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Related Concept Videos

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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Cluster Sampling Method01:20

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

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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.
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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...
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Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example
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Spatial Monte Carlo integration with annealed importance sampling.

Muneki Yasuda1, Kaiji Sekimoto1

  • 1Graduate School of Science and Engineering, Yamagata University, Japan.

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Summary

This study introduces a novel method combining Annealed Importance Sampling (AIS) and Spatial Monte Carlo Integration (SMCI) for accurate Ising model expectation evaluation. The new approach improves accuracy in both high and low temperatures, overcoming limitations of existing methods.

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Area of Science:

  • Statistical Physics
  • Machine Learning
  • Computational Science

Background:

  • Evaluating expectations on Ising models is crucial for statistical machine learning.
  • Traditional methods like Monte Carlo Integration (MCI) struggle with computational complexity and accuracy, especially at low temperatures.
  • Spatial Monte Carlo Integration (SMCI) offers improvements but still faces sampling quality degradation in low-temperature regimes.

Purpose of the Study:

  • To develop a novel approximation method for evaluating expectations on Ising models.
  • To enhance accuracy in both high- and low-temperature regions, addressing limitations of existing techniques.
  • To combine the strengths of Annealed Importance Sampling (AIS) and SMCI for improved performance.

Main Methods:

  • Proposed a hybrid method integrating Annealed Importance Sampling (AIS) with Spatial Monte Carlo Integration (SMCI).
  • Leveraged AIS to mitigate performance degradation in low-temperature regions by utilizing importance weights.
  • Applied the combined AIS-SMCI method to Ising models for expectation evaluation.

Main Results:

  • The proposed AIS-SMCI method demonstrates improved accuracy in evaluating Ising model expectations across a wide temperature range.
  • Successfully suppressed the performance degradation typically observed with SMCI and MCI at low temperatures.
  • Theoretical analysis and numerical simulations confirmed the method's efficiency and effectiveness.

Conclusions:

  • The combined AIS-SMCI approach offers a robust and accurate solution for expectation evaluation in Ising models.
  • This method significantly enhances computational efficiency and reliability, particularly in challenging low-temperature scenarios.
  • The findings have broad implications for statistical machine learning and related computational fields.