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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
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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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While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

Huan Lei1, Jing Li1, Peiyuan Gao1

  • 1Pacific Northwest National Laboratory, Richland, WA 99352.

Computer Methods in Applied Mechanics and Engineering
|February 11, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a new Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework. DSRAR accurately quantifies uncertainty propagation in complex systems using limited data, even with non-Gaussian probability distributions.

Keywords:
arbitrary randomnesscompressed sensingdata-drivenmutual dependencesparsity enhancementuncertainty quantification

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Area of Science:

  • Computational mathematics
  • Uncertainty quantification
  • Scientific computing

Background:

  • Quantifying uncertainty propagation in high-dimensional systems is challenging due to complex input probability distributions.
  • Traditional methods struggle with limited data and arbitrary dependencies between random variables.
  • Existing polynomial chaos expansions often assume mutual independence, limiting their applicability.

Purpose of the Study:

  • To develop a general framework for constructing surrogate models for arbitrary probability measures, handling dependent random inputs.
  • To create a data-driven method for building multivariate polynomial bases that maintain orthogonality for non-Gaussian distributions.
  • To enable accurate uncertainty quantification with limited training data in complex, high-dimensional systems.

Main Methods:

  • Developed a Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework.
  • Constructed multivariate polynomial bases for arbitrary, mutually dependent probability measures.
  • Implemented a sparsity-enhancing rotation procedure ensuring basis orthogonality for rotated random vectors.

Main Results:

  • The DSRAR framework accurately recovers sparse representations of target functions using limited training data.
  • Demonstrated effectiveness in high-dimensional (O(10)) conformational spaces for partial differential equations and molecular systems.
  • Successfully applied to systems with implicitly represented and explicitly given non-Gaussian probability measures.

Conclusions:

  • The DSRAR framework offers a robust solution for uncertainty quantification in systems with complex, arbitrary probability distributions.
  • This data-driven approach overcomes limitations of traditional methods, especially with limited data and dependent random inputs.
  • The method shows significant potential for applications in computational mathematics and scientific computing.