Related papers: Optimal Stopping for Interval Estimation in Bernou…
A set of intervals is independent when the intervals are pairwise disjoint. In the interval selection problem we are given a set $\mathbb{I}$ of intervals and we want to find an independent subset of intervals of largest cardinality. Let…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
This paper studies an optimal stopping problem for L\'evy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…
Given a composite null hypothesis H, test supermartingales are non-negative supermartingales with respect to H with initial value 1. Large values of test supermartingales provide evidence against H. As a result, test supermartingales are an…
In this paper, we study the optimal stopping problem in the case where the reward is given by a family $(\phi(\tau ),\;\;\tau \in \stopo)$ of non negative random variables indexed by predictable stopping times. We treat the problem by means…
Consider a discrete-time optimal selection problem where one observes a sequence of independent Bernoulli trials and receives a nonnegative reward upon stopping on a success. The aim is to find a single-choice strategy that maximises the…
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests…
This paper introduces Conformal Thresholded Intervals (CTI), a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. Unlike existing methods that rely on nested conformal…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit…
Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed…
Suppose we have a memory storing $0$s and $1$s and we want to estimate the frequency of $1$s by sampling. We want to do this I/O-efficiently, exploiting that each read gives a block of $B$ bits at unit cost; not just one bit. If the input…
Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: \emph{when is there already enough…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Given two probability measures $\mu, \nu$ on $\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\tau$ that maximize/minimize the cost functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$, where $(B_t)_t$ is…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is…