does the probability density function have ?
    • 3.6 Tuning the Beta Prior
    • 3.7 The Binomial Data Model and Likelihood
    • 3.8 Beta Posterior Model
    • 3.9 Plot of the Beta Posterior Model
    • 3.10 Effects of New Data ?
    • 3.11 Simulating the Beta-Binomial
    • 3.12 What does this show ?
    • 3.13 Milgram’s behavior study of obedience
    • 3.14 What do you think the prior beliefs were ?
    • 3.15 Let plot them to find out
    • 3.16 So what actually happened ?
    • 3.17 What conclusions can we draw ?
    • 3.18 Let’s plot the prior, likelihood and posterior
    • 3.19 Summary
    • 3.20 Meeting Videos
      • 3.20.1 Cohort 1
      • 3.20.2 Cohort 2
      • 3.20.3 Cohort 3
      • 3.20.4 Cohort 4
  • 4 Balance and Sequentiality in Bayesian Analyses
    • 4.1 Introductory Example
    • 4.2 Different priors, different posteriors
    • 4.3 Different data, different posteriors
    • 4.4 Striking a balance between the prior and data
      • 4.4.1 Connecting concepts to theory
    • 4.5 Sequential analysis: evolving with data
    • 4.6 Meeting Videos
      • 4.6.1 Cohort 1
      • 4.6.2 Cohort 2
      • 4.6.3 Cohort 3
      • 4.6.4 Cohort 4
  • 5 Conjugate Families
    • 5.1 Greek letters
    • 5.2 Revisiting choice of prior
      • 5.2.1 Reminder the Beta-Binomial Model:
    • 5.3 Joy!
    • 5.4 Gamma-Poisson conjugate family 1/8
      • 5.4.1 Prior:
    • 5.5 Gamma-Poisson conjugate family 2/8
      • 5.5.1 Poisson data model:
    • 5.6 Gamma-Poisson conjugate family 3/8
      • 5.6.1 Poisson pmfs with different \(\tau\)
    • 5.7 Gamma-Poisson conjugate family 4/8
      • 5.7.1 Joint probability mass function
    • 5.8 Gamma-Poisson conjugate family 5/8
      • 5.8.1 Potential priors?
    • 5.9 Gamma-Poisson conjugate family 6/8
      • 5.9.1 Gamma prior : Gamma and Exponential models
    • 5.10 Gamma-Poisson conjugate family 6/n
      • 5.10.1 Quiz!
    • 5.11 Gamma-Poisson conjugate family 7/8
      • 5.11.1 Applications!
    • 5.12 Gamma-Poisson conjugate family 8/8
      • 5.12.1 Gamma-Poisson conjugacy
    • 5.13 Normal-Normal conjugate family
    • 5.14 Normal Model
      • 5.14.1 Prior X Likelihood = Posterior
    • 5.15 Why no simulation in this chapter?
    • 5.16 Critiques of conjugate family
    • 5.17 Summary
    • 5.18 Meeting Videos
      • 5.18.1 Cohort 1
      • 5.18.2 Cohort 2
      • 5.18.3 Cohort 3
      • 5.18.4 Cohort 4
  • 6 Approximating the Posterior
    • 6.1 Motivation for approximations
    • 6.2 Coming into View
    • 6.3 Grid Approximaiton
    • 6.4 Beta Binomial Example
    • 6.5 MCMC
    • 6.6 Beta-Binomial MCMC
    • 6.7 Gamma-Poisson MCMC
    • 6.8 Markov chain diagnostics
    • 6.9 Danger Zone
    • 6.10 Summary
    • 6.11 Meeting Videos
      • 6.11.1 Cohort 1
      • 6.11.2 Cohort 2
      • 6.11.3 Cohort 3
      • 6.11.4 Cohort 4
  • 7 MCMC under the Hood
    • 7.1 The big idea 1/2
    • 7.2 The big idea 2/2
    • 7.3 The Metropolis-Hastings algorithm
    • 7.4 Implementing the Metropolis-Hastings
      • 7.4.1 Quiz!
    • 7.5 A Beta-Binomial example
    • 7.6 Why the algorithm works
    • 7.7 Chapter summary
    • 7.8 Meeting Videos
      • 7.8.1 Cohort 1
      • 7.8.2 Cohort 2
      • 7.8.3 Cohort 3
      • 7.8.4 Cohort 4
  • 8 Posterior Inference & Prediction
    • 8.1 Introduction
    • 8.2 Posterior estimation
    • 8.3 Posterior hypothesis testing
    • 8.4 Posterior prediction
    • 8.5 Posterior analysis with MCMC
      • 8.5.1 Posterior simulation
      • 8.5.2 Posterior estimation & hypothesis testing
      • 8.5.3 Posterior prediction
    • 8.6 Bayesian benefits
    • 8.7 Meeting Videos
      • 8.7.1 Cohort 1
      • 8.7.2 Cohort 2
      • 8.7.3 Cohort 3
      • 8.7.4 Cohort 4
  • 9 Simple Normal Regression
    • 9.1 Begining of Unit 3!
    • 9.2 New terms
    • 9.3 Building the regression model
      • 9.3.1 Data model
      • 9.3.2 Normal regression assumptions
      • 9.3.3 Specifying the priors
      • 9.3.4 Putting it all together
    • 9.4 Tuning prior models for regression parameters
    • 9.5 Posterior simulatiion
      • 9.5.1 Simulation via rstanarm
      • 9.5.2 Simulation directly with rstan
    • 9.6 Interpreting the posterior
    • 9.7 Posterior prediction
      • 9.7.1 Building a posterior predictive model
      • 9.7.2 Posterior with rstanarm
    • 9.8 Sequential regression modeling
    • 9.9 Using default rstanarm priors
    • 9.10 Summary
      • 9.10.1 You are not done yet!
    • 9.11 Resources:
    • 9.12 Meeting Videos
      • 9.12.1 Cohort 1
      • 9.12.2 Cohort 2
      • 9.12.3 Cohort 3
      • 9.12.4 Cohort 4
  • 10 Evaluating Regression Models
    • 10.1 More Questions to Consider
    • 10.2 Beware of Biases
    • 10.3 Verifying Normal Regression Assumptions
    • 10.4 Our Case Study
    • 10.5 Posterior Predictive check
    • 10.6 Dealing with Wrong Models
    • 10.7 How Accurate are the Posterior Predictive Models?
      • 10.7.1 Posterior predictive summaries
      • 10.7.2 Cross-validation
      • 10.7.3 Expected log-predictive density
    • 10.8 Improving Posterior Predictive Accuracy
    • 10.9 How good is the MCMC simulation vs how good is the model?
    • 10.10 Meeting Videos
      • 10.10.1 Cohort 1
      • 10.10.2 Cohort 2
      • 10.10.3 Cohort 3
      • 10.10.4 Cohort 4
  • 11 Extending the Normal Regression Model
    • 11.1 Extending the Normal Regression Model
    • 11.2 Utilizing a categorical predictor
    • 11.3 Utilizing two predictors
      • 11.3.1 Simulate 100 datasets from the prior models
      • 11.3.2 Predict 3 p.m. temperature on specific days
    • 11.4 Dreaming bigger: Utilizing more than 2 predictors!
    • 11.5 Model evaluation & comparison
      • 11.5.1 Evaluating predictive accuracy using visualizations
    • 11.6 Evaluating predictive accuracy using cross-validation
    • 11.7 Evaluating predictive accuracy using ELPD
      • 11.7.1 The bias-variance trade-off
    • 11.8 Meeting Videos
      • 11.8.1 Cohort 1
      • 11.8.2 Cohort 2
      • 11.8.3 Cohort 4
  • 12 Poisson & Negative Binomial Regression
    • 12.1 Data Set 1
    • 12.2 Normal Distribution
      • 12.2.1 Exploratory Data Visualization
      • 12.2.2 Outlier
      • 12.2.3 Predictor Variables
    • 12.3 Normal Regression
      • 12.3.1 Posterior Predictive Check
    • 12.4 Poisson Regression
      • 12.4.1 Log-Link Function
      • 12.4.2 rstan
      • 12.4.3 Poisson Regression Assumptions
    • 12.5 Prior Distribution
      • 12.5.1 So Far
    • 12.6 Posterior Distribution
      • 12.6.1 Checks
      • 12.6.2 Posterior Predictive Check
    • 12.7 Interpretation
    • 12.8 Posterior Prediction
    • 12.9 Data Set 2
      • 12.9.1 Poisson Regression
      • 12.9.2 Posterior Predictive Check
      • 12.9.3 Overdispersion
    • 12.10 Negative Binomial Distribution
    • 12.11 Negative Binomial Regression
      • 12.11.1 Prior Distribution
      • 12.11.2 Posterior Predictive Check
      • 12.11.3 Interpretation
    • 12.12 Generalized Linear Models
    • 12.13 Meeting Videos
      • 12.13.1 Cohort 1
      • 12.13.2 Cohort 2
      • 12.13.3 Cohort 4
  • 13 Logistic Regression
    • 13.1 The logistic regression model
      • 13.1.1 Definition of Odds & probability
      • 13.1.2 Specifying the priors:
    • 13.2 Simulating the posterior
    • 13.3 Prediction & classification
    • 13.4 Model evaluation
      • 13.4.1 Confusion matrix
    • 13.5 Extending the model
    • 13.6 Meeting Videos
      • 13.6.1 Cohort 1
      • 13.6.2 Cohort 2
      • 13.6.3 Cohort 4
  • 14 Naive Bayes Classification
    • 14.1 Data: Palmer Penguins
    • 14.2 Naive Bayes Classification
    • 14.3 One Categorical Predictor
      • 14.3.1 Recall: Bayes Rule
      • 14.3.2 Calculation
    • 14.4 One Numerical Predictor
      • 14.4.1 Prior Probability Distributions
    • 14.5 Two Predictor Variables
    • 14.6 Implementation
      • 14.6.1 Models
      • 14.6.2 Predictions
    • 14.7 Validation
      • 14.7.1 Confusion Matrices
      • 14.7.2 Cross-Validation
    • 14.8 Summary
    • 14.9 Meeting Videos
      • 14.9.1 Cohort 1
      • 14.9.2 Cohort 2
      • 14.9.3 Cohort 4
  • I IV Hierarchical Bayesian models
  • 15 Hierarchical Models are Exciting
    • 15.1 Hierarchical Models are Exciting
    • 15.2 Data: Cherry Blossom 5K
    • 15.3 Pooled / Grouped data
    • 15.4 Complete Pooling
      • 15.4.1 Drawbacks of complete pooling
    • 15.5 No pooling
    • 15.6 Hierarchical data
    • 15.7 Partial pooling
    • 15.8 Summary
    • 15.9 Meeting Videos
      • 15.9.1 Cohort 1
      • 15.9.2 Cohort 2
      • 15.9.3 Cohort 4
  • 16 (Normal) Hierarchical Models without Predictors
    • 16.1 Data Set!
    • 16.2 Complete pooled model
      • 16.2.1 Quiz!!
    • 16.3 No pooled model
      • 16.3.1 Same Quiz but with no pooling!!
    • 16.4 Building the hierarchical model
      • 16.4.1 The hierarchy
      • 16.4.2 within- vs -between-group variability
      • 16.4.3 Posterior simulation
      • 16.4.4 Posterior analysis of global parameters
      • 16.4.5 posterior analysis of group specific
    • 16.5 Posterior prediction
      • 16.5.1 First case: Frank Ocean (j=39)
      • 16.5.2 Posterior prediction for an observed group
      • 16.5.3 posterior_predict()
    • 16.6 Shrinkage & bias_variance trade-off
      • 16.6.1 Quizzz!
    • 16.7 Not everything is hierarchical
    • 16.8 Summary
    • 16.9 Meeting Videos
      • 16.9.1 Cohort 1
      • 16.9.2 Cohort 2
      • 16.9.3 Cohort 4
  • 17 (Normal) Hierarchical Models with Predictors
    • 17.0.1 Data set
    • 17.1 Quick: complete pooling option
    • 17.2 Hierarchical Model with varying intercept
      • 17.2.1 Model buildings
    • 17.3 Posterior simulation and analysis
    • 17.4 Hierarchical model with varying intercepts & slopes
      • 17.4.1 Model building
      • 17.4.2 Posterior simulation and anlysis
    • 17.5 Model evaluation and selection
    • 17.6 Posterior prediction
    • 17.7 Details: Longitudinal data
    • 17.8 Example Danceability
    • 17.9 Chapter summary
    • 17.10 Meeting Videos
      • 17.10.1 Cohort 1
      • 17.10.2 Cohort 2
      • 17.10.3 Cohort 4
  • 18 Non-Normal Hierarchical Regression & Classification
    • 18.1 Introduction
    • 18.2 Hierarchical logistic regression
      • 18.2.1 Model building & simulation
      • 18.2.2 Posterior analysis
      • 18.2.3 Posterior classification
      • 18.2.4 Model evaluation
    • 18.3 Hierarchical Poisson & Negative Binomial regression
      • 18.3.1 Model building & simulation
      • 18.3.2 Posterior analysis
      • 18.3.3 Model evaluation
    • 18.4 Meeting Videos
      • 18.4.1 Cohort 1
      • 18.4.2 Cohort 2
      • 18.4.3 Cohort 4
  • 19 Adding More Layers
    • 19.1 Group-level predictors - Airbnb Data Revisited
    • 19.2 Airbnb : Individual-level predictors
    • 19.3 Air-bnb Hierachical structure
    • 19.4 Air-bnb Group Level predictors
    • 19.5 Incorporating group predictors
    • 19.6 Airbnb median model
    • 19.7 Airbnb posterior group-level analysis
    • 19.8 Two or more grouping variables
    • 19.9 Hiearchical model
    • 19.10 Simulating the model
    • 19.11 Posterior summaries
    • 19.12 Group specific parameters
    • 19.13 Check prediction manually
    • 19.14 Further reading
    • 19.15 The End
    • 19.16 Meeting Videos
      • 19.16.1 Cohort 1
      • 19.16.2 Cohort 2
      • 19.16.3 Cohort 4
  • Published with bookdown

Bayes Rules! Book Club

2.8 Links shared in the second meeting

Bayesian probability for babies! (with cookies) : https://raw.githubusercontent.com/epimath/epid-814-materials/master/Lectures/BayesianEstimation.pdf Author: Marisa Eisenberg