Related papers: Optimal Stopping for Interval Estimation in Bernou…
Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus…
This work investigates the optimal selection of the $m$th last success in a sequence of $n$ independent Bernoulli trials. We propose a threshold strategy that is $\varepsilon$-optimal under minimal assumptions about the monotonicity of the…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
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…
We construct exact confidence intervals for the average treatment effect in randomized experiments with binary outcomes using sequences of randomization tests. Our approach does not rely on large-sample approximations and is valid for all…
This paper has been withdrawn by the authors. Please see arXiv:1302.6058. We consider the sequential joint detection and estimation problem. Minimizing the average stopping time subject to a combination of detection and estimation…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple…
This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different…
We analyse the asymptotic behaviour of the probability of observing the expected number of successes at each stage of a sequence of nested Bernoulli trials. Our motivation is the attempt to give a genuinely frequentist interpretation to the…
This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
We study properties of confidence intervals (CIs) for the difference of two Bernoulli distributions' success parameters, $p_x - p_y$, in the case where the goal is to obtain a CI of a given half-width while minimizing sampling costs when…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
In this paper we consider the problem of estimating a Bernoulli parameter using finite memory. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables with expectation $\theta$, where $\theta \in…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
Recently, methodology was presented to facilitate the incorporation of interim analyses in stepped-wedge (SW) cluster randomised trials (CRTs). Here, we extend this previous discussion. We detail how the stopping boundaries, allocation…