Practical Nonparametric and Semiparametric Bayesian Statistics (Lecture Notes in Statistics)

A compilation of original articles by Bayesian experts, this volume presents perspectives on recent developments on nonparametric and semiparametric methods in Bayesian statistics. The articles discuss how to conceptualize and develop Bayesian models using rich classes of nonparametric and semiparametric methods, how to use modern computational tools to summarize inferences, and how to apply these methodologies through the analysis of case studies.

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 Lévy 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 Lévy 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.