Sensitivity estimations for Bayesian inference models solved by MCMC methods

Pérez, Carlos J.; Jd, Martín; Rufo, M. J.

doi:10.1016/j.ress.2005.11.029

Cited by 22 publications

(7 citation statements)

References 7 publications

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“…[15], following many previous theoretical works [4], exchanges the integral in a posterior expectation with the derivative with respect to prior perturbations, giving a robustness estimate that can be evaluated from MCMC samples. [16,17] extends this idea. These approaches exploit importance sampling and / or closed forms for derivatives or posterior densities, and care must be taken to control the variance of the MCMC estimates.…”

Section: Appendices a Robust Bayes With Mcmcmentioning

confidence: 89%

Robust Inference with Variational Bayes

Giordano¹,

Broderick²,

Jordan³

2015

Preprint

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Section: Appendices a Robust Bayes With Mcmcmentioning

confidence: 89%

Robust Inference with Variational Bayes

Giordano¹,

Broderick²,

Jordan³

2015

Preprint

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“…Various statistical inferences can then be made based on these samples. Due to its high efficiency and robustness, MCMC has been widely used in many fields (Pérez et al,2006;Ching and Chen, 2007;Zhao and Wang, 2020). In this study, the BMA method was implemented using the BMS package in R (Zeugner, 2011).…”

Section: Bayesian Model Averaging (Bma)mentioning

confidence: 99%

Forecasting of monthly precipitation based on ensemble empirical mode decomposition and Bayesian model averaging

et al. 2022

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Precipitation prediction is crucial for water resources management and agricultural production. We deployed a hybrid model based on ensemble empirical mode decomposition (EEMD) and Bayesian model averaging (BMA), called EEMD-BMA, for monthly precipitation series data at Kunming station from January 1951 to December 2020. Firstly, the monthly precipitation data series was decomposed into multiple Intrinsic Mode Functions (IMFs) and a residue with EEMD. Next, autoregressive integrated moving average (ARIMA), support vector regression (SVR) and long short-term memory (LSTM) models are used to predict components respectively. The prediction results of EEMD-ARIMA, EEMD-SVR and EEMD-LSTM are obtained by summing the prediction results of each component. Finally, BMA is used to combine the prediction results of the EEMD-ARIMA, EEMA-SVR and EEMD-LSTM models, whose weights are calculated by birth-death Markov Chain Monte Carlo algorithm. The results show that the proposed EEMD-BMA model provides more accurate precipitation predictions than the individual models; the RMSE is 17.2811 mm, the MAE is 12.6999 mm and the R2 is 0.9573. Moreover, the coverage probability (CP) and mean width (MW) of the 90% confidence interval for the predicted values of the EEMD-BMA model are 0.9375 and 60.315 mm, respectively. Therefore, the proposed EEMD-BMA model has good application prospects and can provide a basis for decision makers to develop measures against potential disasters.

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“…i.e., we set both p(β 0 ) ∝ 1 and p(θ 0 ) ∝ 1 and exponential densities with means ξ −1 1 and ξ −1 2 respectively for a β and a η . The exponential distribution is a common choice for the shape parameter of the Gamma-Poisson hierarchical model (see for example George, Makov and Smith (1993), and related applications Pérez, Martín and Rufo (2006) for the PLP hierarchical model. In Section 3 we discuss the specification of ξ 1 and ξ 2 .…”

Section: A Hierarchical Plp Modelmentioning

confidence: 99%

Hierarchical modelling of power law processes for the analysis of repairable systems with different truncation times: An empirical Bayes approach

Reis¹,

Colosimo²,

Gilardoni³

2019

Braz. J. Probab. Stat.

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In the data analysis from multiple repairable systems it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.

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Sensitivity estimations for Bayesian inference models solved by MCMC methods

Cited by 22 publications

References 7 publications

Robust Inference with Variational Bayes

Robust Inference with Variational Bayes

Forecasting of monthly precipitation based on ensemble empirical mode decomposition and Bayesian model averaging

Hierarchical modelling of power law processes for the analysis of repairable systems with different truncation times: An empirical Bayes approach

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