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On the implementation of maximum entropy sampling with unequal probabilities and without replacement.

Philippe Aubry1

  • 1OFB - Office français de la biodiversité - Direction surveillance, évaluation, données - Unité données et appui méthodologique, Saint Benoist, BP 20, F-78612 Le Perray-en-Yvelines, France.

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Summary

This guide provides practical algorithms for maximum entropy sampling in finite populations. It addresses challenges in conditional Poisson sampling, offering a valuable toolkit for researchers and engineers.

Keywords:
Conditional Poisson samplingJoint inclusion probabilitiesMaximum entropy samplingPoisson binomial distributionSampling algorithmsTime complexityUnequal probability sampling

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Area of Science:

  • Statistics
  • Survey Methodology
  • Computational Statistics

Background:

  • Maximum entropy sampling enhances statistical inference robustness.
  • Existing literature lacks practical guides for implementing maximum entropy sampling in finite populations with unequal probabilities and without replacement.

Purpose of the Study:

  • To provide a comprehensive toolkit and reference guide for maximum entropy sampling.
  • To bridge the gap between formal results and practical implementation in programming languages.

Main Methods:

  • Presents formal results for Poisson sampling, Poisson binomial distribution, and conditional Poisson sampling.
  • Details computation of second-order inclusion probabilities for conditional Poisson sampling.
  • Provides ready-to-use algorithms for Poisson sampling, Poisson binomial distribution, and various conditional Poisson sampling methods (rejective, draw-by-draw, sequential, exchange).

Main Results:

  • Formal results for key sampling designs are compiled.
  • Algorithms for implementing Poisson sampling and its distribution are provided.
  • Detailed algorithms for conditional Poisson sampling are presented, addressing a significant statistical challenge.

Conclusions:

  • This work offers a practical implementation guide for maximum entropy sampling.
  • The provided algorithms facilitate the application of complex sampling designs in research and engineering.
  • The toolkit addresses the long-standing challenge of conditional Poisson sampling with fixed sample sizes.