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# Mixtures Of Dirichlet Processes With Applications To Bayesian Nonparametric Problems

C. Antoniak

Published 1974 · Mathematics

process. This paper extends Ferguson's result to cases where the random measure is a mixing distribution for a parameter which determines the distribution from which observations are made. The conditional distribution of the random measure, given the observations, is no longer that of a simple Dirichlet process, but can be described as being a mixture of Dirichlet processes. This paper gives a formal definition for these mixtures and develops several theorems about their properties, the most important of which is a closure property for such mixtures. Formulas for computing the conditional distribution are derived and applications to problems in bio-assay, discrimination, regression, and mixing distributions are given.

This paper references

10.1119/1.1972842

Handbook of Mathematical Functions

M. Abramowitz (1966)

Group Theory. Prentice-Hall, Englewood Cliffs, New Jersey

W. R. SCOTT (1964)

10.2307/1402037

Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. U.S. Department of Commerce, National Bureau of Standards

J. Hemelrijk (1965)

10.2307/1266907

Probability measures on metric spaces

K. Parthasarathy (1967)

A Bayesian approach to Bio-assay

F. L. RAMSEY (1972)

Applied Statistica' Decision Theory

H. RAIFFA (1961)

10.1017/S0021900200108472

A class of distribution function processes which have derivatives

C. Kraft (1964)

10.1201/9781584889328-9

Group Theory.

W. Scott (1964)

10.1214/AOS/1176342360

A Bayesian Analysis of Some Nonparametric Problems

T. S. Ferguson (1973)

Neutrality and Dirichlet distributions. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, and Random Processes

J. FABIUS (1973)

Bayesian bioassay

K. R. PARTHASARATHY (1964)

10.1090/S0002-9904-1963-10992-1

Random distribution functions

L. Dubins (1963)

10.1214/AOS/1176342373

Discreteness of Ferguson Selections

D. Blackwell (1973)

10.1115/1.3625776

Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

Milton Abramowitz (1965)

An Introduction to Probability Theory and its Applications, 1

FELLER (1968)

10.2307/1905668

An Introduction to Probability Theory and Its Applications

W. Feller (1967)

10.1007/978-1-4612-0919-5_26

An Empirical Bayes Approach to Statistics

H. Robbins (1956)

10.1214/AOMS/1177703594

Bayesian Bio-Assay

C. Kraft (1964)

10.1214/AOS/1176342372

Ferguson Distributions Via Polya Urn Schemes

D. Blackwell (1973)

10.1214/AOP/1176996703

Tailfree and Neutral Random Probabilities and Their Posterior Distributions

K. A. Doksum (1974)

10.1214/AOP/1176996898

Contributions to the Theory of Dirichlet Processes

R. Korwar (1973)

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10.1007/S11390-010-1051-1

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D. Görür (2010)

10.1198/1085711031526

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T. Hanson (2003)

10.1198/jbes.2009.07331

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Matt Taddy (2010)

10.1109/ITA.2012.6181768

Exchangeable inconsistent priors for Bayesian posterior inference

M. Welling (2012)

10.3150/13-BEJ548

Optimal filtering and the dual process

O. Papaspiliopoulos (2014)

10.2307/2530153

Bayesian Nonparametric Inference for Effective Doses in a Quantal-Response Experiment

Damon Disch (1981)

10.1007/978-3-642-12683-3_7

Proteome Coverage Prediction for Integrated Proteomics Datasets

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10.1093/bioinformatics/btw662

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10.1186/1471-2105-13-S2-S10

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10.1016/j.tox.2013.04.005

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10.1007/S40745-016-0082-Z

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10.1111/j.1467-9469.2011.00761.x

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L. Nieto-Barajas (2012)

10.1093/NSR/NWX044

Big Learning with Bayesian Methods

J. Zhu (2014)

10.4310/20-sii644

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G. Hu (2020)

10.1137/15M1047908

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J. Prendes (2016)

10.1002/wcm.2678

Unsupervised learning of indoor localization based on received signal strength

L. Li (2016)

Estimating Accuracy from Unlabeled Data: A Bayesian Approach

Emmanouil Antonios Platanios (2016)

10.1016/J.PREVETMED.2004.09.009

Bayesian modeling of animal- and herd-level prevalences.

A. Branscum (2004)

Semantic Analysis for Crowded Scenes Based on Non-Parametric Tracklet Clustering

Allam S. Hassanein (2016)

10.1177/1471082X14549290

Semi-parametric Bayesian analysis of binary responses with a continuous covariate subject to non-random missingness

Frederico Z. Poleto (2015)

10.1111/risa.12484

Nonparametric Estimation of the Probability of Detection of Flaws in an Industrial Component, from Destructive and Nondestructive Testing Data, Using Approximate Bayesian Computation.

M. Keller (2015)

10.1002/0471667196.ESS2161.PUB2

Ramsey's Prior

D. Disch (2006)

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G. Bormetti (2008)

Computational Methods for Investigating Dendritic Cell Biology

Ana Paula de Oliveira (2011)

Crowdclustering

Ryan Gomes (2011)

10.1111/J.1541-0420.2005.00381.X

Subset clustering of binary sequences, with an application to genomic abnormality data.

Peter D. Hoff (2005)

10.1007/s11760-012-0289-1

A fully unsupervised color textured image segmentation algorithm using weighted mean histograms features

M. M. Rahman (2012)

10.18653/v1/D15-1046

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