<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><spa...<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><span style="color:#4F4F4F;font-family:Simsun;white-space:normal;background-color:#FFFFFF;"><span style="font-family:Verdana;">θ</span><sup><span style="font-family:Verdana;">5</span></sup></span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;">from the desired distribution </span><em><span style="font-family:Verdana;">p</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">and estimating the expectation of any </span></span><span><span style="font-family:Verdana;">function </span><em><span style="font-family:Verdana;">h</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;">. Simulation methods can be used for high-dimensional dis</span></span><span style="font-family:Verdana;">tributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important </span><span style="font-family:Verdana;">in making Bayesian inference practical for generic hierarchical models in</span><span style="font-family:Verdana;"> small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity </span><span style="font-family:Verdana;">between the true predictor variables and the spatial random process. The</span><span style="font-family:Verdana;"> performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error </span><span style="font-family:Verdana;">(RMSE), Mean absolute error (MAE) and coverage probability of corres</span><span style="font-family:Verdana;">ponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.</span></span></span></span> </p> <p> <span></span> </p>展开更多
文摘<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><span style="color:#4F4F4F;font-family:Simsun;white-space:normal;background-color:#FFFFFF;"><span style="font-family:Verdana;">θ</span><sup><span style="font-family:Verdana;">5</span></sup></span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;">from the desired distribution </span><em><span style="font-family:Verdana;">p</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">and estimating the expectation of any </span></span><span><span style="font-family:Verdana;">function </span><em><span style="font-family:Verdana;">h</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;">. Simulation methods can be used for high-dimensional dis</span></span><span style="font-family:Verdana;">tributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important </span><span style="font-family:Verdana;">in making Bayesian inference practical for generic hierarchical models in</span><span style="font-family:Verdana;"> small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity </span><span style="font-family:Verdana;">between the true predictor variables and the spatial random process. The</span><span style="font-family:Verdana;"> performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error </span><span style="font-family:Verdana;">(RMSE), Mean absolute error (MAE) and coverage probability of corres</span><span style="font-family:Verdana;">ponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.</span></span></span></span> </p> <p> <span></span> </p>
