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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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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 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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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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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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Bootstrapping01:24

Bootstrapping

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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Related Experiment Video

Updated: Oct 12, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
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A Scalable Bayesian Sampling Method Based on Stochastic Gradient Descent Isotropization.

Giulio Franzese1, Dimitrios Milios1, Maurizio Filippone1

  • 1Data Science Department, Eurecom, 06410 Biot, France.

Entropy (Basel, Switzerland)
|November 27, 2021
PubMed
Summary
This summary is machine-generated.

Stochastic gradient MCMC (SGMCMC) methods improve large-scale Bayesian modeling. This study introduces a novel SGMCMC approach with isotropic noise and a fixed learning rate, achieving competitive performance.

Keywords:
Bayesian samplingMonte Carlo integrationstochastic gradients

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Area of Science:

  • Computational statistics
  • Bayesian inference
  • Machine learning

Background:

  • Stochastic gradient MCMC (SGMCMC) is crucial for large-scale Bayesian modeling.
  • Current SGMCMC methods face challenges with complex models like Deep Nets, particularly regarding noise covariance and non-vanishing learning rates.
  • Satisfying assumptions on loss landscapes and SGMCMC noise behavior simultaneously is difficult.

Purpose of the Study:

  • To propose a novel, practical SGMCMC method addressing current limitations.
  • To ensure isotropic stochastic gradient (SG) noise.
  • To utilize a fixed, analytically determined learning rate.

Main Methods:

  • Developed a novel SGMCMC algorithm.
  • Introduced a method to make the stochastic gradient (SG) noise isotropic.
  • Determined a fixed learning rate analytically.
  • Conducted extensive experimental validations.

Main Results:

  • The proposed method successfully makes the SG noise isotropic.
  • A fixed learning rate was analytically derived and implemented.
  • Experimental results demonstrate the proposal's competitiveness with state-of-the-art SGMCMC algorithms.
  • The method operates effectively with non-vanishing learning rates.

Conclusions:

  • The novel SGMCMC approach offers a practical solution for large-scale Bayesian modeling.
  • Isotropic SG noise and an analytically determined fixed learning rate enhance algorithm performance.
  • This method is competitive with existing state-of-the-art SGMCMC techniques.