Convergence of adaptive direction sampling
Journal of Multivariate Analysis
Bayesian forecasting and dynamic models (2nd ed.)
Bayesian forecasting and dynamic models (2nd ed.)
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Interacting multiple try algorithms with different proposal distributions
Statistics and Computing
Zero variance Markov chain Monte Carlo for Bayesian estimators
Statistics and Computing
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We develop in this paper three multiple-try blocking schemes for Bayesian analysis of nonlinear and non-Gaussian state space models. To reduce the correlations between successive iterates and to avoid getting trapped in a local maximum, we construct Markov chains by drawing state variables in blocks with multiple trial points. The first and second methods adopt autoregressive and independent kernels to produce the trial points, while the third method uses samples along suitable directions. Using the time series structure of the state space models, the three sampling schemes can be implemented efficiently. In our multimodal examples, the three multiple-try samplers are able to generate the desired posterior sample, whereas existing methods fail to do so.