We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P . We show that the upper Snell envelope Z of the reward process Y is a supermarti...

We study the stability of the optimal stopping problem for a discrete-time Markov process on a general space state X. Revenue and cost functions are allowed to be unbounded. The stability (robustness) is understood in the sense that an unknown transition probability p(·|x), x ∈ X, is approximated by the known one p̃(·|x), x ∈ X, and the stopping rule τ̃∗, optimal for the process governed by p̃ is ...

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P. We show that the upper Snell envelope Z of the reward process Y is a supermartin...

In Surrogate-based optimization, each optimization cycle consists of fitting a surrogate to a number of simulations at a set of design points, and performing optimization based on the surrogate to obtain one or more new design points. Algorithms like Efficient Global Optimization (EGO) [1] use uncertainty estimates available with the Kriging surrogate to guide the selection of new point(s). The...

Patients with systemic reactions (SR) to Hymenoptera stings are successfully treated by venom immunotherapy (VIT), but there is not yet a general agreement on the criteria for stopping VIT. We discuss the importance of the venom-specific IgE levels among these criteria. In particular, the results from a recent study evaluating the IgE changes during a 5-year VIT, in patients stung and protected...

In the conduct of sequential clinical trials, primary statistical issues include design , monitoring and reporting. Currently, approaches built upon frequentist inference methodology predominate. Focusing on the design aspect, our objective is the development of a very general Bayesian framework permitting multiple arms with multiple patient endpoints and multiple stopping criteria. It is impor...