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利用自适应筛选程序检测多个可重复信号AI 解读

Replicability is a fundamental quality of scientific discoveries: we are interested in those signals that are detectable in different laboratories, different populations, across time etc. Unlike meta-analysis which accounts for experimental variability but does not guarantee replicability, testing a partial conjunction (PC) null aims specifically to identify the signals that are discovered in multiple studies. In many contemporary applications, for example, comparing…

大规模交叉随机效应回归的回拟合算法AI 解读

Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as N3/2 (or worse) for N observations. Papaspiliopoulos, Roberts and Zanella (Biometrika 107 (2020) 25–40) present a collapsed Gibbs sampler that costs O(N), but under an extremely stringent sampling model. We propose a backfitting algorithm to compute a generalized least squares estimate and prove that it costs…

确定性平行分析：因子与主成分数量选择的改进方法AI 解读

Summary Factor analysis and principal component analysis are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of the most popular state of the art methods is parallel analysis (PA), which compares the observed factor strengths with simulated strengths under a noise-only model. The paper proposes improvements to PA. We first derandomize it,…

通过广义 Stolarsky 不变性近似置换检验 p 值AI 解读

It is common for genomic data analysis to use $p$-values from a large number of permutation tests. The multiplicity of tests may require very tiny $p$-values in order to reject any null hypotheses and the common practice of using randomly sampled permutations then becomes very expensive. We propose an inexpensive approximation to $p$-values for two sample linear test statistics, derived from Stolarsky’s invariance principle. The method creates a geometrically derived…

部分合取检验中的可容许性AI 解读

Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial conjunction null hypothesis is rejected only when at least r of n component hypotheses are nonnull with r = 1 corresponding to a usual meta-analysis. Compared with meta-analysis, it can encourage replicable findings across studies. A by-product…

多重假设检验中的混杂因素调整AI 解读

We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable(s) of interest (e.g., treatment variable, phenotype) and the outcome. Over the past decade, many statistical methods have been proposed to adjust for the confounders in…

可扩展网格：空间填充曲线上的均匀采样AI 解读

Summary We study the properties of points in [0,1]d generated by applying Hilbert's space filling curve to uniformly distributed points in [0, 1]. For deterministic sampling we obtain a discrepancy of O(n−1/d) for d⩾2. For random stratified sampling, and scrambled van der Corput points, we derive a mean-squared error of O(n−1−2/d) for integration of Lipschitz continuous integrands, when d⩾3. These rates are the same as those obtained by sampling on d-dimensional grids and…

效应量具有高斯先验时的最优多重检验AI 解读

We develop a new method for large-scale frequentist multiple testing with Bayesian prior information. We find optimal $p$-value weights that maximize the average power of the weighted Bonferroni method. Due to the nonconvexity of the optimization problem, previous methods that account for uncertain prior information are suitable for only a small number of tests. For a Gaussian prior on the effect sizes, we give an efficient algorithm that is guaranteed to find the optimal…

Zipf–Poisson集合中的正确排序AI 解读

Rankings based on counts are often presented to identify popular items, such as baby names, English words, or Web sites. This article shows that, in some examples, the number of correctly identified items can be very small. We introduce a standard error versus rank plot to diagnose possible misrankings. Then to explain the slowly growing number of correct ranks, we model the entire set of count data via a Zipf–Poisson ensemble with independent Xi ∼ Poi(Ni − α) for α > 1 and…

用非凸惩罚回归检测异常值AI 解读

This article studies the outlier detection problem from the standpoint of penalized regression. In the regression model, we add one mean shift parameter for each of the n data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual L1 penalty yields a convex criterion, but fails to deliver a robust estimator. The L1 penalty corresponds to soft thresholding. We introduce a thresholding (denoted by Θ) based iterative procedure for…

结合扰乱网的局部对偶采样AI 解读

We consider the problem of computing an approximation to the integral I=∫[0, 1]d f(x) dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n−1/2) from n independent random function evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully equispaced evaluation points can attain the rate O(n−1+ɛ) for any ɛ>0 and randomized QMC (RQMC) can attain the RMSE O(n−3/2+ɛ), both under mild conditions on f. Classical variance reduction…

错误发现数量的方差AI 解读

Summary In high throughput genomic work, a very large number d of hypotheses are tested based on n≪d data samples. The large number of tests necessitates an adjustment for false discoveries in which a true null hypothesis was rejected. The expected number of false discoveries is easy to obtain. Dependences between the hypothesis tests greatly affect the variance of the number of false discoveries. Assuming that the tests are independent gives an inadequate variance formula.…

高维函数线性程度的评估AI 解读

Some standard numerical problems become intractable in high dimensions. Yet successes are often achieved in practice. This may be explained in terms of the underlying target function being somehow simpler than assumed in the intractability arguments. A prototypical form of simplicity is approximate linearity. In moderate dimensions, linearity can be investigated by linear regression. In very high dimensions, this becomes computationally inefficient and eventually infeasible,…

光滑函数积分的扰乱网格方差AI 解读

Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. One version, randomized $(t, m, s)$-nets, has the property that the integral estimates are unbiased and that the variance is $o(1/n)$, for any square integrable integrand. Stronger assumptions on the integrand allow one to find rates of convergence. This paper shows that for smooth integrands over…

分布函数的非参数似然置信带AI 解读

Berk and Jones described a nonparametric likelihood test of uniformity with greater asymptotic Bahadur efficiency than any weighted Kolmogorov–Smirnov test at any alternative to U[0, 1]. We invert this test to form confidence bands for a distribution function using Noé's recursion. Nonparametric likelihood bands are narrower in the tails and wider in the center than Kolmogorov-Smirnov bands and are asymmetric about the empirical cumulative distribution function. This article…

拉丁超立方抽样的中心极限定理AI 解读

SUMMARY Latin hypercube sampling (LHS) is a technique for Monte Carlo integration, due to McKay, Conover and Beckman. M. Stein proved that LHS integrals have smaller variance than independent and identically distributed Monte Carlo integration, the extent of the variance reduction depending on the extent to which the integrand is additive. We extend Stein's work to prove a central limit theorem. Variance estimation methods for nonparametric regression can be adapted to…

单个统计泛函的经验似然比置信区间AI 解读

The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable…