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Related Concept Videos

Sampling Methods: Overview01:06

Sampling Methods: Overview

406
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...
406
Sampling Plans01:23

Sampling Plans

235
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
235
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

331
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...
331
Cluster Sampling Method01:20

Cluster Sampling Method

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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...
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Stratified Sampling Method01:16

Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures 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 stratified sample, divide the population into groups called strata and then take a...
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Random Sampling Method01:09

Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures 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. Among the various sampling methods used by...
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Sampling Soils in a Heterogeneous Research Plot
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Perfect sampling from spatial mixing.

Weiming Feng1, Heng Guo1, Yitong Yin2

  • 1School of Informatics University of Edinburgh, Informatics Forum Edinburgh UK.

Random Structures & Algorithms
|January 2, 2023
PubMed
Summary
This summary is machine-generated.

We developed a new perfect sampling method for Gibbs distributions that runs in linear time on many graphs. This technique provides the fastest perfect samplers for graph colorings and monomer-dimer models.

Keywords:
Gibbs distributionperfect samplingspatial mixing

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Area of Science:

  • Statistical Physics
  • Computer Science
  • Algorithms

Background:

  • Perfect sampling is crucial for accurately simulating complex systems.
  • General Gibbs distributions pose significant computational challenges for sampling.
  • Existing methods often lack efficiency for large-scale or complex graph structures.

Purpose of the Study:

  • Introduce a novel perfect sampling algorithm.
  • Achieve linear time complexity under specific conditions.
  • Improve sampling efficiency for Gibbs distributions on graphs.

Main Methods:

  • Developed a new perfect sampling technique applicable to general Gibbs distributions.
  • Analyzed algorithm performance based on correlation decay and neighborhood growth.
  • Demonstrated linear running time for graphs with subexponential neighborhood growth.

Main Results:

  • The algorithm achieves linear time complexity when correlation decays faster than neighborhood growth.
  • Specifically, it runs in linear time on graphs like if Gibbs sampling is rapidly mixing.
  • Established new state-of-the-art perfect samplers for graph colorings and monomer-dimer models.

Conclusions:

  • The proposed perfect sampling technique offers significant efficiency gains.
  • It provides practical improvements for simulating statistical physics models on graphs.
  • This work advances the field of efficient sampling algorithms for complex distributions.