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A novel approach to Bayesian consistency
- Source :
- Electron. J. Statist. 11, no. 2 (2017), 4723-4745
- Publication Year :
- 2017
- Publisher :
- Institute of Mathematical Statistics, 2017.
-
Abstract
- It is well-known that the Kullback–Leibler support condition implies posterior consistency in the weak topology, but is not sufficient for consistency in the total variation distance. There is a counter–example. Since then many authors have proposed sufficient conditions for strong consistency; and the aim of the present paper is to introduce new conditions with specific application to nonparametric mixture models with heavy–tailed components, such as the Student-$t$. The key is a more focused result on sets of densities where if strong consistency fails then it fails on such densities. This allows us to move away from the traditional types of sieves currently employed.
- Subjects :
- Statistics and Probability
Mathematical optimization
Kullback–Leibler divergence
Bayesian probability
posterior consistency
02 engineering and technology
01 natural sciences
010104 statistics & probability
Total variation
Consistency (statistics)
62G07
0202 electrical engineering, electronic engineering, information engineering
Weak topology (polar topology)
62G05
0101 mathematics
62G20
Lévy–Prokhorov metric
Mathematics
business.industry
Nonparametric statistics
Strong consistency
020206 networking & telecommunications
Pattern recognition
Mixture model
mixture of Student’s $t$ distributions
total variation
Artificial intelligence
Statistics, Probability and Uncertainty
business
Subjects
Details
- ISSN :
- 19357524
- Volume :
- 11
- Database :
- OpenAIRE
- Journal :
- Electronic Journal of Statistics
- Accession number :
- edsair.doi.dedup.....77fbcda587dca03dd86e33420bb75546