Posterior Covariance Information Criterion for Weighted Inference

Iba, Yukito; Yano, Keisuke

doi:10.48550/arxiv.2106.13694

Cited by 2 publications

(2 citation statements)

References 41 publications

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“…Although this paper proposed the estimation of η in fully Bayesian framework, the optimal tuning parameter in terms of prediction is also important. In particular, the predictive covariance information criterion (PCIC) recently proposed by Iba and Yano (2021) is based on the quasi-Bayes posterior and the advantage of the PCIC is to calculate by using only one-shot MCMC output. However, in the presence of outliers, the selection of weights in the criterion will be quite challenging.…”

Section: Discussionmentioning

confidence: 99%

Approximate Gibbs sampler for Bayesian Huberized lasso

Kawakami¹,

Hashimoto²

2022

Preprint

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The Bayesian lasso is well-known as a Bayesian alternative for lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be sensitive to outliers. To overcome such problem, robust Bayesian regression models have been proposed in recent years. In this paper, we consider the robust and efficient estimation for the Bayesian Huberized lasso regression in fully Bayesian perspective. A new posterior computation algorithm for the Bayesian Huberized lasso regression is proposed. The proposed approximate Gibbs sampler is based on the approximation of full conditional distribution and it is possible to estimate a tuning parameter for robustness of the pseudo-Huber loss function. Some theoretical properties of the posterior distribution are also derived. We illustrate performance of the proposed method through simulation studies and real data examples.

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Section: Discussionmentioning

confidence: 99%

Approximate Gibbs sampler for Bayesian Huberized lasso

Kawakami¹,

Hashimoto²

2022

Preprint

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“…The risk is − n i=1 E zi {log f IP (ỹ i | z, xi ; ξ)} based on this predictive distribution. A risk combining Bayesian prediction with inverse probability weighting has also been proposed in Iba and Yano (2021), but here our goal is a proposal that places importance on the advantage of propensity score analysis, which returns reasonable results without modeling the relationship between the outcome and confounding variables. For this risk, let − n i=1 log f IP (y i | z, x i ; ξ) be the initial evaluation, and use the asymptotic evaluation of the expectation of…”

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confidence: 99%

Prior Intensified Information Criterion

Ninomiya

2021

Preprint

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The widely applicable information criterion (WAIC) has been used as a model selection criterion for Bayesian statistics in recent years. It is an asymptotically unbiased estimator of the Kullback-Leibler divergence between a Bayesian predictive distribution and the true distribution. Not only is the WAIC theoretically more sound than other information criteria, its usefulness in practice has also been reported. On the other hand, the WAIC is intended for settings in which the prior distribution does not have an asymptotic influence, and as we set the class of the prior distribution to be more complex, it never fails to select the most complex one. To alleviate these concerns, this paper proposed the prior intensified information criterion (PIIC). In addition, it customizes this criterion to incorporate sparse estimation and causal inference. Numerical experiments show that the PIIC clearly outperforms the WAIC in terms of prediction performance when the above concerns are manifested.A real data analysis confirms that the results of variable selection and Bayesian estimators of the WAIC and PIIC differ significantly.

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Posterior Covariance Information Criterion for Weighted Inference

Cited by 2 publications

References 41 publications

Approximate Gibbs sampler for Bayesian Huberized lasso

Approximate Gibbs sampler for Bayesian Huberized lasso

Prior Intensified Information Criterion

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