Open AccessVariational Bayesian with Embedded Laplace Approximation for AR Model with Outliers
Author(s) -
Hongjie Wan,
Haiyun Zhang
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1576/1/012056
Subject(s) - markov chain monte carlo , laplace's method , outlier , laplace distribution , gaussian , bayesian probability , mathematics , computation , algorithm , markov chain , laplace transform , monte carlo method , computer science , bayes estimator , mathematical optimization , artificial intelligence , statistics , mathematical analysis , physics , quantum mechanics
The student-t distributed innovation is robust to Auto regressive (AR) observations with outliers. However, the characteristics of student-t distribution lead to unclosed solution while using Variational Bayesian (VB) to estimate the model parameters. This paper proposed to embed the Laplace approximation in VB framework to get closed form solution. Markov Chain Monte Carlo (MCMC) is a typical method to unclosed form solutions, while it is known that MCMC has large computation costs. The degree of freedom parameter (DOF) changes greatly before and after the outlier points has been deleted, so the estimation can be improved. Experimental results show that, more accurate estimation coefficients estimation are obtained using the proposed methods compared with using the Gaussian innovation, and more accurate estimation is obtained after the additive outlier is deleted.