Abstract:
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Bayesian approach can effectively deal with a wide range of complicated statistical problems like high-dimensional inference, latent variable filtering and statistical learning. In classical Bayesian analysis, we need to fully specify the likelihood of underlying models so as to carry out statistical computation for posterior inference. The requirement of likelihood limits the application of Bayesian approach in solving semi-parametric problems or problems whose full likelihood is computationally intractable. In this paper, we propose an approximate Bayesian inference framework which incorporates pseudo-likelihood. It is expected that without the need of full likelihood specification, we can extend the scope of problems which Bayesian inference can solve. Two examples, the heterogeneous multivariate count data model and the spatiotemporal model, are taken to demonstrate our framework. Results in the examples show that the approximate Bayesian inference framework can provide both consistent estimates as well as good credible interval coverage.
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