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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/51199
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/51199


    Title: 馬可夫鏈蒙地卡羅收斂的研究與貝氏漸進的表現
    A study of mcmc convergence and performance evaluation of bayesian asymptotics
    Authors: 許正宏
    Hsu, Cheng Hung
    Contributors: 翁久幸
    Weng, Chiu Hsing
    許正宏
    Hsu, Cheng Hung
    Keywords: Edgeworth 展開式
    馬可夫鏈蒙地卡羅
    個別後驗分配
    Stein’s 等式
    Edgeworth expansion
    Markov chain Monte Carlo
    marginal posterior distribution
    Stein's identity
    Date: 2010
    Issue Date: 2011-10-05 14:31:53 (UTC+8)
    Abstract: 本論文主要討論貝氏漸近的比較,推導出參數的聯合後驗分配與利用圖形來診斷馬可夫鏈蒙地卡羅的收斂。Johnson (1970)利用泰勒展開式得到個別後驗分配的展開式,此展開式是根據概似函數與先驗分配。 Weng (2010b) 和 Weng and Hsu (2011) 利用 Stein’s 等式且由概似函數與先驗分配估計後驗動差;將這些後驗動差代入Edgeworth 展開式得到近似後驗分配,此近似分配的誤差可精確到大O的負3/2次方與Johnson’s 相同。另外Weng and Hsu (2011)發現Weng (2010b) 和Johnson (1970)的近似展開式各別項誤差到大O的負1次方不一致,由模擬結果得到Weng’s 在此項表現比Johnson’s 好。另外由Weng (2010b)得到一維參數 的Edgeworth 近似後驗分配延伸到二維參數的聯合後驗分配;並應用二維參數的聯合後驗分配於多階段資料。本論文我們提出利用圖形來診斷馬可夫鏈蒙地卡羅收斂的方法,並且應用一般化線性模型與混合常態模型做為模擬。


    關鍵字: Edgeworth 展開式;馬可夫鏈蒙地卡羅;個別後驗分配;Stein’s 等式
    Johnson (1970) obtained expansions for marginal posterior
    distributions through Taylor expansions. The expansion in
    Johnson (1970) is expressed in terms of the likelihood and the prior. Weng (2010b) and Weng and Hsu (2011) showed that by using
    Stein's identity we can approximate the posterior moments in terms
    of the likelihood and the prior; then substituting these
    approximations into an Edgeworth series one can obtain an expansion
    which is correct to O(t{-3/2}), similar to Johnson's.
    Weng and Hsu (2011) found that the O(t{-1}) terms in
    Weng (2010b) and Johnson (1970) do not agree and further
    compared these two expansions by simulation study. The simulations
    confirmed this finding and revealed that our O(t{-1}) term gives
    better performance than Johnson's. In addition to the comparison of
    Bayesian asymptotics, we try to extend Weng (2010a)'s Edgeworth
    series for the distribution of a single parameter to the joint
    distribution of all parameters. Since the calculation is quite
    complicated, we only derive expansions for the two-parameter case
    and apply it to the experiment of multi-stage data. Markov Chain
    Monte Carlo (MCMC) is a popular method for making Bayesian
    inference. However, convergence of the chain is always an issue.
    Most of convergence diagnosis in the literature is based solely on
    the simulation output. In this dissertation, we proposed a graphical
    method for convergence diagnosis of the MCMC sequence. We used some
    generalized linear models and mixture normal models for simulation
    study. In summary, the goals of this dissertation are threefold: to
    compare some results in Bayesian asymptotics, to study the expansion
    for the joint distribution of the parameters and its applications,
    and to propose a method for convergence diagnosis of the MCMC sequence.

    Key words: Edgeworth expansion; Markov Chain Monte Carlo;
    marginal posterior distribution; Stein's identity.
    Reference: Albert, J. H. and Chib, S. (1993), “Bayesian analysis of binary and polychotomous responsedata”, Journal of the American Statistical Association, 88, 669–679.
    Brooks, S. P. and Gelman, A. (1998), “General methods for monitoring convergence ofiterative simulations”, Journal of Computational and Graphical Statistics, 7, 434–455.
    Dellaportas, P. and Smith, A. F. M. (1993), “Bayesian inference for generalized linear andproportional hazards models via gibbs sampling”, Appl. Statist., 42, 443–460.
    Erdelyi, A. (1956), Asympotic Expansions, New York: Dover Publications.
    Finney, D. J. (1947), “The estimation from individual records of the relationship betweendose and quantal response”, Biometrika, 34, 320–334.
    Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995), Bayesian data analysis,New York : Chapman and Hall.4.
    Gelman, A. and Rubin, D. B. (1992), “Inference form iterative simulation using multiplesequences”, Statistical Science, 7, 457–511.
    Geman, S. and Geman, D. (1984), “Stochastic relaxation, gibbs distributions and thebayesian restoration of images”, IEEE Trans. Pattn. Anal. Mach. Intel, 6, 721–741.
    Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1995), Markov Chain Monte Carloin Practice, London: Chapman and Hall.
    Gilks, W. R. and Wild, P. (1992), “Adaptive rejection sampling for gibbs sampling”, Appl.Statist., 41, 337–348.
    Glickman, Mark E. (1993), “Paired comparison models with time-varying parameters”,Ph.D. thesis, Department of Statistics, Harvard University.
    Hinde, J. (1982), Compound Poisson regression models, New York: Springer.
    Hurn, M. W., Barker, N. W., and Magath, T. D. (1945), “The determination of prothrombintime following the administration of dicumarol with specific reference to thromboplastin”,Med., 30, 432–447.
    Johnson, R. (1967), “An asymptotic expansion for posterior distributions”, Ann. Math.Statist., 38, 1899–1906.
    Johnson, R. (1970), “Asymptotic expansions associated with posterior distributions”, Ann. Math. Statist., 41, 851–864.
    Kutner, M. H., Nachtsheim, C. J., and Neter, J. (2004), Applied linear regression models,Boston: McGraw.
    Lunn, D.J., Thomas, A., Best, N., and Spiegelhalter, D. (2000), “Winbugs – a Bayesian modelling framework: concepts structure and extensibility”, Statistics and Computing,10, 325–337.
    Martin, Andrew D., Quinn, Kevin M., and Park, Jong Hee (2010), “MCMCpack:
    Markov chain Monte Carlo (MCMC) Package”, R package version 2.10.0, URL
    http://CRAN.R-project.org/package=MCMCpack.
    McCullagh, P. and Nelder, J. A. (1989), Generalized linear models, New York : Chapman
    and Hall.
    Mendenhall, W. M., Parsons, J. T., Stringer, S. P., Cassissi, N. J., and Million, R. R.(1989), “T2 oral tongue carcinoma treated with radiotherapy: analysis of local control and complications”, Radiotherapy and Oncology, 16, 275–282.
    Minka, T. P. (2001), “A family of algorithms for approximate bayesian inference”, Department of Electrical Engineering and Computer Science, 1–75.
    Myers, R. H. (1990), Classical and Modern Regression with Applications, Boston: PWSKent.
    R Development Core Team (2010), “R: A language and environment for statistical computing”, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, URL http://www.R-project.org.
    Tanner, M. A. (1993), Tools for Statistical Inference, New York: Springer.
    Tierney, L. and Kadane, J. B. (1986), “Accurate approximations for posterior moments and marginal densities”, Journal of the American Statistical Association, 81, 82–86.
    Weng, R. C. (2003), “On Stein’s identity for posterior normality”, Statistica Sinica, 13, 495–506.
    Weng, R. C. (2010a), “A Bayesian Edgeworth expansion by Stein’s Identity”, Bayesian Analysis, 5, 741–764.
    Weng, R. C. (2010b), “A note on posterior distributions”, in JSM Proceedings, Section on
    Bayesian Statistical Science, 2599–2608, Alexandria, VA: American Statistical Association.
    Weng, R. C. and Hsu, C.-H. (2011), “A study of expansions of posterior distributions”, Communications in Statistics - Theory and Methods.
    Weng, R. C. and Tsai, W.-C. (2008), “Asymptotic posterior normality for multiparameter problems”, Journal of Statistical Planning and Inference, 138, 4068–4080.
    Woodroofe, M. (1989), “Very weak expansions for sequentially designed experiments: linear models”, Ann. Statist., 17, 1087–1102.
    Description: 博士
    國立政治大學
    統計研究所
    93354504
    99
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0093354504
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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