Random sampling and reconstruction of concentrated signals in a reproducing kernel space

The underlying objective of epidemiological investigations is to extrapolate results from a sample to the relevant population. The simplest way of achieving this is to adopt a sampling strategy in which each individual in the population has the same chance of being selected--that is, to employ an 'equal probability of selection method' (epsem). The easiest ways of achieving this are to use simple random sampling or stratified random sampling with a constant sampling fraction. These strategies are often impracticable, however, particularly in large investigations covering a wide geographical area where resource implications dictate a more complex approach such as multi-stage or cluster sampling. Following detailed definitions and appropriate illustrations of these terms, the main purpose of this paper is to provide a working guide of how to achieve epsem using these various random sampling techniques. In brief, for multi-stage sampling with the rare feature of equal-sized first stage units, epsem is achieved by applying the above simple or stratified approaches to the first stage units. Even in the more realistic scenario of unequal first stage units, the same options apply provided that a fixed proportion of second stage units are to be selected (cluster sampling is in fact just one example of this, with 100% sampling of second stage units). If on the other hand a fixed number of second stage units are to be selected then for epsem the first stage units should be selected with each one having a probability proportionate to its size.

Sampling and reconstruction of signals in a reproducing kernel subspace of [formula omitted

Compressed sensing (CS) sampling is a sampling method which is based on the signal sparse. Much information can be extracted from as little as possible of the data by applying CS and this method is the idea of great theoretical and applied prospects. In the framework of compressed sensing theory, the sampling rate is no longer decided in the bandwidth of the signal, but it depends on the structure and content of the information in the signal. In this paper, the signal is the sparse in the Fourier transform and random sparse sampling is advanced by programing random observation matrix for peak random base. The signal is successfully restored by the use of Bregman algorithm. The signal is described in the transform space, and a theoretical framework is established with a new signal descriptions and processing. By making the case to ensure that the information loss, signal is sampled at much lower than the Nyquist sampling theorem requiring rate,but also the signal is completely restored in high probability. The random sampling has following advantages: alias-free sampling frequency need not obey the Nyquist limit and higher frequency resolution.

This paper proposes to use simple random walk, a sampling method supported by most online social networks (OSN), to estimate a variety of properties of large OSNs. We show that due to the scale-free nature of OSNs the estimators derived from random walk sampling scheme are much better than uniform random sampling, even when uniform random samples are available disregarding the notorious high cost of obtaining the random samples. The paper first proposes to use harmonic mean to estimate the average degree of OSNs. The accurate estimation of the average degree leads to the discovery of other properties, such as the population size, the heterogeneity of the degrees, the number of friends of friends, the threshold value for messages to reach a large component, and Gini coefficient of the population. The method is validated in complete Twitter data dated in 2009 that contains 42 million nodes and 1.5 billion edges.

This ergonomics exposure assessment study compared the efficiency of eight 1-day-only strategies, that is, the relationship between the number of data collected per subject and the precision of the resulting mean exposure estimate. Whole-day electromyographic recordings from the right upper trapezius muscle in 24 cleaners and 23 office workers were processed to give minute-by-minute values of gap time and jerk time-parameters representing the level and frequency dimensions of muscle activation, respectively. On-site observations provided data on time spent in each of eight exhaustive task categories in the job, seven of which were associated with activities during work, and the last comprising breaks. On average, sampling at fixed intervals without regard to tasks doubled efficiency as compared with random sampling, which in turn was several times as efficient as consecutive sampling. Stratified sampling according to the two broad categories, work and breaks, increased efficiency for random and fixed-interval sampling, but the gain was distinct only among cleaners (about 20%). The commonly used strategy in ergonomic studies of sampling consecutively for short periods within tasks was highly inefficient. Further classification of work into the seven subcategories resulted in marginal additional increases in efficiency; on average less than 2%. A decision algorithm is given for determining appropriate sampling strategies in different types of jobs.

The birth-death process is widely used in phylogenetics to model speciation and extinction. Recent studies have shown that the inferred rates are sensitive to assumptions about the sampling probability of lineages. Here, we examine the effect of the method used to sample lineages. Whereas previous studies have assumed random sampling (RS), we consider two extreme cases of biased sampling: "diversified sampling" (DS), where tips are selected to maximize diversity and "cluster sampling (CS)," where sample diversity is minimized. DS appears to be standard practice, for example, in analyses of higher taxa, whereas CS may occur under special circumstances, for example, in studies of geographically defined floras or faunas. Using both simulations and analyses of empirical data, we show that inferred rates may be heavily biased if the sampling strategy is not modeled correctly. In particular, when a diversified sample is treated as if it were a random or complete sample, the extinction rate is severely underestimated, often close to 0. Such dramatic errors may lead to serious consequences, for example, if estimated rates are used in assessing the vulnerability of threatened species to extinction. Using Bayesian model testing across 18 empirical data sets, we show that DS is commonly a better fit to the data than complete, random, or cluster sampling (CS). Inappropriate modeling of the sampling method may at least partly explain anomalous results that have previously been attributed to variation over time in birth and death rates.

Sampling and Galerkin reconstruction in reproducing kernel spaces

This paper considers the estimation of the Fourier transform of continuous-time deterministic signals from a finite number N of discrete-time nonuniform observations. We first extend the recent results (mean and variance) of Tarczynski and Allay by providing both distributional properties as well as rates of almost sure convergence for the simple random sampling scheme of Tarczynski and Allay. The primary focus is to consider and investigate the properties of a class of stratified random sampling estimates. We establish the statistical properties of the estimates, including precise expressions and rate of convergence of the mean-square errors. We also establish the asymptotic normality of the estimates useful for confidence interval calculations. Further, we optimize over the class of the estimates in order to obtain the best performance. In particular, we show that for functions with a first-order continuous derivative, the mean-square estimation error decays precisely at the fast rate of 1/N/sup 3/. This rate is significantly higher than the rate of 1/N for simple random sampling estimates. The analytical results are illustrated by numerical examples. The effect of observation errors on the performance is also investigated.

Spatiotemporally representative Elementary Sampling Units (ESUs) are required for capturing the temporal variations in surface spatial heterogeneity through field measurements. Since inaccessibility often coexists with heterogeneity, a cost-efficient sampling design is mandatory. We proposed a sampling strategy to generate spatiotemporally representative and cost-efficient ESUs based on the conditioned Latin hypercube sampling scheme. The proposed strategy was constrained by multi-temporal Normalized Difference Vegetation Index (NDVI) imagery, and the ESUs were limited within a sampling feasible region established based on accessibility criteria. A novel criterion based on the Overlapping Area (OA) between the NDVI frequency distribution histogram from the sampled ESUs and that from the entire study area was used to assess the sampling efficiency. A case study in Wanglang National Nature Reserve in China showed that the proposed strategy improves the spatiotemporally representativeness of sampling (mean annual OA = 74.7%) compared to the single-temporally constrained (OA = 68.7%) and the random sampling (OA = 63.1%) strategies. The introduction of the feasible region constraint significantly reduces in-situ labour-intensive characterization necessities at expenses of about 9% loss in the spatiotemporal representativeness of the sampling. Our study will support the validation activities in Wanglang experimental site providing a benchmark for locating the nodes of automatic observation systems (e.g., LAINet) which need a spatially distributed and temporally fixed sampling design.

This study investigates the effect of diverse training samples on machine learning model performance for fine-grained emotion classification. Using four different sampling strategies (random sampling, sampling by topic and two variations of sampling by user), we found the class distribution of28 emotion categories to differ across the samples produced by each sampling strategy. However, combining different sampling strategies is complementary in generating sufficiently diverse training examples for the emotion classifiers. Based on support vector machine (SVM) and Bayesian network learning algorithms, our findings show that a classifier trained on combined data from the four sampling strategies performs better and is more generalizable than a classifier trained only on data from a single sampling strategy. Demonstrating how the diversity of the training samples affect the performance of emotion classifiers is the main contribution of this study.

The signal sampling in random environment is known to be much better option for many signal processing problems. The volume of data is a key factor for performance of many signal reconstruction from random samples. The high computation and resource requirement in processing for large signals introduces data chunking based processing techniques. The motivation from disadvantages of block based compressed sensing the non local self similar path based group block processing observed to be good reconstruction quality. In this paper such similar patches have been used along overlapping blocks followed by Stagewise Orthogonal Matching Pursuit (StOMP) reconstruction algorithm. The simulation results show good performance of the proposed method over existing methods.

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are studied under second order approximation. In third paper some estimators are proposed in two-phase sampling and their properties are studied in the presence of non-response. In fourth chapter a family of median based estimator is proposed in simple random sampling. In fifth paper some difference type estimators are suggested in simple random sampling and stratified random sampling and their properties are studied in presence of measurement error.

Compressive Sensing (CS) can alleviate the sensing effort involved in the acquisition of three dimensional image (3D) data. The most common CS sampling schemes employ uniformly random sampling because it is universal, thus it is applicable to almost any signals. However, by considering general properties of images and properties of the acquisition mechanism, it is possible to design random sampling schemes with variable density that have improved CS performance. We have introduced the concept of non-uniform CS random sampling a decade ago for holography. In this paper we overview the non-uniform CS random concept evolution and application for coherent holography, incoherent holography and for 3D LiDAR imaging.

A comparison of sampling strategies for histological image analysis

In this paper, we address the random sampling problem for the class of functions in the space of Mellin band-limited functions B T , which are concentrated on a bounded cube. It is established that any Mellin band-limited function can be approximated by an element in a finite-dimensional subspace of B T . Utilizing the notion of covering number and Bernstein’s inequality to the sum of independent random variables, we prove that the probabilistic sampling inequality holds for the set of concentrated signals in B T with an overwhelming probability provided the sampling size is large enough.