<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
Urbanization changes have been widely examined and numerous urban growth models have been proposed. We introduce an alternative urban growth model specifically designed to incorporate spatial heterogeneity in urban gr...Urbanization changes have been widely examined and numerous urban growth models have been proposed. We introduce an alternative urban growth model specifically designed to incorporate spatial heterogeneity in urban growth models. Instead of applying a single method to the entire study area, we segment the study area into different regions and apply targeted algorithms in each subregion. The working hypothesis is that the integration of appropriately selected region-specific models will outperform a globally applied model as it will incorporate further spatial heterogeneity. We examine urban land use changes in Denver, Colorado. Two land use maps from different time snapshots (1977 and 1997) are used to detect the urban land use changes, and 23 explanatory factors are produced to model urbanization. The proposed Spatially Heterogeneous Expert Based (SHEB) model tested decision trees as the underlying modeling algorithm, applying them in different subregions. In this paper the segmentation tested is the division of the entire area into interior and exterior urban areas. Interior urban areas are those situated within dense urbanized structures, while exterior urban areas are outside of these structures. Obtained results on this model regionalization technique indicate that targeted local models produce improved results in terms of Kappa, accuracy percentage and multi-scale performance. The model superiority is also confirmed by model pairwise comparisons using t-tests. The segmentation criterion of interior/exterior selection may not only capture specific characteristics on spatial and morphological properties, but also socioeconomic factors which may implicitly be present in these spatial representations. The usage of interior and exterior subregions in the present study acts as a proof of concept. Other spatial heterogeneity indicators, for example landscape, socioeconomic and political boundaries could act as the basis for improved local segmentations.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>
文摘Urbanization changes have been widely examined and numerous urban growth models have been proposed. We introduce an alternative urban growth model specifically designed to incorporate spatial heterogeneity in urban growth models. Instead of applying a single method to the entire study area, we segment the study area into different regions and apply targeted algorithms in each subregion. The working hypothesis is that the integration of appropriately selected region-specific models will outperform a globally applied model as it will incorporate further spatial heterogeneity. We examine urban land use changes in Denver, Colorado. Two land use maps from different time snapshots (1977 and 1997) are used to detect the urban land use changes, and 23 explanatory factors are produced to model urbanization. The proposed Spatially Heterogeneous Expert Based (SHEB) model tested decision trees as the underlying modeling algorithm, applying them in different subregions. In this paper the segmentation tested is the division of the entire area into interior and exterior urban areas. Interior urban areas are those situated within dense urbanized structures, while exterior urban areas are outside of these structures. Obtained results on this model regionalization technique indicate that targeted local models produce improved results in terms of Kappa, accuracy percentage and multi-scale performance. The model superiority is also confirmed by model pairwise comparisons using t-tests. The segmentation criterion of interior/exterior selection may not only capture specific characteristics on spatial and morphological properties, but also socioeconomic factors which may implicitly be present in these spatial representations. The usage of interior and exterior subregions in the present study acts as a proof of concept. Other spatial heterogeneity indicators, for example landscape, socioeconomic and political boundaries could act as the basis for improved local segmentations.
