Likelihood-free Bayesian inference for α-stable models

Computational Statistics and Data Analysis

Volumn 56, Issue 11, 2012, Pages 3743-3756

  Peters, G W ^a   Sisson, S A ^a   Fan, Y ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

stable distributions; Approximate Bayesian computation; Bayesian inference; Likelihood free inference; Multivariate models

Indexed keywords

APPROXIMATE BAYESIAN; BAYESIAN INFERENCE; LIKELIHOOD-FREE INFERENCE; MULTIVARIATE MODELS; STABLE DISTRIBUTIONS;

BAYESIAN NETWORKS; INFERENCE ENGINES; SIGNAL PROCESSING;

MODELS;

EID: 84862018054     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.10.004     Document Type: Article

References (58)

1. R. Alder, R. Feldman, and M.S. Taqqu A Practical Guide to Heavy-Tails: Statistical Techniques for Analysing Heavy-Tailed Distributions 1998 Birkhäuser
2. M.A. Beaumont, W. Zhang, and D.J. Balding Approximate Bayesian computation in population genetics Genetics 162 2002 2025 2035
3. H. Bergstrom On some expansions of stable distributional functions Arkiv för Matematik 2 1953 375 378
4. Blum, M.G.B.; 2010. Approximate Bayesian computation: a non-parametric perspective. Journal of the American Statistical Association (in press).
5. S.P. Brooks, A. Gelman, G. Jones, and X.L. Meng Handbook of Markov chain Monte Carlo 2010 Chapman and Hall/CRC
6. D.J. Buckle Bayesian inference for stable distributions Journal of the American Statistical Association 90 1995 605 613
7. T. Byczkowski, J.P. Nolan, and B. Rajput Approximation of multidimensional stable densities Journal of Multivariate Analysis 46 1993 13 31
8. Casarin, R.; 2004. Bayesian inference for mixtures of stable distributions. Working Paper No. 0428. CEREMADE, University Paris IX.
9. P. Del Moral Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications 2004 Springer New York
10. P. Del Moral, A. Doucet, and A. Jasra Sequential Monte Carlo samplers Journal of the Royal Statistical Society: Series A 68 2006 411 436
11. Del Moral, P.; Doucet, A.; Jasra, A.; 2009. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Technical Report. Uni. of Bordeaux.
12. L. Devroye An automatic method for generating random variates with a given characteristic function SIAM Journal on Applied Mathematics 46 1986 698 719
13. T. Doganoglu, and S. Mittnik An approximation procedure for asymmetric stable paretian densities Computational Statistics 13 1998 463 475
14. Doucet, A.; Johansen, A.M.; 2010. A tutorial on particle filtering and smoothing: fifteen years later. In: Crisan, D.; Rozovsky, B. (Eds.), Oxford Handbook of Nonlinear Filtering. Oxford University Press (in press).
15. Drovandi, C.C.; Pettitt, A.N.; 2010. Estimation of parameters for microparasite population evolution using approximate Bayesian computation. Biometrics (in press). Availble online at: http://onlinelibrary.wiley.com/doi/ 10.1111/j.1541-0420.2010.01410.x/abstract.
16. W. DuMouchel Stable distributions in statistical inference: information from stably distributed samples Journal of the American Statistical Association 70 1975 386 393
17. E. Fama The behaviour of stock market prices The Journal of Business 38 1965 34 105
18. E. Fama, and R. Roll Some properties of symmetric stable distributions Journal of the American Statistical Association 63 1968 817 836
19. Godsill, S.; 2000. Inference in symmetric alpha-stable noise using MCMC and the slice sampler. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing. pp. 3806-3809.
20. Godsill, S.; 1999. MCMC and EM-based methods for inference in heavy-tailed processes with alpha stable innovations. In: Proc. IEEE Signal Processing Workshop on Higher Order Statistics.
21. A. Grelaud, C.P. Robert, J.M. Marin, F. Rodolphe, and J.F. Taly ABC likelihood-free methods for model choice in Gibbs random fields Bayesian Analysis 4 2009 317 336
22. W. Jiang, and B. Turnbull The indirect method: inference based on intermediate statistics - a synthesis and examples Statistical Science 19 2004 238 263
23. I. Koutrouvelis Regression type estimation of the parameters of stable laws Journal of the American Statistical Association 75 1980 918 928
24. Kuruoglu, E.E.; Molina, C.; Godsill, S.J.; Fitzgenrald, W.J.; 1997. A new analytic representation for the alpha stable probability density function. In: Bozdogan, H. Soyer, R. (Eds.), AMS Proceedings, Section on Bayesian Statistics.
25. P. Levy Theorie des erreurs. La loi de Gauss et les lois exceptionelles Bulletin de la Société Mathématique de France 52 1924 49 85
26. J.S. Liu Monte Carlo Strategies in Scientific Computing 2001 Springer-Verlag
27. M.J. Lombardi Bayesian inference for alpha stable distributions: a random walk MCMC approach Computational Statistics & Data Analysis 51 2007 2688 2700
28. M. Lombardi, and S. Godsill On-line Bayesian estimation of AR signals in symmetric alpha-stable noise IEEE Transactions on Signal Processing 2006
29. B. Mandelbrot The Pareto-Levey law and the distribution of income International Economic Review 1 1960 79 106
30. P. Marjoram, J. Molitor, V. Plagnol, and S. Tavare Markov chain Monte Carlo without likelihoods Proceedings of the National Academy of Sciences of the USA 100 2003 15324 15328
31. J.H. McCulloch Numerical approximation of the symmetric stable distribution and density R. Adler, R. Feldman, M.S. Taqqu, A Practical Guide to Heavy Tails: Statistical Techniques and Applications 1998 Birkhäuser Boston
32. J.H. McCulloch Simple consistent estimators of stable distribution parameters Communications in Statistics - Simulation and Computation 15 1986 1109 1136
33. T. McKinley, A.R. Cook, and R. Deardon Inference in epidemic models without likelihoods The International Journal of Biostatistics 5 2009 Article 24
34. Melchiori, M.R.; 2006. Tools for sampling multivariate archimedian copulas. www.YieldCurve.com.
35. S. Mittnik, and S.T. Rachev Alernative multivariate stable distributions and their applications to financial modelling E. Cambanis, G. Samorodnitsky, M.S. Taqqu, Stable Processes and Related Topics 1991 Birkhäuser Boston 107 119
36. R. Modarres, and J.P. Nolan A method for simulating stable random vectors Computational Statistics 9 1994 11 19
37. R. Neal Slice sampling Annals of Statistics 31 2003 705 767
38. C. Nikias, and M. Shao Signal Processing with Alpha Stable Distributions and Applications 1995 Wiley New York
39. J.P. Nolan Numerical computation of stable densities and distributions Communications in Statistics. Simulation and Computation 13 1997 759 774
40. J.P. Nolan Stable Distributions: Models for Heavy-Tailed Data 2007 Birkhäuser
41. Nolan, J.P.; 2008. Stable Distributions: Models for heavy-tailed data. Technical Report. Math/Stat Department, American University.
42. J.P. Nolan, A.K. Panorska, and McCulloch Estimation of stable spectral measures, stable non-Gaussian models in finance and econometrics Mathematical and Computer Modelling 34 2001 1113 1122
43. Peters, G.W.; Fan, Y.; Sisson, S.A.; 2009. On sequential Monte Carlo, partial rejection control and approximate Bayesian computation. Tech. Rep. UNSW.
44. A. Pievatolo, and P. Green Boundary detection through dynamic polygons Journal of the Royal Statistical Society: Series B 60 3 1998 609 626
45. S. Press Estimation in univariate and multivariate stable distributions Journal of the American Statistical Association 67 1972 842 846
46. J.K. Pritchard, M.T. Seielstad, A. Perez-Lezaun, and M.W. Feldman Population growth of human Y chromosomes: a study of Y chromosome microsatellites Molecular Biology and Evolution 16 1999 1791 1798
47. Z. Qiou, and N. Ravishanker Bayesian inference for time series with infinite variance stable innovations Journal of Time Series Analysis 19 1998 235 249
48. Z. Qiou, and N. Ravishanker Bayesian inference for vector ARMA models with stable innovations The Indian Journal of Statistics. Series A 60 1998 459 475
49. O. Ratmann, C. Andrieu, T. Hinkley, 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 USA 106 2009 10576 10581
50. 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.), Proc. 20th Int. Works. Stat. Mod. Australia. 2005. pp. 393-396.
51. Salas-Gonzalez, D.; Kuruoglu, E.E.; Ruiz, D.P.; 2006. Estimation of mixtures of symmetric alpha-stable distributions with an unknown number of components. In: IEEE Int. Conf. on Acoustics, Speech and Sig. Proc. Toulouse. France.
52. G. Samorodnitsky, and M.S. Taqqu Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance 1994 Chapman and Hall/CRC
53. S.A. Sisson, and Y. Fan Likelihood-free Markov chain Monte Carlo S.P. Brooks, A. Gelman, G. Jones, X.L. Meng, Handbook of Markov Chain Monte Carlo 2010 Chapman and Hall/CRC
54. S.A. Sisson, Y. Fan, and M.M. Tanaka Sequential Monte Carlo without likelihoods Proceedings of the National Academy of Sciences 104 2007 1760 1765 Proceedings of the National Academy of Sciences 106 2009 16889 (errata)
55. Sisson, S.A.; Peters, G.W.; Briers, M.; Fan, Y.; 2009. A note on target distribution ambiguity for likelihood-free samplers. Technical Report. University of New South Wales.
56. S. Tavaré, D.J. Balding, R.C. Griffiths, and P. Donnelly Inferring coalescence times from DNA sequence data Genetics 145 1997 505 518
57. R. Weron Modeling and Forecasting Electiricty Loads and Prices: A Statistical Approach 2006 Wiley
58. V.M. Zolotarev One-Dimensional Stable Distributions Translations of Mathematical Monographs 1986 American Mathematical Society