Robust design using Bayesian Monte Carlo

Abstract The need for yield estimation strategies in the design stage is a priority recognized by industry. Yield estimates can be employed to assess the manufacturability of a design, and allow for modification to produce a robust design. Therefore, low yield of products can be avoided and costs for manufacturing can be reduced. This paper presents an accurate and time-efficient yield estimation approach for use with simulation models. We use a metamodel-based method, which is time-efficient compared to crude Monte Carlo yield estimation using the original simulation code. The approach employs a boundary-focused experiment design, which overcomes the inaccuracy of yield estimates that can occur when using a metamodel method. The results of two examples demonstrate the effectiveness of this new approach.

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Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design

Entropy ◽

10.3390/e22020258 ◽

2020 ◽

Vol 22 (2) ◽

pp. 258

Author(s):

Zhihang Xu ◽

Qifeng Liao

Keyword(s):

Monte Carlo ◽

Optimal Design ◽

Information Gain ◽

Computational Cost ◽

Bayesian Optimization ◽

Likelihood Functions ◽

Expected Information ◽

Bayesian Optimal Design ◽

Bayesian Monte Carlo ◽

Expected Information Gain

Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.

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Bayesian Monte Carlo approach for developing stochastic railway track degradation model using expert-based priors

Structure and Infrastructure Engineering ◽

10.1080/15732479.2020.1836001 ◽

2020 ◽

pp. 1-22

Author(s):

Mahsa Movaghar ◽

Saeed Mohammadzadeh

Keyword(s):

Monte Carlo ◽

Railway Track ◽

Degradation Model ◽

Monte Carlo Approach ◽

Bayesian Monte Carlo

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Aging trajectory prediction for lithium-ion batteries via model migration and Bayesian Monte Carlo method

Applied Energy ◽

10.1016/j.apenergy.2019.113591 ◽

2019 ◽

Vol 254 ◽

pp. 113591 ◽

Cited By ~ 15

Author(s):

Xiaopeng Tang ◽

Changfu Zou ◽

Ke Yao ◽

Jingyi Lu ◽

Yongxiao Xia ◽

...

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Lithium Ion Batteries ◽

Lithium Ion ◽

Trajectory Prediction ◽

Model Migration ◽

Bayesian Monte Carlo

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Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes

Statistical Methods in Medical Research ◽

10.1177/0962280219850588 ◽

2019 ◽

Vol 29 (3) ◽

pp. 934-952

Author(s):

Jérémy Seurat ◽

Thu Thuy Nguyen ◽

France Mentré

Keyword(s):

Monte Carlo ◽

Longitudinal Studies ◽

Robust Design ◽

Fisher Information ◽

Model Uncertainty ◽

Fisher Information Matrix ◽

Information Matrix ◽

Average Power ◽

Binary Outcomes ◽

Mixed Effect

To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.

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