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用拟似然估计方程分析空间二元数据AI 解读

The goal of this paper is to describe the application of quasi-likelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov–Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary…

基于周期抽样的自相关置信区间AI 解读

Clinger and Van Ness have shown how to sample a stochastic process in a periodic manner such that the autocorrelation function for that process can be estimated at all lags. We derive approximate confidence intervals for these estimates, focusing on low-order autoregressive moving average processes. Our methods are illustrated with an example from plant disease epidemiology.

基于周期抽样的自相关置信区间AI 解读

Clinger and Van Ness have shown how to sample a stochastic process in a periodic manner such that the autocorrelation function for that process can be estimated at all lags. We derive approximate confidence intervals for these estimates, focusing on low-order autoregressive moving average processes. Our methods are illustrated with an example from plant disease epidemiology.

发现新物种概率的非参数估计AI 解读

A random sample is taken from a population consisting of an unknown number of distinct species. A quantity of interest is the probability of discovering a new species when an additional draw from the population is made. An estimator of this quantity was introduced by Starr (1979). We prove a conjecture of Starr's that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator. A nonparametric maximum likelihood estimator that…

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贝叶斯非参数双臂老虎机AI 解读

Sequential selections are to be made from two stochastic processes, or "arms." At each stage the arm selected for observation depends on past observations. The objective is to maximize the expected sum of the first $n$ observations. For arm 1 the observations are identically distributed with probability measure $P$, and for arm 2 the observations have probability measure $Q; P$ is a Dirichlet process and $Q$ is known. An equivalent problem is deciding sequentially when to…

总体均值的贝叶斯非参数序贯检验AI 解读

We may take observations sequentially from a population with unknown mean $\theta$. After this sampling stage, we are to decide whether $\theta$ is greater or less than a known constant $\nu$. The net worth upon stopping is either $\theta$ or $\nu$, respectively, minus sampling costs. The objective is to maximize the expected net worth when the probability measure of the observations is a Dirichlet process with parameter $\alpha$. The stopping problem is shown to be…