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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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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Improving randomness characterization through Bayesian model selection.

Rafael Díaz Hernández Rojas1, Aldo Solís2, Alí M Angulo Martínez2

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Cd. Mx., C.P., 04510, Mexico.

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This summary is machine-generated.

A new Bayesian method rigorously assesses random number generator quality. This approach is more reliable than existing tests and can characterize the source itself, ensuring true randomness for critical applications.

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Area of Science:

  • Information Theory
  • Quantum Physics
  • Computer Science

Background:

  • Random number generation is crucial for cryptography and probabilistic algorithms.
  • Existing methods for assessing randomness lack rigor or practical applicability.
  • There is a need for a formal, reliable method to evaluate random number sources.

Purpose of the Study:

  • To develop a rigorous and practical method for assessing the quality of random number generators.
  • To overcome limitations of current randomness testing suites.
  • To provide a formal framework for characterizing random number sources.

Main Methods:

  • Bayesian model selection is employed for rigorous assessment.
  • Analytic expressions for model likelihood are derived.
  • Posterior distributions are computed for robust inference.

Main Results:

  • The proposed Bayesian method is more rigorous than the NIST test suite and Borel-Normality criterion.
  • The method is straightforward to implement.
  • Applied to a quantum device (spontaneous parametric down-conversion), it confirmed genuine quantum random number generation.

Conclusions:

  • The developed Bayesian approach offers a superior method for evaluating random number generators.
  • This technique provides a formal characterization of the random number source, not just individual sequences.
  • It enables reliable assessment of randomness for advanced technological applications.