Related papers: Efficient uncertainty quantification for Monte Car…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
Importance sampling and independent Metropolis-Hastings (IMH) are among the fundamental building blocks of Monte Carlo methods. Both require a proposal distribution that globally approximates the target distribution. The Radon-Nikodym…
Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…
Monte Carlo (MC) is generally considered as the most accurate dose calculation tool for particle therapy. However, a proper description of the beam particles kinematics is a necessary input for a realistic simulation. Such a description can…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…
Classifying variable stars is key for understanding stellar evolution and galactic dynamics. With the demands of large astronomical surveys, machine learning models, especially attention-based neural networks, have become the…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
This paper introduces a new approach to quantify the impact of forward propagated demand and weather uncertainty on power system planning and operation models. Recent studies indicate that such sampling uncertainty, originating from demand…
A platform trial with a master protocol provides an infrastructure to ethically and efficiently evaluate multiple treatment options in multiple diseases. Given that certain study drugs can enter or exit a platform trial, the randomization…
Background: Inverse probability of treatment weighting (IPTW) is used for confounding adjustment in observational studies. Newer weighting methods include energy balancing (EB), kernel optimal matching (KOM), and tailored-loss covariate…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance…
This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…
Cancer is a primary cause of morbidity and mortality worldwide. The radiotherapy plays a more and more important role in cancer treatment. In the radiotherapy, the dose distribution maps in patient need to be calculated and evaluated for…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
Understanding decisions made by neural networks is key for the deployment of intelligent systems in real world applications. However, the opaque decision making process of these systems is a disadvantage where interpretability is essential.…
The interplay between the beam delivery time structure and the patient motion makes 4D dose calculation (4DDC) important when treating moving tumors with intensity modulated proton therapy. 4DDC based on phase sorting of a 4DCT suffers from…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided…