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Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection

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Seminar on Stochastic Analysis, Random Fields and Applications IV

Part of the book series: Progress in Probability ((PRPR,volume 58))

Abstract

We develop a Bayesian hierarchical logistic regression model to predict the credit risk of companies classified in different sectors. Explanatory variables derived by experts from balance-sheets are included. Markov chain Monte Carlo (MCMC) methods are used to estimate the proposed model. In particular we show how the delaying rejection strategy outperforms the standard Metropolis-Hastings algorithm in terms of asymptotic efficiency of the resulting estimates. The advantages of our model over others proposed in the literature are discussed and tested via cross-validation procedures.

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References

  1. S.P. Brooks, P. Giudici and G.O. Roberts, Efficient construction of reversible jump Markow chain Monte Carlo proposal distributions (with discussion), J. Royal Statist. Soc. Series B, 65 (2003), 3–55.

    Article  MathSciNet  MATH  Google Scholar 

  2. P.J. Green and A. Mira, Delayed rejection in reversible jump Metropolis-Hastings, Biometrika, 88 (2001), 1035–1053.

    MathSciNet  MATH  Google Scholar 

  3. G. King and L. Zeng, Logistic regression in rare events data, Political Analysis, 9 (2) (2001), 137–163.

    Article  Google Scholar 

  4. P.H. Peskun, Optimum Monte Carlo sampling using Markov chains, Biometrika, 60 (1973), 607–612.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.D. Sokol, Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms, Cours de Troisième Cycle de la Physique en Suisse Romande, Lausanne, (1989).

    Google Scholar 

  6. L. Tierney, Markov chains for exploring posterior distributions, Annals of Statistics, 22 (1994), 1701–1762.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Tierney and A. Mira, Some adaptive Monte Carlo methods for Bayesian inference, Statistics in Medicine, 18 (1999), 2507–2515.

    Article  Google Scholar 

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© 2004 Springer Basel AG

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Mira, A., Tenconi, P. (2004). Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications IV. Progress in Probability, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7943-9_17

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  • DOI: https://doi.org/10.1007/978-3-0348-7943-9_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9630-6

  • Online ISBN: 978-3-0348-7943-9

  • eBook Packages: Springer Book Archive

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