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Related Experiment Videos

Estimating probabilities from experimental frequencies.

Inés Samengo1

  • 1Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Río Negro, Argentina. samengo@cab.cnea.gov.ar

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
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This study introduces a method to estimate probability distributions from sampled data, revealing the probability of a true distribution given observed frequencies. It defines a thermodynamic potential for evaluating distribution divergence and analyzes key statistical properties for large sample sizes.

Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Machine Learning

Background:

  • Estimating probability distributions from finite samples often introduces errors.
  • Histograms or frequency counts are commonly used to represent sampled data.
  • Understanding the relationship between observed frequencies and the true underlying distribution is crucial.

Purpose of the Study:

  • To study the probability of a true distribution (q) given a sampled frequency count (f).
  • To define a thermodynamic potential for evaluating the Kullback-Leibler divergence between true and measured distributions.
  • To analyze statistical properties like moments, entropy, and mutual information for large sample sizes.

Main Methods:

  • Formulating the probability of the true distribution as a Gibbs distribution.

Related Experiment Videos

  • Defining a thermodynamic potential to simplify the calculation of mean Kullback-Leibler divergence.
  • Expanding expectation values of functions of q in powers of the inverse sample number for large datasets.

    • Main Results:

    • The probability of a true distribution given observed frequencies can be expressed as a Gibbs distribution.
    • A novel thermodynamic potential facilitates the evaluation of the mean Kullback-Leibler divergence.
    • Asymptotic expansions provide insights into the behavior of statistical properties for large sample sizes.

    Conclusions:

    • The proposed framework offers a robust method for statistical inference of probability distributions.
    • The defined thermodynamic potential simplifies the assessment of distribution estimation accuracy.
    • The analysis of moments, entropy, and mutual information highlights the practical implications for data analysis.