New Search

Export article

Convergence of spectral likelihood approximation based on q-Hermite polynomials for Bayesian inverse problems

Zhiliang Deng, Xiaomei Yang

Abstract: In this paper, q-Gaussian distribution, q-analogy of Gaussian distribution, is introduced to characterize the prior information of unknown parameters for inverse problems. Based on q-Hermite polynomials, we propose a spectral likelihood approximation (SLA) algorithm of Bayesian inversion. Convergence results of the approximated posterior distribution in the sense of Kullback–Leibler divergence are obtained when the likelihood function is replaced with the SLA and the prior density function is truncated to its partial sum. In the end, two numerical examples are displayed, which verify our results.
Keywords: function / Hermite / polynomials / Bayesian / Gaussian / analogy / posterior / partial / sum / Kullback

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

Share this article

Click here to see the statistics on "Proceedings of the American Mathematical Society" .
References (26)
    Cited by 1 articles
      Back to Top Top