Likelihood-free Bayesian estimation of multivariate quantile distributions

Computational Statistics and Data Analysis

Volumn 55, Issue 9, 2011, Pages 2541-2556

  Drovandi, Christopher C ^a   Pettitt, Anthony N ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Approximate Bayesian computation; Copula; g and k distribution; Multivariate; Quantile distributions; Sequential Monte Carlo

Indexed keywords

APPROXIMATE BAYESIAN; COPULA; G-AND-K DISTRIBUTION; MULTIVARIATE; QUANTILE DISTRIBUTIONS; SEQUENTIAL MONTE CARLO;

ADAPTIVE ALGORITHMS; BAYESIAN NETWORKS; MONTE CARLO METHODS; STATISTICAL METHODS; TIME SERIES;

IMAGE SEGMENTATION;

EID: 79956069368     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2011.03.019     Document Type: Article

References (39)

1. D. Allingham, R. King, and K. Mengersen Bayesian estimation of quantile distributions Statistics and Computing 19 2009 189 201
2. Attias, H., 1999. Inferring parameters and structure of latent variable models by variational Bayes. In: Proc. 15th Conf. on Uncertainty in Artificial Intelligence, vol. 2.
3. S. Badrinath, and S. Chatterjee On measuring skewness and elongation in common stock return distributions: the case of the market index The Journal of Business 61 4 1988 451 472
4. M.A. Beaumont, J.-M. Cornuet, J.-M. Marin, and C.P. Robert Adaptive approximate Bayesian computation Biometrika 96 4 2009 983 990
5. M.A. Beaumont, W. Zhang, and D.J. Balding Approximate Bayesian computation in population genetics Genetics 162 2002 2025 2035 (Pubitemid 36114682)
6. Bowley, A., 1920. Elements of statistics. PS King.
7. N. Chopin A sequential particle filter method for static models Biometrika 89 3 2002 539 551 (Pubitemid 41311963)
8. E. Crow, and M. Siddiqui Robust estimation of location Journal of the American Statistical Association 62 318 1967 353 389
9. P. Del Moral, A. Doucet, and A. Jasra Sequential Monte Carlo samplers Journal of the Royal Statistical Society: Series B 68 3 2006 411 436 (Pubitemid 43742903)
10. Del Moral, P., Doucet, A., Jasra, A., 2008. On adaptive resampling procedures for sequential Monte Carlo methods. Tech. rep., Inria.
11. Del Moral, P., Doucet, A., Jasra, A., 2009. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Tech. rep., Institute of Statistical Mathematics, Tokyo, Japan.
12. C.C. Drovandi, and A.N. Pettitt Estimation of parameters for macroparasite population evolution using approximate Bayesian computation Biometrics 67 1 2011 225 233
13. C.C. Drovandi, A.N. Pettitt, and M.J. Faddy Approximate Bayesian computation using indirect inference Journal of the Royal Statistical Society: Series C (Applied Statistics) 60 3 2011 503 524
14. Fearnhead, P., Prangle, D., 2011. Constructing summary statistics for approximate Bayesian computation: Semi-automatic ABC. arXiv:1004.1112v2.
15. Fearnhead, P., Taylor, B.M., 2010. An adaptive sequential Monte Carlo sampler. arXiv:1005.1193v2.
16. C. Field, and M. Genton The multivariate g-and-h distribution Technometrics 48 1 2006 104 111 (Pubitemid 43288399)
17. M. Fischer Generalized Tukey-type distributions with application to financial and teletraffic data Statistical Papers 51 1 2010 41 56
18. M. Fischer, A. Horn, and I. Klein Tukey-type distributions in the context of financial data Communications in Statistics. Theory and Methods 36 1 2007 23 35 (Pubitemid 46324064)
19. Fisher, R.A., Yates, F., 1948. Statistical Tables for Biological, Agricultural, and Medical Research. Hafner, New York.
20. W. Gilchrist Statistical Modelling with Quantile Functions 2000 Chapman & Hall/CRC London
21. K. Heggland, and A. Frigessi Estimating functions in indirect inference Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66 2 2004 447 462 (Pubitemid 38652731)
22. D. Hinkley On power transformations to symmetry Biometrika 62 1 1975 101 111
23. P.D. Hoff Extending the rank likelihood for semiparametric copula estimation The Annals of Applied Statistics 1 1 2007 265 283
24. F. Luciani, S.A. Sisson, H. Jiang, A.R. Francis, and M.M. Tanaka The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis Proceedings of the National Academy of Sciences of the United States of America 106 34 2009 14711 14715
25. P. Marjoram, J. Molitor, V. Plagonal, and S. Tavar Markov chain Monte Carlo without likelihoods Proceedings of the National Academy of Sciences of the United States of America 100 26 2003 15324 15328 (Pubitemid 38020988)
26. McVinish, R., 2010. Improving ABC for quantile distributions. Statistics and Computing (in press) doi:10.1007/s11222-010-9209-9.
27. T. Mills Modelling skewness and kurtosis in the London stock exchange FT-SE index return distributions Journal of the Royal Statistical Society: Series D (The Statistician) 44 3 1995 323 332
28. J. Møller, A.N. Pettitt, R. Reeves, and K.K. Berthelsen An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants Biometrika 93 2 2006 451 458 (Pubitemid 43992204)
29. J. Moors A quantile alternative for kurtosis Journal of the Royal Statistical Society: Series D (The Statistician) 37 1 1988 25 32
30. Peters, G.W., Sisson, S.A., 2006. Bayesian inference, Monte Carlo sampling and operational risk. Tech. rep., University of New South Wales.
31. Peters, G., Sisson, S., Fan, Y., 2010. Likelihood-free Bayesian inference for alpha-stable models. doi:10.1016/j.csda.2010.10.004.
32. O. Ratmann, C. Andrieu, C. Wiuf, and S. Richardson Model criticism based on likelihood-free inference, with an application to protein network evolution Proceedings of the National Academy of Sciences of the United States of America 106 26 2009 10576 10581
33. G. Rayner, and H. MacGillivray Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions Statistics and Computing 12 1 2002 57 75 (Pubitemid 37132838)
34. Reeves, R.W., Pettitt, A.N., 2005. A theoretical framework for approximate Bayesian computation. In: Francis, A.R., Matawie, K.M., Oshlack, A., Smyth, G.K. (Eds.), Proceedings of the 20th International Workshop on Statistical Modelling. Sydney, Australia, pp. 393396.
35. Robert, C.P., Cornuet, J.-M., Marin, J.-M., Pillai, N.S., 2011. Lack of confidence in ABC model choice. arXiv:1102.4432v1.
36. Sisson, S.A., Fan, Y., 2011. Handbook of Markov Chain Monte Carlo. Chapman & Hall, Ch. Likelihood-free Markov chain Monte Carlo (in press).
37. S. Sisson, Y. Fan, and M. Tanaka Correction for Sisson et al. sequential Monte Carlo without likelihoods Proceedings of the National Academy of Sciences 106 39 2009 16889 16890
38. S. Sisson, Y. Fan, and M. Tanaka Sequential Monte Carlo without likelihoods Proceedings of the National Academy of Sciences 104 6 2007 1760 1765 (Pubitemid 46239852)
39. G.W. Tukey Exploratory Data Analysis 1977 Addison-Wesley Reading