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稀疏捕获数据的多系统估计：名单不重叠时的推断挑战AI 解读

Multiple systems estimation strategies have recently been applied to quantify hard-to-reach populations, particularly when estimating the number of victims of human trafficking and modern slavery. In such contexts, it is not uncommon to see sparse or even no overlap between some of the lists on which the estimates are based. These create difficulties in model fitting and selection, and we develop inference procedures to address these challenges. The approach is based on…

通过贝叶斯先验—后验转移拟合实现时间扭曲的多分辨率方法AI 解读

Summary Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian…

小波阈值的经验贝叶斯选择AI 解读

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also…

大海捞针：可能稀疏序列的经验贝叶斯估计AI 解读

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density γ, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If estimation is then carried out using the posterior median, this is a random thresholding procedure. Other thresholding…

小波阈值估计的后验概率区间AI 解读

Summary We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable modification of the discrete wavelet transform allows the posterior…

通过系数依赖阈值扩展小波回归方法的适用范围AI 解读

Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques to irregularly spaced data, to regularly spaced datasets of arbitrary size, to heteroscedastic and correlated data, and to data that contain outliers. The core of the methodology is an algorithm for finding ail of the variances and within-level covariances in the wavelet table of a sequence with given covariance structure. If…

相关噪声数据的小波阈值估计AI 解读

Summary Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coefficients in the wavelet transform. A variety of threshold choices is proposed, including one based on an unbiased estimate of mean-squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological context. The theoretical properties of the estimators are investigated…

通过范数选择实现平滑函数主成分分析AI 解读

The principal components analysis of functional data is often enhanced by the use of smoothing. It is shown that an attractive method of incorporating smoothing is to replace the usual $L^2$-orthonormality constraint on the principal components by orthonormality with respect to an inner product that takes account of the roughness of the functions. The method is easily implemented in practice by making use of appropriate function transforms (Fourier transforms for periodic…

正电子发射断层成像及相关逆问题的估计速度AI 解读

Several algorithms for image reconstruction in positron emission tomography (PET) have been described in the medical and statistical literature. We study a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations. Given a large sample of indirect observations, we consider the size of the equivalent sample of observations, whose original exact positions would allow equally accurate…

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密度及其导数核估计的弱、强一致收敛AI 解读

The estimation of a density and its derivatives by the kernel method is considered. Uniform consistency properties over the whole real line are studied. For suitable kernels and uniformly continuous densities it is shown that the conditions $h \rightarrow 0$ and $(nh)^{-1} \log n \rightarrow 0$ are sufficient for strong uniform consistency of the density estimate, where $n$ is the sample size and $h$ is the "window width." Under certain conditions on the kernel, conditions…