Related papers: Optimal Stopping for Interval Estimation in Bernou…

We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on…

We consider the problem of finding a proper confidence interval for the mean based on a single observation from a normal distribution with both mean and variance unknown. Portnoy (2017) characterizes the scale-sign invariant rules and shows…

In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…

We propose and analyze a continuous-time robust reinforcement learning framework for optimal stopping under ambiguity. In this framework, an agent chooses a robust exploratory stopping time motivated by two objectives: robust…

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…

We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…

We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…

We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…

A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation…

Conventional test-time adaptation (TTA) approaches typically adapt the model using only a small fraction of test samples, often those with low-entropy predictions, thereby failing to fully leverage the available information in the test…

We propose a sequential design method aiming at the estimation of an extreme quantile based on a sample of dichotomic data corresponding to peaks over a given threshold. This study is motivated by an industrial challenge in material…

We consider estimation of an optimal individualized treatment rule from observational and randomized studies when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying expected…

We consider the L\'evy model of the perpetual American call and put options with a negative discount rate under Poisson observations. Similar to the continuous observation case as in De Donno et al. [24], the stopping region that…

Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…

We present a method for computing optimal fixed-width confidence intervals for a single, bounded parameter, extending a method for the binomial due to Asparaouhov and Lorden, who called it the Push algorithm. The method produces the…

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed…

This paper introduces a novel $\mathcal{H}_{\infty}$-optimal interval observer synthesis for bounded-error/uncertain locally Lipschitz nonlinear continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations.…