Bayesian inference on mixture models and their applications
Mixture models are useful in describing a wide variety of random phenomena because of their flexibility in modeling. They have continued to receive increasing attention over the years from both a practical and theoretical point of view. In their applications, estimating the number of mixture compone...
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| Format: | Others |
| Language: | en_US |
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Texas A&M University
2006
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| Online Access: | http://hdl.handle.net/1969.1/3990 |
| Summary: | Mixture models are useful in describing a wide variety of random phenomena because
of their flexibility in modeling. They have continued to receive increasing attention
over the years from both a practical and theoretical point of view. In their applications,
estimating the number of mixture components is often the main research
objective or the first step toward it. Estimation of the number of mixture components
heavily depends on the underlying distribution. As an extension of normal
mixture models, we introduce a skew-normal mixture model and adapt the reversible
jump Markov chain Monte Carlo algorithm to estimate the number of components
with some applications to biological data.
The reversible jump algorithm is also applied to the Cox proportional hazard
model with frailty. We consider a regression model for the variance components in
the proportional hazards frailty model. We propose a Bayesian model averaging procedure
with a reversible jump Markov chain Monte Carlo step which selects the model
automatically. The resulting regression coefficient estimates ignore the model uncertainty
from the frailty distribution. Finally, the proposed model and the estimation
procedure are illustrated with simulated example and real data. |
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