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.