Introduction: Proton therapy is a type of radiation treatment that it uses protons to treat cancer. Because of the protons’ unique ability to distribute the radiation dose more directly to the tumor, it minimizes the damage to nearby healthy tissues. The rate of energy loss by the ion in the target is called stopping power. The total stopping power is sum nuclear and electroni...

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in...

A new stopping rule is proposed for linear, iterative signal restoration using the gradient descent and conjugate gradient algorithms. The stopping rule attempts to minimize MSE under the assumption that the signal arises from a white noise process. This assumption is appropriate for many coherent imaging applications. The stopping rule is trivial to compute, and for xed relaxation parameters, ...

Information search is critical in most decision-making tasks. An important aspect of information search is the stopping rule used by the decision maker to terminate information acquisition. Decision-making problems may be usefully decomposed into design problems and choice problems. The distinction is critical because the goals of stopping behavior in the two types of problems are quite differe...

Group sequential stopping rules are often used as guidelines in the monitoring of clinical trials in order to address the ethical and efficiency issues inherent in human testing of a new treatment or preventive agent for disease. Such stopping rules have been proposed based on a variety of different criteria, both scientific (e.g. estimates of treatment effect) and statistical (e.g. frequentist...

in a subclass of the scale-parameter exponential family, we consider the sequential pointestimation of a function of the scale parameter under the loss function given as the sum of the weightedsquared error loss and a linear cost. for a fully sequential sampling scheme, second order expansions areobtained for the expected sample size as well as for the regret of the procedure. the former resear...

Multi-arm group sequential clinical trials are efficient designs to compare multiple treatments to a control. They allow one to test for treatment effects already in interim analyses and can have a lower average sample number than fixed sample designs. Their operating characteristics depend on the stopping rule: We consider simultaneous stopping, where the whole trial is stopped as soon as for ...