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Title On Bayesian analyses and finite mixtures for proportions
Edition Volume 11, Number 2
Call Number
ISBN/ISSN 0960-3174
Author(s) S. P. BROOKS
Series Title Statistics and Computing
GMD Electronic Journal
Language English
Publisher Springer Netherlands
Publishing Year 2001
Publishing Place Netherlands
Collation 12p
Abstract/Notes When the results of biological experiments are tested for a possible difference between treatment
and control groups, the inference is only valid if based upon a model that fits the experimental
results satisfactorily. In dominant-lethal testing, foetal death has previously been assumed to follow
a variety of models, including a Poisson, Binomial, Beta-binomial and various mixture models.
However, discriminating between models has always been a particularly difficult problem. In this
paper, we consider the data from 6 separate dominant-lethal assay experiments and discriminate
between the competing models which could be used to describe them.We adopt a Bayesian approach
and illustrate how a variety of different models may be considered, using Markov chain Monte
Carlo (MCMC) simulation techniques and comparing the results with the corresponding maximum
likelihood analyses.We present an auxiliary variable method for determining the probability that any
particular data cell is assigned to a given component in a mixture and we illustrate the value of this
approach. Finally,we showhowthe Bayesian approach provides a natural and unique perspective on the
model selection problem via reversible jump MCMC and illustrate how probabilities associated with
each of the different models may be calculated for each data set. In terms of estimationwe showhow, by
averaging over the different models,we obtain reliable and robust inference for any statistic of interest
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