Practical Nonparametric and Semiparametric Bayesian Statistics

I Dirichlet and Related Processes.- 1 Computing Nonparametric Hierarchical Models.- 1.1 Introduction.- 1.2 Notation and Perspectives.- 1.3 Posterior Sampling in Dirichlet Process Mixtures.- 1.4 An Example with Poisson-Gamma Structure.- 1.5 An Example with Normal Structure.- 2 Computational Methods for Mixture of Dirichlet Process Models.- 2.1 Introduction.- 2.2 The Basic Algorithm.- 2.3 More Efficient Algorithms.- 2.4 Non-Conjugate Models.- 2.5 Discussion.- 3 Nonparametric Bayes Methods Using Predictive Updating.- 3.1 Introduction.- 3.2 Onn=1.- 3.3 A Recursive Algorithm.- 3.4 Interval Censoring.- 3.5 Censoring Example.- 3.6 Mixing Example.- 3.7 Onn= 2.- 3.8 Concluding Remarks.- 4 Dynamic Display of Changing Posterior in Bayesian Survival Analysis.- 4.1 Introduction and Summary.- 4.2 A Gibbs Sampler for Censored Data.- 4.3 Proof of Proposition 1.- 4.4 Importance Sampling.- 4.5 The Environment for Dynamic Graphics.- 4.6 Appendix: Completion of the Proof of Proposition 1.- 5 Semiparametric Bayesian Methods for Random Effects Models.- 5.1 Introduction.- 5.2 Normal Linear Random Effects Models.- 5.3 DP priors in the Normal Linear Random Effects Model.- 5.4 Generalized Linear Mixed Models.- 5.5 DP priors in the Generalized Linear Mixed Model.- 5.6 Applications.- 5.7 Discussion.- 6 Nonparametric Bayesian Group Sequential Design.- 6.1 Introduction.- 6.2 The DP Mixing Approach Applied to the Group Sequential Framework.- 6.3 Model Fitting Techniques.- 6.4 Implementation of the Design.- 6.5 Examples.- II Modeling Random Functions.- 7 Wavelet-Based Nonparametric Bayes Methods.- 7.1 Introduction.- 7.2 Discrete Wavelet Transformations.- 7.3 Bayes and Wavelets.- 7.4 Other Problems.- 8 Nonparametric Estimation of Irregular Functions with Independent or Autocorrelated Errors.- 8.1 Introduction.- 8.2 Nonparametric Regression for Independent Errors.- 8.3 Nonparametric Regression for Data with Autocorrelated Errors.- 9 Feedforward Neural Networks for Nonparametric Regression.- 9.1 Introduction.- 9.2 Feed Forward Neural Networks as Nonparametric Regression Models.- 9.3 Variable Architecture FFNNs.- 9.4 Posterior Inference with the FFNN Model.- 9.5 Examples.- 9.6 Discussion.- III Levy and Related Processes.- 10 Survival Analysis Using Semiparametric Bayesian Methods.- D. Sinha.- D. Dey.- 10.1 Introduction.- 10.2 Models.- 10.3 Prior Processes.- 10.4 Bayesian Analysis.- 10.5 Further Readings.- 11 Bayesian Nonparametric and Covariate Analysis of Failure Time Data.- 11.1 Introduction.- 11.2 Cox Model with Beta Process Prior.- 11.3 The Computational Model.- 11.4 Illustrative Analysis.- 11.5 Conclusion.- 12 Simulation of Levy Random Fields.- 12.1 Introduction and Overview.- 12.2 Increasing Independent-Increment Processes: A New Look at an Old Idea.- 12.3 Example: Gamma Variates, Processes, and Fields.- 12.4 Inhomogeneous Levy Random Fields.- 12.5 Comparisons with Other Methods.- 12.6 Conclusions.- 13 Sampling Methods for Bayesian Nonparametric Inference Involving Stochastic Processes.- 13.1 Introduction.- 13.2 Neutral to the Right Processes.- 13.3 Mixtures of Dirichlet Processes.- 13.4 Conclusions.- 14 Curve and Surface Estimation Using Dynamic Step Functions.- 14.1 Introduction.- 14.2 Some Statistical Problems.- 14.3 Some Spatial Statistics.- 14.4 Prototype Prior.- 14.5 Posterior Inference.- 14.6 Example in Intensity Estimation.- 14.7 Discussion.- IV Prior Elicitation and Asymptotic Properties 15 Prior Elicitation for Semiparametric Bayesian Survival Analysis.- 15.1 Introduction.- 15.2 The Method.- 15.3 Sampling from the Joint Posterior Distribution of(ss? ao).- 15.4 Applications to Variable Selection.- 15.5 Myeloma Data.- 15.6 Discussion.- 16 Asymptotic Properties of Nonparametric Bayesian Procedures.- 16.1 Introduction.- 16.2 Frequentist or Bayesian Asymptotics?.- 16.3 Consistency.- 16.4 Consistency in Bellinger Distance.- 16.5 Other Asymptotic Properties.- 16.6 The Robins-Ritov Paradox.- 16.7 Conclusion.- V Case Studies.- 17 Modeling Travel Demand in Portland, Oregon.- 17.1 Introduction.- 17.2 The Data.- 17.3 Poisson/Gamma Random Field Models.- 17.4 The Computational Scheme.- 17.5 Posterior Analysis.- 17.6 Discussion.- 18 Semiparametric PK/PD Models.- 18.1 Introduction.- 18.2 A Semiparametric Population Model.- 18.3 Meta-analysis Over Related Studies.- 18.4 Discussion.- 19 A Bayesian Model for Fatigue Crack Growth.- 19.1 Introduction.- 19.2 The Model.- 19.3 A Markov Chain Monte Carlo Method.- 19.4 An Example: Growth of Crack Lengths.- 19.5 Discussion.- 20 A Semiparametric Model for Labor Earnings Dynamics.- 20.1 Introduction.- 20.2 Longitudinal Earnings Data.- 20.3 A Parametric Random Effects Model.- 20.4 A Semiparametric Model.- 20.5 Predictive Distributions.- 20.6 Conclusion.