Special Topics in Uncertainty Quantification via Tree-based Models and Approximate Computations

 

• • Syllabus
  • Slides 1: Introduction
  • Slides 2: Ball Drop Experiment; Gaussian Processes
  • Slides 3: Correlation Functions; Unconditional Realizations (source)
  • Slides 4: GP Emulator; BLUP; Frequentist Model Fitting
  • Slides 5: Variogram; Continuity Properties; Single Path Inference (source, source)
  • Slides 6: Likelihood Estimation; Compact Covariances (source, source)
  • Slides 7: Stochastic Gradient Descent and GPs for Big Data (source)
  • Slides 8: Experimental Design and Sensitivity Analysis (source)
  • Slides 9: Bayesian Models (conjugacies, source)
  • Slides 10: Bayesian Gaussian Process Regression (source, source)
  • Slides 11: Bayesian Single Tree Models (source)
  • Slides 12: Bayesian Treed Gaussian Process (source)
  • Slides 13: Bayesian Additive Regression Trees (source)
  • Slides 14: More BART
  • Slides 15: Basic MCMC Diagnostics (source)
  • Slides 16: Calibration (source, source)

 

References
Sacks, Welch, Mitchell and Wynn: Design and Analysis of Computer Experiments
Santner, Williams and Notz: The Design and Analysis of Computer Experiments
Cressie: Statistics for Spatial Data
Bevilaqua, Faouzi, Furrer and Porcu: Estimation and Prediction using Generalized Wendland Covariance Functions under Fixed Domain Asymptotics
Bottou: Large-Scale Machine Learning with Stochastic Gradient Descent
McKay, Beckman and Conover: Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
Jones, Schonlau and Welch: Efficient Global Optimization of Expensive Black Box Functions
Oakley: Eliciting Gaussian Process Priors for Complex Computer Codes
Chipman, George and McCulloch: Bayesian CART Model Search
Chipman, George and McCulloch: BART: Bayesian Additive Regression Trees 
Pratola: Efficient Metropolis–Hastings Proposal Mechanisms for Bayesian Regression Tree Models
Gramacy and Lee: Bayesian Treed Gaussian Process Models With an Application to Computer Modeling
Cowles and Carlin: MCMC Convergence Diagnostics: A Comparative Review
Geyer: Practical MCMC
Raftery and Lewis: How Many Iterations in the Gibbs Sampler?
Geweke: Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments
Gelman and Rubin: Inference from Iterative Simulation Using Multiple Sequences
Kennedy and O’Hagan: Bayesian Calibration of Computer Models

Assignments
Assignment 1
Assignment 2 (frankesinputs.dat)
Assignment 3 (co2plume.dat, co2holdout.dat)

Project
Project outline is here.