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Sampling Methods: Overview

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling.
In analytical chemistry, the choice of sampling...

Cluster Sampling Method

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Sampling Distribution

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...

Sampling Methods: Sample Types

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...

Sampling Continuous Time Signal

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

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Related Experiment Video

Updated: May 28, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Towards robust topology of sparsely sampled data.

Carlos D Correa¹, Peter Lindstrom

¹Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, USA. correac@llnl.gov

IEEE Transactions on Visualization and Computer Graphics

|October 29, 2011

Summary

This study introduces novel neighborhood graphs for analyzing sparse data. These graphs enhance the accuracy of topological data analysis and visualization at reduced computational cost.

Related Experiment Videos

Last Updated: May 28, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

Data analysis
Computational topology
Scientific visualization

Background:

Sparse, irregular data sampling presents challenges for signal reconstruction and analysis.
Existing neighborhood selection methods (k-nearest neighbors, Delaunay triangulation) have limitations in accuracy, robustness, and computational cost for high-dimensional data.
Robust neighborhood selection is critical for accurate topological decomposition, clustering, and gradient estimation.

Purpose of the Study:

To develop new neighborhood graph types for robust analysis of sparsely sampled data.
To improve the accuracy and efficiency of neighborhood-based analytical tools.
To enable more reliable topological representations and visualization of complex datasets.

Main Methods:

Introduction of two novel neighborhood graph types, building upon empty region graphs.
Development of strategies for computing and applying these new neighborhood graphs.
Evaluation of neighborhood graph performance in topological decomposition and data analysis.

Main Results:

The proposed neighborhood graphs significantly improve the robustness of neighborhood-based analysis tools.
These graphs yield more accurate topological representations for both low- and high-dimensional datasets.
The new methods offer substantial reductions in storage and computation time compared to existing approaches.

Conclusions:

The novel neighborhood graphs provide a more accurate and computationally efficient solution for analyzing sparse, high-dimensional data.
These findings have significant implications for advancing data analysis and visualization techniques.
The presented strategies facilitate the application of robust neighborhood graphs in diverse scientific domains.