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- W167575377 abstract "vVe propose a method for approximating integrated likelihoods, or posterior normalizing constants, in finite mixture models, for which analytic approximations such as the Laplace method are invalid. Integrated likelihoods are key components of Bayes factors and of the posterior model probabilities used in Bayesian model averaging. The method starts by formulating the model in terms of the unobserved group memberships, Z, and making these, rather than the model parameters, the variables of integration. The integral is then evaluated using importance sampling over the Z. The tricky part is choosing the importance sampling function, and we study the use of mixtures as importance sampling functions. vVe propose two forms of this: defensive mixture importance sampling (DMIS), and Z-distance importance sampling. We choose the parameters of the mixture adaptively, and we show how this can be done so as to approximately minimize the variance of the approximation to the integral. The resulting method is easy to implement, involving only simple multinomial sampling, it is almost as easy for complex mixture models as for simple ones, and it extends easily to more complicated mixture models. The simulated values on which it is based are independent, and so it avoids problems of convergence due to dependence of successive iterates. We also propose a way of dealing with the label-switching problem. The method provides a standard error, and so is to some extent self-monitoring. In simulations based on a problem in molecular biology, the methods performed well. The approach can be applied more generally to models that are simple when written in a complete-data form, Le. that are amenable to the EM algorithm, such as models for missing data, for censoring or truncated data, random effects or variance components." @default.
- W167575377 created "2016-06-24" @default.
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- W167575377 date "2001-07-01" @default.
- W167575377 modified "2023-09-23" @default.
- W167575377 title "Easy Computation of Bayes Factors and Normalizing Constants for Mixture Models via Mixture Importance Sampling" @default.
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- W167575377 doi "https://doi.org/10.21236/ada459760" @default.
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