Related papers: Design and performance evaluation in Kiefer-Weiss …
We present a computational approach to solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the…
In this paper, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations we obtain the form of…
A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size of a sequential test. However, instead of…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
In this paper we deal with the problem of sequential testing of multiple hypotheses. The main goal is minimizing the expected sample size (ESS) under restrictions on the error probabilities. We take, as a criterion of minimization, a…
In this paper, we deal with sequential testing of multiple hypotheses. In the general scheme of construction of optimal tests based on the backward induction, we propose a modification which provides a simplified (generally speaking,…
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A-, D-, and E-optimal…
Hyperparameter tuning is one of the the most time-consuming parts in machine learning. Despite the existence of modern optimization algorithms that minimize the number of evaluations needed, evaluations of a single setting may still be…
This paper investigates the problem of online statistical inference of model parameters in stochastic optimization problems via the Kiefer-Wolfowitz algorithm with random search directions. We first present the asymptotic distribution for…
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…
The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For…
The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…
The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an…
We consider an input-to-response (ItR) system characterized by (1) parameterized input with a known probability distribution and (2) stochastic ItR function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme…
In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure. The further investigations…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…