Nonparametric Bayesian Inference

This book is a compilation of unpublished papers written by Jean-Marie Rolin (with several co-authors) on nonparametric bayesian estimation. Jean-Marie was professor of statistics at University of Louvain and died on November 5th, 2018. He made important contributions in mathematical statistics with applications to different fields like econometrics or biometrics.These papers cover a variety of topics, including:

• The Mathematical structure of the Bayesian model and the main concepts (sufficiency, ancillarity, invariance)

• Representation of the Dirichlet processes and of the associated Polya urn model and applications to nonparametric bayesian analysis.

• Contributions to duration models and to their non parametric bayesian treatment.

Presents a rigorous foundations of Bayesian statistics Analyzes Dirichlet processes generated by the marginal of Dirichlet prior nonparametric model Includes nonparametric durations models including competing risk models

Autorentext

Jean-Pierre Florens is an influential French econometrician at Toulouse School of Economics. He is known for his research on Bayesian information, econometrics of stochastic processes, causality, frontier estimation, and inverse problems. He has written 3 books and over 100 articles. Born in Marseille in 1947, France, he completed his undergraduate studies in economics, political science, and mathematics at the Aix-Marseille University. He pursued graduate studies in mathematics at the University of Rouen. He is a fellow of the Econometric Society.

Michel Mouchart was born in Huy in 1939, Belgium. He completed undergraduate studies in Commercial Sciences at the Institut Supérieur Saint-Ignace (Antwerp) and Economics at the University of Louvain, along with a PhD in Economics. He has been an Elected Member of International Statistical and member of Institute Société Belge de Statistique. He is also a member of the Editorial Boards: Statistica, Internationale Econometric Review. His biography has 101 articles and 3 books (as author or co-author).

Klappentext

This book is a compilation of unpublished papers written by Jean-Marie Rolin (with several co-authors) on nonparametric bayesian estimation. Jean-Marie was professor of statistics at University of Louvain and died on November 5th, 2018. He made important contributions in mathematical statistics with applications to different fields like econometrics or biometrics.These papers cover a variety of topics, including: The Mathematical structure of the Bayesian model and the main concepts (sufficiency, ancillarity, invariance ) Representation of the Dirichlet processes and of the associated Polya urn model and applications to nonparametric bayesian analysis. Contributions to duration models and to their non parametric bayesian treatment.

Inhalt

Chapter 1. On the a-Algebraic Realization Problem.- Chapter 2. Weak Conditional Independence And Relative Invariance in Bayesian Statistics.- Chapter 3. Some Useful Properties of the Dirichlet Process.- Chapter 4. On the Distribution of Jumps of the Dirichlet Process.- Chapter 5. Bayes, Bootstrap, Moments.- Chapter 6. Smooth vs. likelihood estimation for a class of mixtures of discrete distributions.- Chapter 7. Bayesian Encompassing Specification Tests of a Parametric Model against a Non Parametric Alternative.- Chapter 8. Nonparametric Bayesian Survival Analysis.- Chapter 9. Simulation of Posterior Distributions in Nonparametric Censored Analysis.- Chapter 10. Bayesian Identification of Semi-Parametric Binary Response Models.- Chapter 11. Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysis.- Chapter 12. Nonparametric Competing Risks Models: Identification and Strong Consistency.