Related papers: An optimised multi-arm multi-stage clinical trial …
Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
We introduce a new multiple type I error criterion for clinical trials with multiple populations. Such trials are of interest in precision medicine where the goal is to develop treatments that are targeted to specific sub-populations…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…
This paper introduces a new Phase I design aimed at enhancing the performance of existing methods, including algorithm-based, model-based, and model-assisted designs. The design, developed by integrating the concept of Fisher information,…
A common method to reduce the uncertainty of causal inferences from experiments is to assign treatments in fixed proportions within groups of similar units: blocking. Previous results indicate that one can expect substantial reductions in…
We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Randomization is a common technique used in clinical trials to eliminate potential bias and confounders in a patient population. Equal allocation to treatment groups is the standard due to its optimal efficiency in many cases. However, in…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a…
An important task in early phase drug development is to identify patients, which respond better or worse to an experimental treatment. While a variety of different subgroup identification methods have been developed for the situation of…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…