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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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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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Sampling Plans01:23

Sampling Plans

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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...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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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...
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Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

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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...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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On the Change of Measure for Brownian Processes.

Entropy (Basel, Switzerland)·2025
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Related Experiment Video

Updated: Nov 7, 2025

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
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A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space.

Francis J Pinski1

  • 1Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA.

Entropy (Basel, Switzerland)
|April 30, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Markov Chain Monte Carlo (MCMC) method using Ornstein-Uhlenbeck bridges within a Hybrid Monte Carlo (HMC) framework. This approach enhances sampling efficiency for complex, high-dimensional distributions.

Keywords:
Brownian dynamicssampling path spacestochastic processestransition paths

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Area of Science:

  • Computational Statistics
  • Stochastic Processes
  • Applied Mathematics

Background:

  • Hybrid Monte Carlo (HMC) methods are used for sampling complex, high-dimensional distributions.
  • Existing HMC algorithms approximate measures on infinite-dimensional Hilbert spaces using finite-dimensional methods.
  • A key component in HMC is the choice of the mass operator, which influences algorithm performance.

Purpose of the Study:

  • To develop a novel Hybrid Monte Carlo on Hilbert spaces (HMC-HS) algorithm.
  • To introduce a new mass operator choice using Ornstein-Uhlenbeck (OU) bridges.
  • To create a Markov Chain Monte Carlo (MCMC) method well-defined on Hilbert spaces for efficient sampling.

Main Methods:

  • Building upon the HMC-HS framework, utilizing an enlarged phase space with Ornstein-Uhlenbeck bridges.
  • Defining a new mass operator and deriving the corresponding Hamiltonian flow equations.
  • Employing numerical integration for evolution equations and the Metropolis-Hastings acceptance rule.

Main Results:

  • The proposed algorithm is well-defined on the Hilbert space, overcoming limitations of previous methods using Brownian bridges.
  • The use of OU bridges, with covariance independent of path length, improves acceptance rates compared to Brownian bridges.
  • Computer experiments demonstrate the algorithm's effectiveness in sampling target distributions in an almost dimension-free manner.

Conclusions:

  • The novel HMC algorithm with OU bridges offers a robust and efficient method for sampling complex distributions.
  • This approach alleviates diffusive behavior inherent in some MCMC methods.
  • The method shows promise for applications in statistical physics and other fields requiring high-dimensional sampling.