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Resources

These are links to resources related to questions asked during the workshop. Let us know if we forgot anything!

Books

  • "Bayesian Data Analysis 3rd", Andrew Gelman et al., book, webpage
  • "Statistical Rethinking", Richard McElreath, webpage, youtube

Other Stan tutorials

Bayesian Workflow

  • "Visualization in Bayesian workflow", Jonah Gabry et al., paper code
  • "The prior can generally only be understood in the context of the likelihood", Andrew Gelman et al., link

Modeling techniques

Reparameterizations:

  • "Diagnosing Biased Inference with Divergences", Michael Betancourt, link
  • "QR Reparameterization", Stan Manual, link
  • "Fitting The Cauchy Distribution", Michael Betancourt, link
  • "Reparameterization", Stan Manual, link
  • "Hamiltonian Monte Carlo for Hierarchical Models", Michael Betancourt et al., link

Mixture models:

  • "Finite Mixtures", Stan Manual, link
  • "Identifying Bayesian Mixture Models", Michael Betancourt, link

Multivariate normal distributions:

  • "Multivariate priors for hierarchical regressions", Stan Manual, link
  • "Gaussian processes", Stan manual, link

Missing data

Zero-inflated Poisson models in Stan

  • "Zero-Inflated and Hurdle Models", Stan manual, link

Truncated distributions in Stan

Parallelization in Stan

Applications

Multilevel regression and poststratification (MRP) in Stan

Multiarmed bandits in Stan

Causal inference in Stan:

  • "Model-based Inference for Causal Effects in Completely Randomized Experments", Joon-Ho Lee et al. link

SEM Modeling in Stan

  • "Adapting Structural Equation Modeling Fit indices into Bayesian SEM, Psychological Methods", Mauricio Garnier-Villarreal et al., discourse paper

Spatial modeling

  • "Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan", Mitzi Morris et al., link
  • Multiple Output Gaussian Processes, Rob Trangucci, link

Software

Regression Interfaces for Stan

Minimal interfaces to Stan

Probabilistic meaning of Stan syntax:

  • What does y ~ normal(mu, sigma); mean?, "Sampling Statements", Stan Manual, link
  • How do constraints work real<lower = 0.0> sigma;?, "Constraint Transforms", Stan Manual, link

Details on vectors, matrices and arrays in Stan

  • "Matrices, Vectors, and Arrays", Stan manual, link
  • Matrix multiplication vs. elementwise multiplication, Stan manual, link

Conditions for reproducibility in Stan

  • "Reproducibility", Stan manual, link

Multiple models

Automated model comparison/model checking:

Model averaging with Stan

  • "Using Stacking to Average Bayesian Predictive Distributions (with Discussion)", Yuling Yao et al., link
  • "Bayesian Stacking and Pseudo-BMA weights using the loo package", Aki Vehtari and Jonah Gabry, link

Folk theorem

Markov-Chain Monte Carlo

Comparison of sampling algorithms:

  • Figure 7 in "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo", Matt Hoffman, link
  • Table 2 in "Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo", Cole C. Monnahan et al., link
  • Gibbs vs. Stan for IRT modeling, "Fitting Bayesian item response models in Stata and Stan", link

Convergence Diagnostics, Rhat and Effective Sample Size (ESS):

  • These largely replace traceplots and autocorrelation plots)
  • "New R-hat and ESS", Aki Vehtari, link
  • "Rank-normalization, folding, and localization: An improved Rˆ for assessing convergence of MCMC", Aki Vehtari et al., link
  • "Rank-normalization, folding, and localization: An improved Rˆ for assessing convergence of MCMC (online appendix)", Aki Vehtari et al., link

Hamiltonian Monte Carlo:

  • "MCMC using Hamiltonian dynamics", Radford Neal, link
  • "A Conceptual Introduction to Hamiltonian Monte Carlo", Michael Betancourt, link
  • "Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo", Cole C. Monnahan et al., link
  • Monte Carlo algorithm animations, Chi Feng, link

Metropolis algorithm:

  • Page 279 of "Bayesian Data Analysis", Andrew Gelman et al., link

Data subsampling

  • "The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling", Michael Betancourt, link

Variational Inference