Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

Chen, Zhiyong; Chen, Jianbao

doi:10.3390/sym13091635

Cited by 3 publications

(5 citation statements)

References 56 publications

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“…DiMatteo et al [7] set conjugate priors for a, and integrated the coefficients out of the posterior analytically, leaving n and r as the unknowns to be sampled. Similar work can be seen in Fan et al [8], Poon and Wang [9], and Chen and Chen [10]. However, for most inverse problems, conjugate priors for the coefficients a are not available due to the nature of the forward model g. In some practical problems, like the recovery of continuous physical properties of the earth [11,12] or the inversion of pressure field on engineering structures [13], the forward model can be non-linear or implicit.…”

Section: Introductionmentioning

confidence: 74%

“…. Accept this proposal, m t = m * , based on the acceptance ratio with equation ( 6); otherwise, reject the proposal: m t = m t−1 ; (5) finally, update C t−1 to C t using equations (10) and (11).…”

Section: Methodsmentioning

confidence: 99%

“…Adapt Ct −1 using equations (10) and (11) Adapt Ct −1 using equations ( 10) and ( 11) and adjust sc with equation ( 12)…”

Section: Efficiency Examinationmentioning

confidence: 99%

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Adaptive tempered reversible jump algorithm for Bayesian curve fitting

Tian,

Lee,

Zhou

2024

Inverse Problems

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Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without appropriately tuned proposals. As a remedy, we present an adaptive RJMCMC algorithm for the curve fitting problems by extending the Adaptive Metropolis sampler from a fixed-dimensional to a trans-dimensional case. In this presented algorithm, both the size and orientation of the proposal function can be automatically adjusted in the sampling process. Specifically, the curve fitting setting allows for the approximation of the posterior covariance of the a priori unknown function on a representative grid of points. This approximation facilitates the definition of efficient proposals. In addition, we introduce an auxiliary-tempered version of this algorithm via non-reversible parallel tempering. To evaluate the algorithms, we conduct numerical tests involving a series of controlled experiments. The results demonstrate that the adaptive algorithms exhibit significantly higher efficiency compared to the conventional ones. Even in cases where the posterior distribution is highly complex, leading to ineffective convergence in the auxiliary-tempered conventional RJMCMC, the proposed auxiliary-tempered adaptive RJMCMC performs satisfactorily. Furthermore, we present a realistic inverse example to test the algorithms. The successful application of the adaptive algorithm distinguishes it again from the conventional one that fails to converge effectively even after millions of iterations.

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Section: Introductionmentioning

confidence: 74%

Section: Methodsmentioning

confidence: 99%

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Adaptive tempered reversible jump algorithm for Bayesian curve fitting

Tian,

Lee,

Zhou

2024

Inverse Problems

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“…However, the relationship between the response variable and the explanatory variable is not always linear but also nonlinear. If the model ignores nonlinear functional forms, it can lead to inconsistent parameter estimators and inaccurate conclusions [7]. The nonparametric regression method is better suited for data with a nonlinear connection because it does not need linear assumptions.…”

Section: Introductionmentioning

confidence: 99%

Application of Panelized Spline-Spatial Autoregressive Model to Hiv Case Data in Indonesia

Pigitha

Djuraidah

Wigena

2023

BAREKENG: J. Math. & App.

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Spatial regression analysis is a statistical method used to perform modeling by considering spatial effects. Spatial models generally use a parametric approach by assuming a linear relationship between explanatory and response variables. The nonparametric regression method is better suited for data with a nonlinear connection because it does not need linear assumptions. One of the nonparametric regression methods is penalized spline regression (P-Spline). The P-spline has a simple mathematical relationship with mixed linear model. The use of a mixed linear model allows the P-Spline to be combined with other statistical models. PS-SAR is a combination of the P-Spline and the SAR spatial model so that it can analyze spatial data with a semiparametric approach. Based on data from monitoring the development of the HIV situation in 2018, the number of HIV cases in Indonesia shows a clustered pattern that indicate spatial dependence. In addition, the relationship between the number of positive cases and the factors tends to be nonlinear. Therefore, this study aims to apply the PS-SAR model to HIV case data in Indonesia. The resulting model is evaluated based on the estimates of autoregressive spatial coefficient, MSE, MAPE, and Pseudo R2. Based on the results, the PS-SAR model has an autoregressive spatial coefficient similar to the SAR model and has smaller MSE and MAPE than the SAR model.

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“…According to the regression object of the model, the semiparametric spatial econometric model usually includes mean regression model and quantile regression model. Most of the spatial econometric models involved in the existing literature belong to the former [26][27][28][29]. The mean regression model can only reflect the location information of the conditional distribution of dependent variable and cannot describe its scale and shape.…”

Section: Introductionmentioning

confidence: 99%

Bayesian P-Splines Quantile Regression of Partially Linear Varying Coefficient Spatial Autoregressive Models

Chen

2022

Symmetry

Self Cite

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This paper deals with spatial data that can be modelled by partially linear varying coefficient spatial autoregressive models with Bayesian P-splines quantile regression. We evaluate the linear and nonlinear effects of covariates on the response and use quantile regression to present comprehensive information at different quantiles. We not only propose an empirical Bayesian approach of quantile regression using the asymmetric Laplace error distribution and employ P-splines to approximate nonparametric components but also develop an efficient Markov chain Monte Carlo technique to explore the joint posterior distributions of unknown parameters. Monte Carlo simulations show that our estimators not only have robustness for different spatial weight matrices but also perform better compared with quantile regression and instrumental variable quantile regression estimators in finite samples at different quantiles. Finally, a set of Sydney real estate data applications is analysed to illustrate the performance of the proposed method.

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Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

Cited by 3 publications

References 56 publications

Adaptive tempered reversible jump algorithm for Bayesian curve fitting

Adaptive tempered reversible jump algorithm for Bayesian curve fitting

Application of Panelized Spline-Spatial Autoregressive Model to Hiv Case Data in Indonesia

Bayesian P-Splines Quantile Regression of Partially Linear Varying Coefficient Spatial Autoregressive Models

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