Sampling Theory Research Articles

Estimands and Cumulative Incidence Function Regression in Clinical Trials: Some New Results on Interpretability and Robustness.

Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks include the Fine-Gray model and models based on direct binomial regression. Using large sample theory we derive the limiting values of treatment effect estimators based on such models when the data are generated according to multiplicative intensity-based models, and show that the estimand is sensitive to several process features. The rejection rates of hypothesis tests based on cumulative incidence function regression models are also examined for null hypotheses of different types, based on which a robustness property is established. In such settings supportive secondary analyses of treatment effects are essential to ensure a full understanding of the nature of treatment effects. An application to a palliative study of individuals with breast cancer metastatic to bone is provided for illustration.

Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains

Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by Ensemble Monte Carlo we allow the number of Markov chains to vary by exchanging particles with a reservoir, controlled by a parameter analogous to a chemical potential μ, which effectively establishes a random process that samples microstates from a macrocanonical instead of a canonical ensemble. In this paper, we develop the theory of macrocanonical sampling for statistical inference on the basis of Bayesian macrocanonical partition functions, thereby bringing to light the relations between information-theoretical quantities and thermodynamic properties. Furthermore, we propose an algorithm for macrocanonical sampling, 𝙰𝚟𝚊𝚕𝚊𝚗𝚌𝚑𝚎 𝚂𝚊𝚖𝚙𝚕𝚒𝚗𝚐, and apply it to various toy problems as well as the likelihood on the cosmological parameters Ωm and w on the basis of data from the supernova distance redshift relation.

Construction of virtual test scenarios for intelligent car-pedestrian interaction

Aiming at the needs of intelligent car and pedestrian interaction testing under urban conditions, this paper proposes a scenario generation method that comprehensively considers the frequency of scenarios in the real world and the degree of challenge to human-vehicle interaction performance. First, according to the key features of intelligent car and pedestrian interaction, the original scene data of pedestrians crossing the road is extracted from the natural driving dataset; then, according to the needs of accelerated testing, a key scenario extraction method based on importance sampling theory is designed to extract and construct important scenarios for intelligent car-pedestrian interaction testing from the original scenes; finally, by comparing the data distribution of important scenarios with original scenarios, it is shown that this method can effectively screen out scenarios that may challenge safety performance during driving, thereby realizing accelerated testing, while taking into account the statistical characteristics of the test scenarios.

Sensor placement method for water distribution networks based on sampling of non-bandlimited graph signals

Monitoring water distribution networks (WDNs) requires careful consideration of sensor placement, which is essential for obtaining comprehensive information about the network. A natural graphical structure underlies WDN, making graph sampling theory advantageous for selecting monitoring nodes. However, graph sampling theory is only applied only to restrictive band-limited signals, while the pressure data of WDN is a restrictive non-band-limited signal. To address this issue, this paper presents an approximate conversion method for transforming non-band-limited signals into band-limited signals, accompanied by an optimal spectrum threshold formula. This formula is used to perform spectral screening in the graph frequency domain, effectively converting non-band-limited signals into band-limited signals that preserve the major frequency components while ignoring smaller-value frequency components. By sampling band-limited signal, we identify sampling nodes that perfectly recover the signal. These sampling nodes act as monitoring nodes that can perform a comprehensive inspection of the WDN and accurately locate leaks. The accuracy of our method in recovering the signal and locating the leak is demonstrated by comparing it with two existing sensor placement optimization methods.

Katuk Leaves (Sauropus androgynus (L.) Merr) on Hemoglobin Level among Pregnant Women in Third Trimester

Background: In 2018, 41,8% of amternal mortality in developing countries was caused by anemia in pregnancy, the prevalence of anemia in Indonesia is still very high at 44,2%. One of the causes of anemia is a lack of iron in the body. Anemia can be prevented by consuming foods that contain iron and vitamin C to help the absorbtion process, by consuming katuk leaves while continuing to consume Fe Tablets according to government recommendations.Purpose: This study aims to determine the effect of Katuk Leaves (Sauropus androgynus) and Fe Tablets on hemoglobin levels among pregnant women in third trimester.Methods: This research is aquassy experiment pre and post test with control group design. The population in this study was 86 third trimester pregnant women which 45 had anemia in last 6 month at Private Midwifery Practice N. The sample were divided by intervention group and cotrol group, each group was 15 pregnant women, according to sample theory of experimental research. The sampling technique used purposive sampling. The research instrument used observation sheets and Digital Hemoglobinometer. The data analyzed with parametric test, the t-test.Results: The result of statistic tests showed that there was an effect of katuk leaves and Fe tablets on hemoglobin level with p value of 0,00 (0,005).Conclusion: Consumption katuk leaves and Fe tablet is more effective in changing hemoglobin levels compared to consuming Fe tablets only.

Minimum habitat size required to detect new rare species.

Conservation of species requires the protection of the associated suitable habitat. However, it is usually not known how much habitat is required to detect a single rare species. This problem is important, and it is related directly to the success and optimization of conservation planning. However, to date, no statistical methods have been developed to address this problem adequately. In this study, from a statistical sampling theory, we propose an estimator to estimate the minimum area required to conserve one or more additional new rare species. The estimator is highly accurate, as demonstrated by numerical tests. Applying the estimator in a tropical forest plot showed that the additional habitat size required for discovering an additional individual of a previously unseen tropical tree species is about 3.86 ha with a SE of 1.10 ha. In conclusion, the proposed estimator may be applied to conservation planning by assisting conservation biologists and policymakers to balance urban-related and conservation-related land uses by estimating the minimum detection areas required for species.

On Gabor frames generated by B-splines, totally positive functions, and Hermite functions

The frame set of a window ϕ∈L2(R) is the subset of all lattice parameters (α,β)∈R+2 such that G(ϕ,α,β)={e2πiβm⋅ϕ(⋅−αk):k,m∈Z} forms a frame for L2(R). In this paper, we investigate the frame set of B-splines, totally positive functions, and Hermite functions. We derive a sufficient condition for Gabor frames using the connection between sampling theory in shift-invariant spaces and Gabor analysis. As a consequence, we obtain a new frame region belonging to the frame set of B-splines and Hermite functions. For a class of functions that includes certain totally positive functions, we prove that for any choice of lattice parameters α,β>0 with αβ<1, there exists a γ>0 depending on αβ such that G(ϕ(γ⋅),α,β) forms a frame for L2(R). Our results give explicit frame bounds.

HUMAN THOUGHT PROCESS ON HOTEL ADVERTISEMENTS:

Conceptual Blending (CB) is a framework within Cognitive Linguistics to create meaning construction that determines brain cognitive functions upon reading hotel advertisements which the study aimed to illustrate and elaborate. The study utilized advancement theory of CB by applying intertextuality concept to create multiple meanings done from prior studies. The study also utilized qualitative method to analyze a poster from ANA Intercontinental Manza Beach Resort through applying non-participant observation, purposive sampling, and triangulation theory methods. To analyze the data, the concepts of data collection, data condensation, data display and data conclusion were used. The study found that the processes of composition, completion, and elaboration within blended space of CB built the meaning construction within human brain. Composition stage created arrays of features from composing features within input spaces that build up new concepts within completion stage. The completion stage then created new concepts based on cultural knowledge combining all the features composed within composition process and the meanings were broaden by elaboration stage which cleared out what the new concepts actually meant for. These processes created the emergent structure which carries novelty meanings from the analysis. In this stage, the meaning has been completely concluded from all the elaborated meaning happening on prior stages.

Discrete linear canonical transform on graphs: Uncertainty principle and sampling

With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we initially propose the uncertainty principle of the graph linear canonical transform (GLCT), which is based on a class of graph signals maximally concentrated in both vertex and graph spectral domains. Subsequently, leveraging the uncertainty principle, we establish conditions for recovering bandlimited signals of the GLCT from a subset of samples, thereby formulating the sampling theory for the GLCT. We elucidate interesting connections between the uncertainty principle and sampling. Further, by employing sampling set selection and experimental design sampling strategies, we introduce optimal sampling operators in the GLCT domain. Finally, we evaluate the performance of our methods through simulations and numerical experiments across applications.

Path ahead: Tackling the Challenge of Computationally Estimating Lithium Diffusion in Cathode Materials.

In the roadmap toward designing new and improved materials for Lithium ion batteries, the ability to estimate the diffusion coefficient of Li atoms in electrodes, and eventually solid-state electrolytes, is key. Nevertheless, as of today, accurate prediction through computational tools remains challenging. Its experimental measurement does not appear to be much easier. In this work, we devise a computational protocol for the determination of the Li-migration energy barrier and diffusion coefficient, focusing on a common cathode material such as LiNiO2, which represents a prototype of the widely adopted NMC (LiNi1-x-y Mn x Co y O2) class of materials. Different methodologies are exploited, combining ab initio metadynamics, path sampling, and density functional theory. Furthermore, we propose a novel, fast, and simple 1D approximation for the estimation of the effective frequency. The outlined computational protocol aims to be generally applicable to Lithium diffusion in other materials and components for batteries, including anodes and solid electrolytes.

Unifying approaches to understanding capacity in change detection.

To navigate changes within a highly dynamic and complex environment, it is crucial to compare current visual representations of a scene to previously formed representations stored in memory. This process of mental comparison requires integrating information from multiple sources to inform decisions about changes within the environment. In the present article, we combine a novel systems factorial technology change detection task (Blunden et al., 2022) with a set size manipulation. Participants were required to detect 0, 1, or 2 changes of low and high detectability between a memory and probe array of 1-4 spatially separated luminance discs. Analyses using systems factorial technology indicated that the processing architecture was consistent across set sizes but that capacity was always limited and decreased as the number of distractors increased. We developed a novel model of change detection based on the statistical principles of basic sampling theory (Palmer, 1990; Sewell et al., 2014). The sample size model, instantiated parametrically, predicts the architecture and capacity results a priori and quantitatively accounted for several key results observed in the data: (a) increasing set size acted to decrease sensitivity (d') in proportion to the square root of the number of items in the display; (b) the effect of redundancy benefited performance by a factor of the square root of the number of changes; and (c) the effect of change detectability was separable and independent of the sample size costs and redundancy benefits. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Amplitude rise time sensitivity in children with and without dyslexia: differential task effects and longitudinal relations to phonology and literacy.

The speech amplitude envelope carries important acoustic information required for speech intelligibility and contains sensory cues (amplitude rise times, ARTs) that play a key role in both sensory rhythm perception and neural speech encoding. Individual differences in children's sensitivity to ARTs have been related to the development of children's phonological processing skills across languages by the Temporal Sampling theory. Impaired processing of ARTs also characterises children with dyslexia. However, different ART tasks have been employed in different studies, in different languages, and at different ages. Here, we compare the sensitivity of three frequently used ART tasks (based on synthetic syllables, sine tones, and speech-shaped noise) in a longitudinal study of English-speaking children with and without dyslexia. Children's ability to discriminate rising frequency, duration, and intensity was also tested. ART discrimination in all 3 tasks was significantly inter-related, but different relations to phonology and literacy were found for different ART tasks at different ages. In particular, the often-used sine tone and speech-shaped noise ART tasks showed greater sensitivity in older children, while the synthetic syllable task (/ba/ rise) showed greater sensitivity in younger children. Sensitivity to rising frequency was also related to phonology and literacy across ages. The data are interpreted with respect to the Temporal Sampling theory of developmental dyslexia.

Evaluation of different estimator approaches based on COVID-19 data and a simulation study

Sampling is crucial in basic statistics due to the large size of certain populations. Sampling theory focuses on selecting samples based on appropriate population characteristics and approaches to estimating population characteristics from the sample. Firstly, we use the ratio-type estimator proposed by Prasad (1989). We adapt this unbiased ratio-type estimator to two new different estimators using the Hartley-Ross and non-response approaches. Finally, we combine these approaches and propose a new estimator. The theoretical results were supported by COVID-19 data and a simulation study with various scenarios. Based on the COVID-19 data result, it was concluded that the new tN3 estimator is the most effective estimator among those proposed and compared, with the minimum MSE and maximum PRE. Upon examining the changes in the COVID-19 data set in detail, it is evident that the PRE value increases with an increase in sample size, non-response rate, and k values. As in the COVID-19 dataset, the tN3 estimator was the most effective in the simulation study results. It is also important to note that these results are not applicable to only one scenario in simulation study. The tN2 estimator was the most effective in the scenario with rho=0.90, T=1000, n=400, non-response rate=0.30 and k equal to 2, 4 and 5.

Unbiased process capability estimation for autocorrelated data using exhaustive systematic sampling

AbstractIt is well known that process control index estimators are inflated when naively applied to positively autocorrelated data. The autocorrelation is a nuisance and not a feature that is captured in the process capability indices. This paper proposes exhaustive systematic sampling to create a pooled variance estimator that replaces the biased estimator of the process data standard deviation when data are autocorrelated. The proposed method is effective because the observations within a systematic sample are spread out in time and should be less correlated with each other as a result. It is similar to Bayesian thinning as a strategy for reducing the impact of autocorrelation except no observations are dropped. Properties of estimated process control indices are derived using quadratic forms and large sample theory that is nonparametric in the sense no distribution or time series model is assumed. Approximately unbiased estimates can be achieved for sufficiently large systematic sampling interval. The proposed method is compared to the time series method in a simulation study that demonstrates similar performance. The proposed method is applied to two examples that use because the target is not the midpoint of the specification limits and the mean differs from the target.

Quality Assessment Method for Insulator Sample Bank Based on Sampling Theory

Abstract Insulator strings are important components in power systems to support and isolate transmission lines. Due to long-term exposure to the natural environment, insulator strings are susceptible to damage, such as self-explosion, broken umbrella skirts, and galvanic corrosion, which is one of the most common failures. Once damaged, it can lead to widespread power outage, which affects people’s life and industrial production, so it is necessary to inspect and replace the damaged insulator strings regularly. This thesis proposes a quadratic sampling based approach to assess the quality of insulator string sample banks. Through simple random sampling, estimation and interval estimation of the sample pool, the pass rate and average number of labels of the original sample pool are initially assessed and compared with the usage requirements to decide whether to carry out a second sampling or not; the second sampling used SADS as an evaluation metric to assess the performance of the insulator string sample bank.

A Novel Feature Selection Approach-Based Sampling Theory on Grapevine Images Using Convolutional Neural Networks

AbstractFeature selection, reducing number of input variables to develop classification model, is an important process to reduce computational and modeling complexity and affects the performance of image process. In this paper, we have proposed new statistical approaches for feature selection based on sample selection. We have applied our new approaches to grapevine leaves data that possess properties of shape, thickness, featheriness, and slickness that are investigated in images. To analyze such kind of data by using image process, thousands of features are created and selection of features plays important role to predict the outcome properly. In our numerical study, convolutional neural networks have been used as feature extractors and then obtained features from the last average pooling layer to detect the type of grapevine leaves from images. These features have been reduced by using our suggested four statistical methods: simple random sampling, ranked set sampling, extreme ranked set sampling, moving extreme ranked set sampling. Then, selected features have been classified with artificial neural network and we obtained the best accuracy of 97.33% with our proposed approaches. Based on our empirical analysis, it has been determined that the proposed approach exhibits efficacy in the classification of grapevine leaf types. Furthermore, it possesses the potential for integration into various computational devices.

Plug-in bandwidth selection rules for the kernel quantile estimator

The large sample theory of the kernel quantile estimator is extended by separately treating the cases where the underlying density has critical points. Our attempts of improving the quality of quantile estimation resulted in proposing the beta distribution’s bandwidth selection method that is quite successful in the case of a normal distribution. The performance of the beta reference rule is compared to that of two other plug-in type bandwidth selectors. Based on the theoretical and numerical results, we provide certain recommendations regarding using different type of estimators in practice. In particular, the beta reference rule and truncated normal rule are recommended for estimating the quantiles of the distributions close to normal. The sample quantile estimator worked well in all simulation settings and is thus recommended as a default quantile estimation method in a non-normal case.

Designing count‐based studies in a world of hierarchical models

AbstractAdvances in hierarchical modeling have improved estimation of ecological parameters from count data, especially those quantifying population abundance, distribution, and dynamics by explicitly accounting for observation processes, particularly incomplete detection. Even hierarchical models that account for incomplete detection, however, cannot compensate for data limitations stemming from poorly planned sampling. Ecologists therefore need guidance for planning count‐based studies that follow established sampling theory, collect appropriate data, and apply current modeling approaches to answer their research questions. We synthesize available literature relevant to guiding count‐based studies. Considering the central historical and ongoing contributions of avian studies to ecological knowledge, we focus on birds as a case study for this review, but the basic principles apply to all populations whose members are sufficiently observable to be counted. The sequence of our review represents the thought process in which we encourage ecologists to engage 1) the research question(s) and population parameters to measure, 2) sampling design, 3) analytical framework, 4) temporal design, and 5) survey protocol. We also provide 2 hypothetical demonstrations of these study plan components representing different research questions and study systems. Mirroring the structure of hierarchical models, we suggest researchers primarily focus on the ecological processes of interest when designing their approach to sampling, and wait to consider logistical constraints of data collection and observation processes when developing the survey protocol. We offer a broad framework for researchers planning count‐based studies, while pointing to relevant literature elaborating on particular tools and concepts.

Within-well patterns in bigeye tuna catch composition and implications for purse-seine port-sampling and catch estimation for the Eastern Pacific Ocean

In response to concerns about the stock status of bigeye tuna (BET) in the Eastern Pacific Ocean, the Inter-American Tropical Tuna Commission adopted additional management measures for BET in 2021, including an individual-vessel catch threshold system for the purse-seine fishery. Development of an enhanced port-sampling program for estimation of trip-level BET catch was also mandated to support member countries and their purse-seine vessels in their conservation efforts. To this end, a pilot study was conducted in the ports of Manta and Posorja, Ecuador, in 2022. In these ports, well unloading often takes place with small containers, which are used to transport fish from inside the well to the vessel’s wet deck. Using a high-frequency systematic sampling protocol, 63 wells of 37 trips with catch exclusively from floating-object (OBJ) sets were sampled from the start to the end of unloading, at a fixed interval from a random starting point, sampling about 10 % of all the containers of fish unloaded from each well. Notable large-scale pattern in the proportion of BET per container was found for 38 of the 56 wells that had BET catch. The proportion of BET per container, which could be high at the beginning, middle or end of the well unloading, sometimes varied by 0.40 or more. The magnitude of this large-scale within-well pattern had a significant increasing relationship with the number of OBJ sets associated with the well catch, consistent with variability in species composition among OBJ sets being an important factor in determining variability in species composition during catch unloading. Simulation studies demonstrated that such large-scale within-well pattern has potential implications for OBJ-set well-level sampling design, where, as expected from sampling theory, a systematic sampling protocol for containers of fish generally resulted in lower mean squared error (MSE) on the proportion of BET in the well, compared to simple random sampling of containers of fish. The reduction in MSE was largely due to a reduction in variance. Simulations also showed that the within-well variance component of the trip-level estimator for the proportion of BET can be larger than the among-well variance component, unless the within-well sampling coverage is relatively high. To minimize the negative impact of within-well variability on the precision of the estimator, results indicate that for a sampling protocol with one systematic sample per well, the within-well coverage should be at least 2 % of containers of fish unloaded from the well, and preferably more than 3 %. Finally, simulation studies were conducted with observer well plan data from 2013 to 2022 to put the well-level results in a larger context. Results indicated that the level of within-well sampling coverage may affect the variance on fleet-level estimates of the proportion of BET in the catch, with potentially substantially higher variance when the within-well sampling coverage is low. Taken together, these results suggest that both the type of within-well sampling and the level of within-well sampling coverage have important implications for the variance on BET catch estimates, from the well level to the fleet level.

Yet Another Attempt to Classify Positive Univariate Probability Distributions

We propose an original classification of several discrete and continuous probability distributions. We establish links between these distributions, in particular the little known relationship between the negative hypergeometric distribution and the beta distribution. These relations allow us to propose a structure of relations which is summarized in graphic form.Our classification emphasises the analogy between certain discrete and continuous distributions. This analogy makes it possible to establish relations between the theory of point processes and the theory of survey sampling. It also makes it possible to envisage the use of link functions that are little used in generalised regression.