论文检索

多臂老虎机问题：一种有效率的非参数解法AI 解读

Lai and Robbins (Adv. in Appl. Math. 6 (1985) 4–22) and Lai (Ann. Statist. 15 (1987) 1091–1114) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback–Leibler information of the reward distributions, estimated from specified parametric families. In recent years, there has been renewed interest in the multi-armed bandit…

多数据流中的最优序贯检测AI 解读

Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the (optimal) detection delay depends on the fraction of data streams undergoing…

条件矩不等式的多尺度自适应推断AI 解读

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple analytic formula, and to prove the asymptotic validity of a modified bootstrap procedure. The asymptotic distribution is extreme value, and the proof uses new techniques to overcome several technical obstacles. The test detects local…

多样本对齐稀疏信号的最优检测AI 解读

We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk–Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the…

隐马尔可夫模型粒子滤波的一般理论及应用AI 解读

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.

利用平均似然比统计量检测空间聚集AI 解读

Generalized likelihood ratio (GLR) test statistics are often used in the detection of spatial clustering in case-control and case-population datasets to check for a significantly large proportion of cases within some scanning window. The traditional spatial scan test statistic takes the supremum GLR value over all windows, whereas the average likelihood ratio (ALR) test statistic that we consider here takes an average of the GLR values. Numerical experiments in the…

神经脉冲序列概率模型的若干理论结果AI 解读

This article contains two main theoretical results on neural spike train models, using the counting or point process on the real line as a model for the spike train. The first part of this article considers template matching of multiple spike trains. P-values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system. By identifying the pattern with an experimental stimulus, multiple spike trains can be deciphered…

具有先后约束的一类序贯控制问题的最优策略AI 解读

Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown…

带权观测的扫描统计量AI 解读

We examine scan statistics for one-dimensional marked Poisson processes. Such statistics tabulate the maximum weighted count of event occurrences within a window of predetermined width over all windows within an observed interval. We derive analytical formulas and also give an importance sampling method for approximating the tail probabilities of scan statistics. Because high-throughput genomic sequencing has led to the availability of massive amounts of biomolecular…

指数族中序贯检验与固定样本量检验错误概率的渐近近似AI 解读

Asymptotic approximations for the error probabilities of sequential tests of composite hypotheses in multiparameter exponential families are developed herein for a general class of test statistics, including generalized likelihood ratio statistics and other functions of the sufficient statistics. These results not only generalize previous approximations for Type I error probabilities of sequential generalized likelihood ratio tests, but also pro- vide a unified treatment of…