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研究生:陳宣佑
研究生(外文):Hsuan-Yu Chen
論文名稱:截切多變量t分佈的動差與切片抽樣
論文名稱(外文):On Moments and Slice Sampling for Truncated Multivariate t Distributions
指導教授:林宗儀林宗儀引用關係
口試委員:吳宏達王婉倫
口試日期:2011-06-18
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:37
中文關鍵詞:輔助變數切片抽樣截切t分佈均勻分佈
外文關鍵詞:auxiliary variableGibbs samplingslice samplingtruncated normal distributiontruncated t distributionuniform distribution
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截切分佈已經被廣泛運用於解決各式的科學問題,而如何從截切分佈中抽樣的議題,在文獻上也有許多的探討。然而,相關的研究在截切多變量t分佈上(TMVT),卻鮮少被提及。在此篇文章中,我們首先推導出當左右端點皆被限制於固定區間時,TMVT分佈一階及二階動差的通式,其結果是以矩陣形式表示之,利用程式軟體即可快速的計算出真實值。另外,我們也探討如何利用切片抽樣演算法生成隨機變數。此方法乃是藉由引進輔助變數,將原本從多變量分佈的抽樣,轉換成從一序列具均勻分佈形式的條件機率密度中抽樣。最後,文中也提供了一些實例及應用。


The use of truncated distributions arises often in a wide variety of scientific problems. There have been a lot of sampling schemes and proposals developed for various specific truncated distributions. In the literature, the study of the truncated multivariate t (TMVT) distribution has rarely been discussed. In this paper, we first present general formulae for computing the first and second moments of the TMVT distribution under the doubly truncated case. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for truncation on the left and right can be viewed as special cases. We apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are all uniform distributions. Several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results.

1. Introduction.......................................... 1
2. Moments of truncated t distribution................... 4
2.1. The univariate case................................. 4
2.2. The multivariate case............................... 6
3. Sampling of truncated t distribution................. 10
3.1. Slice sampling..................................... 10
3.2. The univariate case................................ 11
3.3. The multivariate case.............................. 13
4. Application.......................................... 19
4.1. Bayesian model with heavily-tailed t distribution.. 19
4.2. Bayesian regression with noninformative priors..... 20
4.3. Maximum likelihood estimation for multivariate skew t distributions........................................... 21
5. Conclusion........................................... 24
6. Supplementary Material............................... 25
7. References........................................... 35


Damien, P., Wakefield, J., and Walker, S. (1999), Gibbs Sampling for Bayesian Non-conjugate and Hierarchical Models by Using Auxiliary Variables, Journal of Royal Statistical Society B, 61, part 2, 331-344.

Damien, P., Walker, S. G. (2001), Sampling Truncated Normal, Beta, and, Gamma Densities, Journal of Computational and Graphical Statistics, Vol. 10, No. 2,
206-215.

Dempster, A. P., Lard, N.M., and Rubin, D.B. (1977), Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc.
Ser. B 39, 1-38.

Devroye, L. (1986), Non-uniform random variate generation. New York: Springer-Verlag.

Gelfand, A. E., Smith, A. F. M., and Lee, T. M. (1992), Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling, Journal of the American Statistical Association, 87, 523-532.

Geman, S., and Geman, D. (1984), Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.

Geweke, J. (1986), Exact Inference in the Inequality Constrained Normal Linear Regression Model, Journal of Applied Econometrics, Vol. 1, 127-142.

Hill, B. M. (1974), On Coherence, Inadmissibility and Inference About Many Parameters in the Theory of Least Squares, in Studies in Bayesian Econometrics and Statistics, eds. S. E. Fienberg and A. Zellner, Amsterdam: North-Holland, pp. 555-584.

Horrace, W. C. (2005), Some results on the multivariate truncated normal distribution, J. Multi. Ana. 94, 209-221.

Jawitz, J. W. (2004), Moments of truncated continuous univariate distributions, Advances in Water Resources, 27, 269-281.

Kim, H. J. (2008), Moments of Truncated Student-t Distribution, Journal of the Korean Statistical Society, 37, 81-87.

Lange, K. L., Little, R. J. A., and Taylor, J. M. G. (1989), Robust statistical modeling using the t distribution. J. Amer. Statist. Assoc. 84, 881-896.
Lien, DHD. (1985) Moments of truncated bivariate log-normal distributions, Economics Letters, Vol. 19, 243-247.

Lin, T. I. (2010), Robust mixture modeling using multivariate skew t distributions, Statistics and Computing, Vol. 20, No. 3, 343-356.

Meng, X. L., and Rubin, D.B. (1993), Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267–278.

Nadarajah1, S. and Kotz, S. (2004), Multivariate t Distributions and Their Applications. third ed. Cambridge University Press, New York.

Neal, R. M. (1997), Markov chain Monte Carlo methods based on ‘slicing’ the density function. Technical Report, Department of Statistics, University of Toronto.

Neal, R. M. (2003), Slice Sampling, The Annals of Statistics, Vol. 31, No. 3, 705-767.

O’Haggan, A. (1988), Modelling with Heavy Tails. In: Bernardo, J. M. et al. (eds) Bayesian Statistics 3, 569-577. Oxford Univ. Press, Oxford.

Philippe, A. and Robert, C. P. (2003), Perfect Simulation of Positive Gaussian Distributions, Statistics and Computing, Vol. 13, 179V186.

Robert, C. P. (1995), Simulation of truncated normal variables, Statistics and Computing, 5, 121-125.

Savenkov, M. (2009), On the Truncated Weibull Distribution and its Usefulness in Evaluating the Theoretical Capacity Factor of Potential Wind (or Wave) Energy Sites, University Journal of Engineering and Technology, Vol. 1, 21-25.

Sahu, S. K., Dey, D. K., and Branco, M. D. (2003), A new class of multivariate skew distributions with applications to bayesian regression models, Canad. J.

Statist. 31, 129-150. Talis, G. M. (1961), The Moment Generating Function of the Truncated Multinormal
Distribution, Journal of the Royal Statistical Society, Series B, 23, 223-229.

Zellner, A., Tiao, G. C. (1964), Bayesian analysis of the regression model with autocorrelated errors. Journal of the American Statistical Association, 59, 763-778


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