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Mixtures Of Dirichlet Processes With Applications To Bayesian Nonparametric Problems

C. Antoniak
Published 1974 · Mathematics

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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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T. Hanson (2003)
10.1198/jbes.2009.07331
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M. Welling (2012)
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10.2307/2530153
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10.1007/978-3-642-12683-3_7
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10.1137/15M1047908
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Emmanouil Antonios Platanios (2016)
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A. Branscum (2004)
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Allam S. Hassanein (2016)
10.1177/1471082X14549290
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10.1111/risa.12484
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M. Keller (2015)
10.1002/0471667196.ESS2161.PUB2
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G. Bormetti (2008)
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10.1007/s11760-012-0289-1
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10.18653/v1/D15-1046
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