Exact Sampling Research Articles

Efficient solving algorithm for determining the exact sampling condition of limited-angle computed tomography reconstruction.

Total variation (TV) regularization-based iterative reconstruction algorithms have an impressive potential to solve limited-angle computed tomography with insufficient sampling projections. The analysis of exact reconstruction sampling conditions for a TV-minimization reconstruction model can determine the minimum number of scanning angle and minimize the scanning range. However, the large-scale matrix operations caused by increased testing phantom size are the computation bottleneck in determining the exact reconstruction sampling conditions in practice. When the size of the testing phantom increases to a certain scale, it is very difficult to analyze quantitatively the exact reconstruction sampling condition using existing methods. In this paper, we propose a fast and efficient algorithm to determine the exact reconstruction sampling condition for large phantoms. Specifically, the sampling condition of a TV minimization model is modeled as a convex optimization problem, which is derived from the sufficient and necessary condition of solution uniqueness for the L1 minimization model. An effective alternating direction minimization algorithm is developed to optimize the objective function by alternatively solving two sub-problems split from the convex problem. The Cholesky decomposition method is used in solving the first sub-problem to reduce computational complexity. Experimental results show that the proposed method can efficiently solve the verification problem of the accurate reconstruction sampling condition. Furthermore, we obtain the lower bounds of scanning angle range for the exact reconstruction of a specific phantom with the larger size.

Law of the First Passage Triple of a Spectrally Positive Strictly Stable Process

For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the “first passage triple” that consists of the time of first passage and the undershoot and the overshoot at first passage. The result leads to several corollaries, including (1) the joint law of the first passage triple and the pre-passage running supremum, and (2) at a fixed time point, the joint law of the process’ value, running supremum, and the time of the running supremum. The representation can be decomposed as a sum of strictly positive functions that allow exact sampling of the first passage triple.

Sampling depth of L-band radiometer measurements of soil moisture and freeze-thaw dynamics on the Tibetan Plateau

Knowing the exact sampling depth of microwave radiometry is essential for quantifying the performance and appreciation of the applicability of satellite soil moisture products. We investigate in this study the sampling depth (δSM) of the L-band microwave emission under frozen and thawed soil conditions on the Tibetan Plateau. Two years of diurnal brightness temperature (TBp) measurements at a time interval of 30 min are collected by the ELBARA-III radiometer deployed at a Tibetan meadow site. Vertical profiles of soil temperature and volumetric liquid water content (θliq) are measured simultaneously at soil depths up to 1 m below the surface. The impact of the θliq measured at different depths on the microwave emission simulations is assessed using the τ-ω emission model, whereby the permittivity of frozen and thawed soil is estimated by the four-phase dielectric mixing model. It is found that: 1) the sampling depth for the effective temperature depends on the magnitude of θliq, and is estimated to be, on average, about 50 and 15 cm for the cold dry and wet warm period, respectively, because of the seasonality in θliq; 2) the δSM is determined at 2.5 cm for both frozen and thawed soil conditions during both cold and warm periods, which is shallower than the commonly used θliq measurement depth (i.e. 5 cm) adopted for the in-situ monitoring networks across the globe; 3) the TBp simulations performed with the θliq measurements taken at the estimated δSM of 2.5 cm result in lower unbiased root mean squared errors, about 14% (3.16 K) and 22% (3.36 K) for the horizontal and vertical polarizations respectively, in comparison to the simulations with the θliq measurements taken from 5 cm soil depth; and 4) the θliq retrieved with the single channel algorithm from the ELBARA-III measured vertically polarized TBp are in better agreement with the θliq measured at 2.5 cm than the one measured at 5 cm. These findings are crucial for developing strategies for the calibration/validation as well as the application of satellite based soil moisture products relying on the L-band radiometry.

A novel approach for selecting sampling points locations to river water quality monitoring in data-scarce regions

In order to rationalize a surface water quality monitoring network (WQMN), it is critical to appropriately design surface water quality sampling locations. This is due to high installation, operational, and maintenance costs for each sampling representative of the whole water system conditions. The main objective of this study was to propose an integrated method to determine the most appropriate sampling points in the Khoy watershed northwest of Iran, where financial resources and water quality data are limited. Multi criteria evaluation method including analytic network process (ANP) and Fuzzy logic were incorporated in River Mixing Length (RML) procedure in order to identify exact locations of sampling points. Based on RML procedure, 15 candidate sampling points were identified to suitably select sampling points based on budget deficiency. Relative weights for 12 criteria and 10 sub-criteria related to non-point sources and surficial rocks as well as criteria of topography were then calculated by the ANP method. According to the obtained results, a new total potential pollution score (TPPS) was presented to prioritize 15 candidate sampling points. Then, the values of TPPS were classified and fuzzified to distinguish real differences between scores. Based on current monitoring stations and budget deficiency, the hierarchy value, and Fuzzy rank, six points are proposed as the most appropriate locations for surface water quality monitoring. Furthermore, four points are identified as the second most appropriate for enhancing a robust WQMN in the study area in order for an expansion plan in the future. The results of this study should be valuable for water quality monitoring agencies looking for an efficient approach for selecting exact sampling locations.

Non-Asymptotic Guarantees for Sampling by Stochastic Gradient Descent

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, it is only very recently that a mathematical theory providing non-asymptotic guarantees for approximate sampling problem in the high-dimensional settings started to be developed. In this paper we introduce a new mathematical framework that helps to analyze the Stochastic Gradient Descent as a method of sampling, closely related to Langevin Monte-Carlo.

Exact sampling of the infinite horizon maximum of a random walk over a nonlinear boundary

AbstractWe present the first algorithm that samples maxn≥0{Sn − nα}, where Sn is a mean zero random walk, and nα with $\alpha \in ({1 \over 2},1)$ defines a nonlinear boundary. We show that our algorithm has finite expected running time. We also apply this algorithm to construct the first exact simulation method for the steady-state departure process of a GI/GI/∞ queue where the service time distribution has infinite mean.

Preanalytical challenges - time for solutions.

The European Federation of Clinical Chemistry and Laboratory Medicine (EFLM) Working Group for the Preanalytical Phase (WG-PRE) was originally established in 2013, with the main aims of (i) promoting the importance of quality in the preanalytical phase of the testing process, (ii) establishing best practices and providing guidance for critical activities in the preanalytical phase, (iii) developing and disseminating European surveys for exploring practices concerning preanalytical issues, (iv) organizing meetings, workshops, webinars or specific training courses on preanalytical issues. As education is a core activity of the WG-PRE, a series of European conferences have been organized every second year across Europe. This collective article summarizes the leading concepts expressed during the lectures of the fifth EFLM Preanalytical Conference "Preanalytical Challenges - Time for solutions", held in Zagreb, 22-23 March, 2019. The topics covered include sample stability, preanalytical challenges in hematology testing, feces analysis, bio-banking, liquid profiling, mass spectrometry, next generation sequencing, laboratory automation, the importance of knowing and measuring the exact sampling time, technology aids in managing inappropriate utilization of laboratory resources, management of hemolyzed samples and preanalytical quality indicators.

A Stochastic Spatial Simulation Method for Self-Assembly Reactions

The ability of collections of molecules to spontaneously assemble into large functional complexes is central to all cellular processes. Yet the fine details of complex self-assembly processes normally cannot be directly experimentally observed due to their small scale and rapid dynamics. Intractability of experimental approaches is particularly acute for understanding self-assembly in vivo, which may operate quite differently from purified in vitro models due to such effects as spatial confinement, macromolecular crowding, and influences of extrinsic cellular factors. Simulation has thus proven a valuable adjunct to experimental methods, facilitating interpretation of experimental data and inferences about experimentally unobservable aspects of self-assembly. A variety of simulation methodologies have been used for modeling self-assembly dynamics --- including approaches based on Differential Equations (DE), Gillespie Algorithm (SSA), Brownian Dynamics (BD), Green's Function Reaction Dynamics (GFRD), and variations thereon --- each offering tradeoffs with respect to the ranges of phenomena they can model, their computational tractability, and the difficulty of fitting them to experimental measurements. Here, we explore a multiscale approach combining efficient SSA-like sampling suitable for well-mixed systems with the slower but space-aware GFRD model, assuming as with GFRD that reactions occur in a spatially heterogeneous environment that must be explicitly modeled. We generalize the GFRD model to more efficiently handle bimolecular association reactions fundamental to self-assembly, using a rejection method for exact and efficient sampling of reaction locations in spatially heterogeneous regions. To further accelerate models with minimal loss of accuracy, we are exploring regression-based methods for approximate integration. While the resulting model remains a theoretical abstraction, future work will explore its ability to capture an important subset of cellular self-assembly for which classic SSA is too simplified but GFRD and BD too inefficient to capture accurately the phenomena in realistic biological parameter ranges.

Variability and stability of the false discovery proportion

Much effort has been done to control the “false discovery rate” (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the “false discovery proportion” $\text{FDP}=V/R$ given by the ratio of the number of false rejections $V$ and all rejections $R$. In this paper, we have a closer look at the FDP for adaptive linear step-up multiple tests. These tests extend the well known Benjamini and Hochberg test by estimating the unknown amount $m_{0}$ of the true null hypotheses. We give exact finite sample formulas for higher moments of the FDP and, in particular, for its variance. Using these allows us a precise discussion about the stability of the FDP, i.e., when the FDP is asymptotically close to its mean. We present sufficient and necessary conditions for this stability. They include the presence of a stable estimator for the proportion $m_{0}/m$. We apply our results to convex combinations of generalized Storey type estimators with various tuning parameters and (possibly) data-driven weights. The corresponding step-up tests allow a flexible adaptation. Moreover, these tests control the FDR at finite sample size. We compare these tests to the classical Benjamini and Hochberg test and discuss the advantages of them.

Gaussian boson sampling using threshold detectors

We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all Boson Sampling models that employ Gaussian states and threshold detectors.

Double-blinded randomized controlled trial to evaluate a multimedia surgical care tour in improving patient satisfaction and knowledge after functional endoscopic sinus surgery.

Current delivery of patient education is done during the clinic visit, where physicians or clinic staff have limited time for each patient. One potential solution is to provide a multimedia surgical care tour delivered to patients throughout the perioperative period. The purpose of the study is to evaluate the effectiveness of this surgical care tour in enhancing patient knowledge and satisfaction after functional endoscopic sinus surgery (FESS). A total of 121 patients were enrolled and a double-blinded randomized controlled trial was initiated. Patients in the experimental group received 4 educational videos and automated reminders to take medications. The control group received a sham platform. Patients were randomized by MEDUMO software, and physicians, clinic staff, and patients were blinded. Patient satisfaction was measured by Consumer Assessment of Healthcare Providers and Systems (CAHPS) Surgical Care Survey Version 2.0. Patient knowledge was graded by the blinded surgeon and clinic staff. Fischer's exact test and 2-tailed independent samples Student t test were used to compare the satisfaction and patient knowledge outcomes, respectively. Patients in the experimental group were more likely to answer "Yes, definitely" to "Did these pictures drawings models or videos help you better understand your condition and its treatment?" (95.7% vs 74.1%, p = 0.011). The mean ± standard deviation clinic staff assessment of patient knowledge was 3.04 ± 1.05 in the control group and 3.68 ± 1.41 in the experimental group (p = 0.043). A multimedia surgical care tour was developed and has promising effects on patient satisfaction and knowledge after FESS.

A Note on Karl Pearson’s 1900 Chi-Squared Test: Two Derivations of the Asymptotic Distribution, and Uses in Goodness of Fit and Contingency Tests of Independence, and a Comparison with the Exact Sample Variance Chi-Square Result

Karl Pearson’s chi-squared test is widely known and used, both as a goodness-of-fit test for hypothesized distributions or frequencies, and in tests of independence in contingency tables. The test was introduced in Pearson (1900), but the derivation in that paper is almost incomprehensible. Two derivations of the asymptotic distribution are given here. The first uses joint characteristic functions, and the second uses a multivariate central limit theorem. Goodness-of-fit tests and contingency table tests of independence are discussed, and the asymptotic chi-square distribution result for Pearson’s test statistic is compared and contrasted with the exact chi-square result for the sample variance estimator.

Design and construction of a variables switch-based sampling system for product acceptance determination

This article proposes a variables switch-based sampling system, called the quick-switching sampling (QSS) system, based on one-sided capability indices for product acceptance determination when the quality characteristic of interest follows a normal distribution and has a unilateral specification limit. The QSS system is among the simplest sampling systems that involves a normal plan and a tightened plan under switching rules. The operating characteristic function of the proposed system is derived from an exact sampling distribution. The plan parameters are determined by a mathematical model that ensures the prescribed quality and risk requirements. The performance and behavior of the proposed variables QSS system are discussed and compared with those of conventional plans. For practical purposes, this article provides tables of the plan parameters under various conditions, and illustrates the method on an example taken from the integrated circuit industry.

An evaluation roadmap for critical quality attributes from tier 1 in analytical similarity assessment.

Analytical similarity assessment of critical quality attributes (CQAs) serves as a foundation for the development of biosimilar products and facilitates an abbreviated subsequent clinical evaluation. In this study, we establish a statistical evaluation roadmap with statistical approaches for some selected CQAs from Tier 1, because they are most relevant to clinical outcomes and require the most rigorous statistical methods. In the roadmap, we incorporate 3 methods—ranking and tier assignment of quality attributes, the equivalence test, and the Mann–Whitney test for equivalence—that are important to determine analytical similarity between the reference and biosimilar products. For the equivalence test, we develop a power calculation formula based on the two one-sided tests procedure. Exact sample sizes can be numerically calculated. Then, we propose a flexible idea for selecting the number of reference lots (nR) and the number of biosimilar lots (nT) to adjust for serious unbalanced sample sizes. From results of extensive simulations under various parameter settings, we obtain a workable strategy to determine the optimum sample size combination (nT, nR) for the equivalence test of CQAs from Tier 1. R codes are provided to facilitate implementation of the roadmap and corresponding methods in practice.

Ge and Si isotope signatures in rivers: A quantitative multi-proxy approach

Solutes derived from the dissolution of silicate minerals play a key role in Earth's climate via the carbon and other biogeochemical cycles. Silicon (Si) is a unique constituent of silicate minerals and a biologically important nutrient, so tracing its behavior in near-surface environments may provide important insights into weathering processes. However, Si released by weathering is variably incorporated into secondary mineral phases and biota, obscuring signals derived from primary weathering processes. Due to chemical similarities, Germanium (Ge) may help better understand the Si cycle and its relationship to chemical weathering. With this aim, we report new measurements of the concentration and isotopic composition of Ge for both the dissolved and particulate phases of a variety of global rivers. These measurements are combined with analyses of concentration and isotopic ratio of Si on the exact same sample set in order to make direct comparisons of the behavior of these two elements in natural river systems. With this dataset, we develop a new modeling framework describing the full elemental and isotopic systems of these solutes in rivers (i.e., Ge/Si, δ74Ge, and δ30Si). This multi-proxy approach allows us to ascertain the relative importance of biological versus mineral uptake in modulating the fluxes of these elements delivered to the modern ocean.Dissolved δ74Ge composition of rivers studied thus far range from 0.9 to 5.5‰ with a discharge-weighted global average of 2.6 ± 0.5‰. The Ge isotope composition of riverine suspended and bedload sediments is indistinguishable from silicate source rocks, which is consistent with mass balance expectations. The multi-proxy modeling suggests that, among the watersheds studied here, the isotopic fractionation of Si during secondary mineral phase precipitation (Δ30Sisec) ranges from −2.7 to −0.2‰, which removes between 19–79% of the initial dissolved Si, while between 12–54% is incorporated by biota. For Ge, modeling indicates that 79–98% of the dissolved load is incorporated into secondary mineral phases with a Δ74Gesec ranging from −4.9 to −0.3‰. The fractionation induced by biological uptake is calculated to range from −2.6 to −1.3‰ for Δ30Sibio and −0.7 ± 0.7‰ for Δ74Gebio. In addition to improving our understanding of the coupled Ge and Si cycles, our study provides a framework for using multiple isotopic tracers to elucidate the chemical behavior of solutes in natural waters.

Inspection tables for single acceptance sampling with crisp and fuzzy formulation of quality limits

PurposeThe purpose of this paper is to construct innovative exact and approximative sampling plans for acceptance sampling in statistical quality control. These sampling plans are determined for crisp and fuzzy formulation of quality limits, various lot sizes and common α- and β-levels.Design/methodology/approachThe authors use generalized fuzzy hypothesis testing to determine sampling plans with fuzzified quality limits. This test method allows a consideration of the indifference zone related to expert opinion or user priorities. In addition to the exact sampling plans calculated with the hypergeometric operating characteristic function, the authors consider approximative sampling plans using a little known, but excellent operating characteristic function. Further, a comprehensive sensitivity analysis of calculated sampling plans is performed, in order to examine how the inspection effort depends on crisp and fuzzy formulation of quality limits, the lot size and specifications of the producer’s and consumer’s risks.FindingsThe results related the parametric sensitivity analysis of the calculated sampling plans and the conclusions regarding the approximation quality provide the user a comprehensive basis for a direct implementation of the sampling plans in practice.Originality/valueThe constructed sampling plans ensure the simultaneous control of producer’s and consumer’s risks with the smallest possible inspection effort on the one hand and a consideration of expert opinion or user priorities on the other hand.

Integrative metabolic and transcriptomic profiling of prostate cancer tissue containing reactive stroma

Reactive stroma is a tissue feature commonly observed in the tumor microenvironment of prostate cancer and has previously been associated with more aggressive tumors. The aim of this study was to detect differentially expressed genes and metabolites according to reactive stroma content measured on the exact same prostate cancer tissue sample. Reactive stroma was evaluated using histopathology from 108 fresh frozen prostate cancer samples gathered from 43 patients after prostatectomy (Biobank1). A subset of the samples was analyzed both for metabolic (n = 85) and transcriptomic alterations (n = 78) using high resolution magic angle spinning magnetic resonance spectroscopy (HR-MAS MRS) and RNA microarray, respectively. Recurrence-free survival was assessed in patients with clinical follow-up of minimum five years (n = 38) using biochemical recurrence (BCR) as endpoint. Multivariate metabolomics and gene expression analysis compared low (≤15%) against high reactive stroma content (≥16%). High reactive stroma content was associated with BCR in prostate cancer patients even when accounting for the influence of Grade Group (Cox hazard proportional analysis, p = 0.013). In samples with high reactive stroma content, metabolites and genes linked to immune functions and extracellular matrix (ECM) remodeling were significantly upregulated. Future validation of these findings is important to reveal novel biomarkers and drug targets connected to immune mechanisms and ECM in prostate cancer. The fact that high reactive stroma grading is connected to BCR adds further support for the clinical integration of this histopathological evaluation.

Exact and Approximate Power and Sample Size Calculations for Analysis of Covariance in Randomized Clinical Trials With or Without Stratification

ABSTRACTAnalysis of covariance (ANCOVA) is commonly used in the analysis of randomized clinical trials to adjust for baseline covariates and improve the precision of the treatment effect estimate. We derive the exact power formulas for testing a homogeneous treatment effect in superiority, noninferiority, and equivalence trials under both unstratified and stratified randomizations, and for testing the overall treatment effect and treatment × stratum interaction in the presence of heterogeneous treatment effects when the covariates excluding the intercept, treatment, and prestratification factors are normally distributed. These formulas also work very well for nonnormal covariates. The sample size methods based on the normal approximation or the asymptotic variance generally underestimate the required size. We adapt the recently developed noniterative and two-step sample size procedures to the above tests. Both methods take into account the nonnormality of the t statistic, and the lower order variance term commonly ignored in the sample size estimation. Numerical examples demonstrate the excellent performance of the proposed methods particularly in small samples. We revisit the topic on the prestratification versus post-stratification by comparing their relative efficiency and power. Supplementary materials for this article are available online.

The Bland-Altman range of agreement: Exact interval procedure and sample size determination

The Bland-Altman analysis has been widely used to assess the agreement between two quantitative methods of measurement. The range of agreement is thus represented by the designated central proportion of the distribution of the paired differences. This article aims to provide concrete guidance on the use of accurate confidence intervals of the range of agreement. Theoretical examination and numerical comparison are conducted to support the exact approach and to demonstrate the disadvantages of the currently suggested methods for confidence interval estimation of the range of agreement. For the purpose of design planning, the associated sample size calculations for precise interval estimation of the range of agreement are delineated under the expected width and assurance probability considerations. To enhance the utility of the recommended confidence interval and sample size procedures in practical applications, both SAS and R computer algorithms are also developed.

Bayesian inference of selection in the Wright-Fisher diffusion model.

The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of selection acting on the population(s), from such data. Existing methods for this problem in the setting of the Wright-Fisher diffusion model are primarily likelihood-based, and rely on numerical approximation for likelihood computation and on bootstrapping for assessment of variability in the resulting estimates, requiring extensive computation. Recent work has provided a method for obtaining exact samples from general Wright-Fisher diffusion processes, enabling the development of methods for Bayesian estimation in this setting. We develop and implement a Bayesian method for estimating the strength of selection based on the Wright-Fisher diffusion for data sampled at a single time point. The method utilizes the latest algorithms for exact sampling to devise a Markov chain Monte Carlo procedure to draw samples from the joint posterior distribution of the selection coefficient and the allele frequencies. We demonstrate that when assumptions about the initial allele frequencies are accurate the method performs well for both simulated data and for an empirical data set on hypoxia in flies, where we find evidence for strong positive selection in a region of chromosome 2L previously identified. We discuss possible extensions of our method to the more general settings commonly encountered in practice, highlighting the advantages of Bayesian approaches to inference in this setting.