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Stochastic cusp catastrophe model and its Bayesian computations.

Ding-Geng Chen1,2,3, Haipeng Gao4,5, Chuanshu Ji4

  • 1School of Social Work, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.

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Summary
This summary is machine-generated.

This study introduces a new Bayesian method to analyze the complex cusp catastrophe model, overcoming challenges with intractable likelihood functions for stochastic differential equations. The approach shows promise for financial modeling, including exchange rates.

Keywords:
60G25Bayesian inferenceCusp catastrophe modelHamiltonian Monte CarloHermite expansionstochastic differential equationtransition density

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Area of Science:

  • Catastrophe Theory
  • Stochastic Differential Equations
  • Bayesian Statistics

Background:

  • The classical cusp catastrophe model is vital in understanding system bifurcations.
  • Statistical inference for stochastic cusp differential equations is analytically intractable due to complex transition densities.

Purpose of the Study:

  • To address the unsolved statistical inference problem for the stochastic cusp differential equation.
  • To develop a novel Bayesian approach for analyzing the cusp catastrophe model.

Main Methods:

  • A novel Bayesian framework was developed.
  • Hamiltonian Monte Carlo (HMC) was combined with Euler approximation and Hermite expansion for likelihood approximation.
  • The approach was validated using simulation studies.

Main Results:

  • The proposed Bayesian method successfully handles the analytically intractable likelihood function.
  • Simulation studies confirmed the validity and efficacy of the novel approach.
  • The method demonstrated practical applicability in analyzing real-world financial data.

Conclusions:

  • The novel Bayesian approach provides a viable solution for statistical inference in stochastic cusp differential equations.
  • This method offers a powerful tool for analyzing complex systems exhibiting catastrophic bifurcations.
  • The approach has potential applications in econometrics and financial market analysis, such as exchange rate modeling.