Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

Cancho, Vicente G.; Dey, Dipak K.; Lachos, Víctor H.; Andrade, Marinho G.

doi:10.1016/j.csda.2010.05.032

Cited by 50 publications

(42 citation statements)

References 22 publications

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“…The stochastic representation of the skew-t distribution has been studied by several researchers [1,11]. Following the representation of Cancho et al (2011) [11], we arrive at the following hierarchical structure…”

Section: Likelihood Functionmentioning

confidence: 99%

A variational Bayesian approach for inverse problems with skew-t error distributions

Guha

Efendiev

et al. 2015

Journal of Computational Physics

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Please cite this article in press as: N. Guha et al., A variational Bayesian approach for inverse problems with skew-t error distributions, J. Comput. Phys. (2015), http://dx. AbstractIn this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.

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Section: Likelihood Functionmentioning

confidence: 99%

A variational Bayesian approach for inverse problems with skew-t error distributions

Guha

Efendiev

et al. 2015

Journal of Computational Physics

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“…The basic idea is to explore the joint posterior distributions of the model parameters together with latent variables x i and u i , when informative priors are employed. Bayesian influence diagnostics can be treated via the Kullback-Leibler divergence, as proposed by Cancho et al (2010).…”

Section: Final Conclusionmentioning

confidence: 99%

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

2011

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In this paper, we discuss the extension of some diagnostic procedures to multivariate measurement error models with scale mixtures of skew-normal distributions (Lachos et al., Statistics 44:541-556, 2010c). This class provides a useful generalization of normal (and skew-normal) measurement error models since the random term distributions cover symmetric, asymmetric and heavy-tailed distributions, such as skew-t, skew-slash and skew-contaminated normal, among others. Inspired by the EM algorithm proposed by Lachos et al. (Statistics 44:541-556, 2010c), we develop a local influence analysis for measurement error models, following Zhu and Lee's (J R Stat Soc B 63:111-126, 2001) approach. This is because the observed data loglikelihood function associated with the proposed model is somewhat complex and Cook's well-known approach can be very difficult to apply to achieve local influence measures. Some useful perturbation schemes are also discussed. In addition, a score test for assessing the homogeneity of the skewness parameter vector is presented. Finally, the methodology is exemplified through a real data set, illustrating the usefulness of the proposed methodology.

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“…For example, [12] developed the robust estimation and the local influence analysis for regression model with SMSN distribution. From Bayesian point of view, [13] considered the Bayesian estimation and the case influence diagnostics for nonlinear regression models with SMSN distributions. More related literature could be found in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions

Chen

Zeng

Song

2014

Abstract and Applied Analysis

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This paper deals with the issue of the likelihood inference for nonlinear models with a flexible skew-t-normal (FSTN) distribution, which is proposed within a general framework of flexible skew-symmetric (FSS) distributions by combining with skew-t-normal (STN) distribution. In comparison with the common skewed distributions such as skew normal (SN), and skew-t (ST) as well as scale mixtures of skew normal (SMSN), the FSTN distribution can accommodate more flexibility and robustness in the presence of skewed, heavy-tailed, especially multimodal outcomes. However, for this distribution, a usual approach of maximum likelihood estimates based on EM algorithm becomes unavailable and an alternative way is to return to the original Newton-Raphson type method. In order to improve the estimation as well as the way for confidence estimation and hypothesis test for the parameters of interest, a modified Newton-Raphson iterative algorithm is presented in this paper, based on profile likelihood for nonlinear regression models with FSTN distribution, and, then, the confidence interval and hypothesis test are also developed. Furthermore, a real example and simulation are conducted to demonstrate the usefulness and the superiority of our approach.

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Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

Cited by 50 publications

References 22 publications

A variational Bayesian approach for inverse problems with skew-t error distributions

A variational Bayesian approach for inverse problems with skew-t error distributions

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions

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