Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines
This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can...
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| Format: | Article |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1635 |
| _version_ | 1797517138897928192 |
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| author | Zhiyong Chen Jianbao Chen |
| author_facet | Zhiyong Chen Jianbao Chen |
| author_sort | Zhiyong Chen |
| collection | DOAJ |
| description | This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset. |
| first_indexed | 2024-03-10T07:10:38Z |
| format | Article |
| id | doaj.art-71a378679db44b4e8f3011d158f4c808 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:10:38Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-71a378679db44b4e8f3011d158f4c8082023-11-22T15:27:45ZengMDPI AGSymmetry2073-89942021-09-01139163510.3390/sym13091635Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot SplinesZhiyong Chen0Jianbao Chen1School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, ChinaSchool of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, ChinaThis article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.https://www.mdpi.com/2073-8994/13/9/1635spatial datapartially linear additive model spatial autoregressivefree-knot splinesMCMC toolsGibbs sampler |
| spellingShingle | Zhiyong Chen Jianbao Chen Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines Symmetry spatial data partially linear additive model spatial autoregressive free-knot splines MCMC tools Gibbs sampler |
| title | Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines |
| title_full | Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines |
| title_fullStr | Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines |
| title_full_unstemmed | Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines |
| title_short | Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines |
| title_sort | bayesian analysis of partially linear additive spatial autoregressive models with free knot splines |
| topic | spatial data partially linear additive model spatial autoregressive free-knot splines MCMC tools Gibbs sampler |
| url | https://www.mdpi.com/2073-8994/13/9/1635 |
| work_keys_str_mv | AT zhiyongchen bayesiananalysisofpartiallylinearadditivespatialautoregressivemodelswithfreeknotsplines AT jianbaochen bayesiananalysisofpartiallylinearadditivespatialautoregressivemodelswithfreeknotsplines |