A nonparametric predictive alternative to the Imprecise Dirichlet Model: The case of a known number of categories
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This paper develops NPI for multinomial data when the total number of possible categories for the data is known and presents the upper and lower probabilities for events involving the next observation and several of their properties.About:
This article is published in International Journal of Approximate Reasoning.The article was published on 2009-02-01 and is currently open access. It has received 57 citations till now. The article focuses on the topics: Upper and lower probabilities & Predictive inference.read more
Citations
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Nonparametric Predictive Inference.
TL;DR: Nonparametric predictive inference (NPI) is a statistical method based on Hill’s assumption A(n), which gives a direct conditional probability for a future observable random quantity, conditional on observed values of related random quantities.
Inferences from multinomial data: Learning about a bag of marbles - Discussion
Anthony O'Hagan,C.A.B. Smith,Christopher Jennison,George A. Barnard,A.N. Bisson,N. Wilson,C. Palmer,David Spiegelhalter,Nicky Best,A. P. Dawid,C.J. Geyer,M. Aitkin,Bartlett,Philip J. Brown,Chris Chatfield,Frank P. A. Coolen,David Cox,Seymour Geisser,M. Golstein,Irving John Good,Frank R. Hampel,Jane L. Hutton,H.E. Kyburg,I. Levi,Dennis V. Lindley,Luis R. Pericchi,R. Rotondi,Teddy Seidenfeld,Larry Wasserman,Stephen G. Walker +29 more
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Imprecision and Prior-Data Conflict in Generalized Bayesian Inference
GM Gero Walter,Thomas Augustin +1 more
TL;DR: This paper considers a general class of recently studied imprecise probability models, including the Imprecise Dirichlet Model under prior information, and more generally the framework of Quaeghebeur and de Cooman for imprecising inference in canonical exponential families, and proposes an extension reestablishing the natural relationship between knowledge and imprecision.
Journal ArticleDOI
Predictive inference for system reliability after common-cause component failures
TL;DR: The nonparametric predictive inference approach is presented for a basic scenario of a system consisting of only a single type of components and without consideration of failure behaviour over time, it provides many opportunities for more general modelling and inference.
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Classification with decision trees from a nonparametric predictive inference perspective
TL;DR: In a bias-variance study of the errors, it is proved that the procedure with the NPI model has a lower variance than the one with the IDM, implying a lower level of over-fitting.
References
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Book
Theory of probability
Harold Jeffreys,R. Bruce Lindsay +1 more
TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.
BookDOI
Predictive Inference: An Introduction
TL;DR: Non-Bayesian predictive approaches for Bayesian prediction of process control and optimization and Multivariate normal prediction problems.
Book ChapterDOI
Statistical Decision Theory
TL;DR: Any attempt at a general review of decision theory is doomed; all that can be done is to present a description of some of the underlying ideas.