This gives an overview of Dirichlet processes and Gaussian processes and places these methods in the context of popular frequentist nonparametric estimation methods for, e. Lecture notes on Bayesian nonparametrics. A great introduction to foundations of Bayesian nonparametrics, and provides many references for those who want a more in-depth understanding of topics.
References on Bayesian nonparametrics
Ghosal and van der Vaart. Fundamentals of Bayesian Nonparametric Inference.
- YES IV: “Bayesian Nonparametric Statistics” – Eurandom;
- Living the French Revolution, 1789-99.
- Red River Blues: The Blues Tradition in the Southeast.
- Variational Russian Roulette for Deep Bayesian Nonparametrics!
- The External Control of Organizations: A Resource Dependence Perspective (Stanford Business Books)!
- Streaming, Distributed Variational Inference for Bayesian Nonparametrics.
- Background: probability.
Cambridge Series in Statistical and Probabilistic Mathematics, The most recent textbook on Bayesian nonparametrics, focusing on topics such as random measures, consistency, contraction rates, and also covers topics such as Gaussian processes, Dirichlet processes, beta processes. Kleijn, van der Vaart, van Zanten. Lectures on Nonparametric Bayesian Statistics. Lecture notes with some similar topics as and partly based on the Ghosal and van der Vaart textbook, including a comprehensive treatment of posterior consistency.
Everything you wanted to know about Poisson processes. See Orbanz lecture notes above for more references on even more topics on general point process theory.
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- Müller , Mitra : Bayesian Nonparametric Inference – Why and How.
- ICERM - Bayesian Nonparametrics.
- Prophecy and Diplomacy: The Moral Doctrine of John Paul II?
- Lectures on infinite-dimensional Lie algebra;
- Bayesian Analysis.
Combinatorial stochastic processes. Exchangeability and related topics. Orbanz and Roy. Hierarchical models, nested models, and completely random measures. Broderick, Jordan, Pitman. Cluster and feature modeling from combinatorial stochastic processes. Having basic familiarity with measure-theoretic probability is fairly important for understanding many of the ideas in this section. Many of the introductory references aim to avoid measure theory especially for the discrete models , but even this is not always the case, so it is helpful to have as much exposure as possible.
Category:Nonparametric Bayesian statistics - Wikipedia
Measure and probability. Lecture notes. There are too many papers on nonparametric Bayesian models and inference methods. The above tutorials contain many more references. Markov Chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics , Blei and Jordan.
Variational inference for Dirichlet process mixtures. Bayesian Analysis , Teh, Jordan, Beal, Blei. Hierarchical Dirichlet processes. Journal of the American Statistical Association , Hoffman, Blei, Wang, Paisley. Stochastic variational inference. Journal of Machine Learning Research , Rodriguez, Dunson, Gelfand.
The Nested Dirichlet process. Blei, Griffiths, Jordan. The nested Chinese restaurant process and Bayesian nonparametric inference of topic hierarchies. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions.
Basic density estimation using Dirichlet Process Mixture models
While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. The authors thank the section officers for the support and encouragement. Source Bayesian Anal. Zentralblatt MATH identifier Keywords Nonparametric models Dirichlet process Polya tree dependent Dirichlet process.
Bayesian Nonparametric Inference — Why and How. Bayesian Anal. Article information Source Bayesian Anal. Export citation.