Related papers: Optimal Stopping for Interval Estimation in Bernou…
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
For the problem of sequential detection of changes, we adopt the probability maximizing approach in place of the classical minimization of the average detection delay, and propose modified versions of the Shiryaev, Lorden and Pollak…
We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Gaussian tails, and \emph{asymmetric}…
Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t "as close as possible" to its eventual supremum M_T:=sup{X_t: 0<=t<=T}, when…
The Birnbaum-Saunders distribution has been widely applied in several areas of science and although several methodologies related to this distribution have been proposed, the problem of determining the optimal sample size for estimating its…
The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…
In this paper, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and…
Suppose that $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. A Bernoulli factory for a function $f$ takes as input $X_1,X_2,\ldots$ and outputs a random variable that is Bernoulli with mean…
We propose a Bayesian Sequential procedure to test hypotheses concerning the Relative Risk between two specific treatments based on the binary data obtained from the two-arm clinical trial. Our development is based on the optimal sequential…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
In this paper, we propose a Thompson Sampling algorithm for \emph{unimodal} bandits, where the expected reward is unimodal over the partially ordered arms. To exploit the unimodal structure better, at each step, instead of exploration from…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
We initiate the study of the Interval Selection problem in the (streaming) sliding window model of computation. In this problem, an algorithm receives a potentially infinite stream of intervals on the line, and the objective is to maintain…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…
Interval designs are a class of phase I trial designs for which the decision of dose assignment is determined by comparing the observed toxicity rate at the current dose with a prespecified (toxicity tolerance) interval. If the observed…
Simultaneous perturbation stochastic approximation (SPSA) has proven to be efficient for recursive optimization. SPSA uses a centered difference approximation to the gradient based on two function evaluations regardless of the dimension of…