핵심 개념
새로운 샘플링 방법인 기하광학 근사법을 통해 베이지안 역문제에 대한 효율적인 해결책 제시
초록
Markov chain Monte Carlo (MCMC) simulations are commonly used for Bayesian inference.
The proposed geometric optics approximation method (GOAM) eliminates the need for MCMC simulations.
Reflectors in optical systems redirect light to achieve desired density distributions.
The reflector shape design problem involves constructing reflecting surfaces for specific light distributions.
The method of supporting ellipsoids iteratively scales ellipsoid diameters to achieve desired target densities.
The supporting ellipsoid method ensures the reflector passes through a specific point and converges to a solution.
The stability of the geometric optics approximation measure with respect to the target domain is crucial.
The well-posedness of the reflector shape design problem is essential for efficient sampling.
The proposed method demonstrates efficiency and robustness in various numerical examples.
통계
MCMC 시뮬레이션은 베이지안 추론에 널리 사용됩니다.
기하광학 근사법은 MCMC 시뮬레이션의 필요성을 제거합니다.
인용구
"Our method is rooted in the problem of reflector shape design, which focuses on constructing a reflecting surface that redirects rays from a source."
"The proposed sampler, employing the geometric optics approximation method, demonstrates efficiency and robustness."