Comparison of Second-Order Derivatives and Metamodel-Based Monte-Carlo Approaches to Estimate Statistics for Robust Design of a Transonic Wing

2008 ◽  
Author(s):  
Massimiliano Martinelli ◽  
Regis Duvigneau
Keyword(s):  
Monte Carlo ◽  
Robust Design ◽  
Second Order

Production Yield Estimation by the Metamodel Method With a Boundary-Focused Experiment Design

1997 ◽  
Author(s):  
Chinghsin Tu ◽  
Russell R. Barton
Keyword(s):  
Monte Carlo ◽  
Robust Design ◽  
Simulation Models ◽  
Experiment Design ◽  
Production Yield ◽  
Design Stage ◽  
Yield Estimation ◽  
Simulation Code ◽  
New Approach ◽  
A Priority

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.

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

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.

A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

2019 ◽  
Vol 25 (4) ◽  
pp. 341-361
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Malliavin Calculus ◽  
Second Order ◽  
Discretization Method ◽  
Local Approximations ◽  
Backward Sdes

Abstract The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers

2013 ◽  
Vol 9 (10) ◽  
pp. 4396-4402 ◽  
Author(s):  
Soohaeng Yoo Willow ◽  
Matthew R. Hermes ◽  
Kwang S. Kim ◽  
So Hirata
Keyword(s):  
Monte Carlo ◽  
Convergence Acceleration ◽  
Second Order ◽  
Many Body
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