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Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models

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  • Yuanyuan Ju

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
    State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China
    Key Laboratory of Industrial Engineering Statistical Analysis, Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Yan Yang

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Mingxing Hu

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Lin Dai

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Liucang Wu

    (Center for Applied Statistics, Kunming University of Science and Technology, Kunming 650500, China)

Abstract

In spatial data analysis, outliers or influential observations have a considerable influence on statistical inference. This paper develops Bayesian influence analysis, including the local influence approach and case influence measures in skew-normal spatial autoregression models (SSARMs). The Bayesian local influence method is proposed to evaluate the impact of small perturbations in data, the distribution of sampling and prior. To measure the extent of different perturbations in SSARMs, the Bayes factor, the ϕ -divergence and the posterior mean distance are established. A Bayesian case influence measure is presented to examine the influence points in SSARMs. The potential influence points in the models are identified by Cook’s posterior mean distance and Cook’s posterior mode distance ϕ -divergence. The Bayesian influence analysis formulation of spatial data is given. Simulation studies and examples verify the effectiveness of the presented methodologies.

Suggested Citation

  • Yuanyuan Ju & Yan Yang & Mingxing Hu & Lin Dai & Liucang Wu, 2022. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1306-:d:793868
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    References listed on IDEAS

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    Cited by:

    1. Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
    2. Yuanying Zhao & Dengke Xu, 2023. "A Bayesian Variable Selection Method for Spatial Autoregressive Quantile Models," Mathematics, MDPI, vol. 11(4), pages 1-19, February.

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