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Interaction Order Estimation in Tensor Curie-Weiss Models.

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Summary
This summary is machine-generated.

Estimating the interaction parameter p in spin Curie-Weiss models is impossible if the inverse temperature β is unknown. Consistent estimation of p is possible only when β is known and exceeds a specific threshold related to p.

Keywords:
Curie–Weiss modelcontiguityinteraction orderjoint estimation

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Area of Science:

  • Statistical physics
  • Information theory
  • Probability theory

Background:

  • The Curie-Weiss model is a fundamental model in statistical mechanics.
  • Estimating model parameters is crucial for understanding physical systems.
  • The interaction parameter 'p' and inverse temperature 'β' are key characteristics of the p-spin Curie-Weiss model.

Purpose of the Study:

  • To investigate the possibility of estimating the interaction parameter 'p' of a p-spin Curie-Weiss model from a single observation.
  • To determine the conditions under which parameter estimation is feasible.
  • To extend these findings to the p-spin Erdös-Rényi Ising model.

Main Methods:

  • Contiguity arguments from statistical inference.
  • Analysis of parameter identifiability in statistical models.
  • Mathematical modeling of magnetic systems.

Main Results:

  • Joint estimation of 'p' and 'β' is impossible.
  • Estimation of 'p' is impossible when 'β' is unknown.
  • An increasing threshold function β*(p) was identified.
  • Consistent estimation of 'p' is impossible for β < β*(p) and possible for β > β*(p) when 'β' is known.

Conclusions:

  • Parameter estimation in complex statistical models can be fundamentally limited.
  • The relationship between parameters significantly impacts their estimability.
  • The findings provide theoretical bounds for statistical inference in spin models.