Error of calculating the optimal Bayesian estimate using the Monte Carlo method in nonlinear problems

  • Authors:

  • N. A. Berkovskii;O. A. Stepanov

  • Affiliations:

  • Central Research Institute Elektropribor, St. Petersburg, Russia and St. Petersburg State Polytechnical University, St. Petersburg, Russia;Central Research Institute Elektropribor, St. Petersburg, Russia and St. Petersburg State Polytechnical University, St. Petersburg, Russia

  • Venue:
  • Journal of Computer and Systems Sciences International
  • Year:
  • 2013

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Abstract

We propose a procedure for evaluating the error in calculating the optimal Bayesian estimate based on the analysis of the probability density function for the ratio of two integrals calculated by the Monte Carlo method. Relationship between the proposed method and the well-known delta method is revealed. Results of numerical experiments for a test problem and the landmark navigation problem are presented. These results prove the efficiency of the proposed method and the validity of conclusions.