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題名 The Influence of Variance in Two-Armed Bandit Problems
作者 黃秋霖
Huang, Qiu-Lin
貢獻者 余清祥
Yu, Qing-Xiang
黃秋霖
Huang, Qiu-Lin
關鍵詞 Two-armed bandit問題
治療法
策略
效用函數
變異因子
日期 1995
上傳時間 28-Apr-2016 15:06:28 (UTC+8)
摘要 本論文主要是發掘變異數在Two-armed Bandit問題中的影響。在文中我們假設兩種治療法的成功率分別是θ1和θ2，且以π1~Beta(cα,cβ)和π2~Beta(α,β)為其驗前機率分配。此外，我們假設所有病人數(N)已知。
The focus of the report is to find the influence of variance in Two-armed Bandit problems. In this report, we consider the case when the success probabilities of the two treatmentsθ1,θ2 haveπ1~Beta(cα,cβ) andπ2~Beta(α,β) as their priors, and the total number of patients, N is known.
參考文獻 [1] Apostal, T. M. (1975) Mathematical analysis. Addison- Wesley.
     [2] Berry, D. A. and Fristedt, B. (1985) Bandit problems - Sequential allocation of experiments, Ch.apm.an and Hall.
     [3] Berry, D. A. and Pearson, L. (1984) Optimal design for two-stage clinical trials with dichotomous responses. Unit. of Minnesota Tech.. Rep.
     [4] Canner, P. L. (1970). Selecting one of the two treatments when the responses are dichotomous, J.A.S.A. , 65, 293-306.
     [5] Chernoff, H. and Ray, S. N. (1965). A bayes sequential sampling inspection plan. Ann. Math.. Statist. 36, 1387-1407.
     [6] Clayton, M. K. and ` Witmer, J. A. (1988) Two-stage bandit , Annals of Stat. Vo1.16 , No.2, 887-894.
     [7] Colton, T. (1963) A model for selecting one of two medical treatment. J.A.S.A. , 58, 388-400.
     [8] Cornfield, J., Halperin, M. , and Greenhouse, S.W. (1969). An adaptive procedure for sequential clinical trials. 1. A.S.A, 64, 759- 770.
     [9] Eick, S. G. (1988) The two-armed bandit with delayed responses, Annals of Stat, Vol.l6, No.2: 254-264.
     [10] Eick, S. G. (1988) Gittins procedures for bandits with delayed responses: J.R.S.S. , Soc. B , 50, No.1, 125-132 .
     [11] Petkau, A. J. (1978) Sequential medical trials for comparing an experimental with a standard treatment. 1. Am.er. Statist. Assoc, 73, 328-338.
     [12] Witmer, J. A. (1983) Bayesian multistage decision problems, Ph. D. Thesis.
     [13] Witmer , J. A. (1986) Bayesian multistage decision problems, Annals of Stat., Vol. 14, No. 1. 283-297.
描述 碩士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002003013
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.advisor Yu, Qing-Xiangen_US
dc.contributor.author (Authors) 黃秋霖zh_TW
dc.contributor.author (Authors) Huang, Qiu-Linen_US
dc.creator (作者) 黃秋霖zh_TW
dc.creator (作者) Huang, Qiu-Linen_US
dc.date (日期) 1995en_US
dc.date.accessioned 28-Apr-2016 15:06:28 (UTC+8)-
dc.date.available 28-Apr-2016 15:06:28 (UTC+8)-
dc.date.issued (上傳時間) 28-Apr-2016 15:06:28 (UTC+8)-
dc.identifier (Other Identifiers) B2002003013en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/87532-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) 本論文主要是發掘變異數在Two-armed Bandit問題中的影響。在文中我們假設兩種治療法的成功率分別是θ1和θ2，且以π1~Beta(cα,cβ)和π2~Beta(α,β)為其驗前機率分配。此外，我們假設所有病人數(N)已知。zh_TW
dc.description.abstract (摘要) The focus of the report is to find the influence of variance in Two-armed Bandit problems. In this report, we consider the case when the success probabilities of the two treatmentsθ1,θ2 haveπ1~Beta(cα,cβ) andπ2~Beta(α,β) as their priors, and the total number of patients, N is known.en_US
dc.description.tableofcontents Abstract i
     1INTRODUCTION 1
     1.1PRELIMINARIES..........1
     1.2LITERATURE REVIEW..........4
     2MODEL 7
     2.1INTRODUCTION..........7
     2.2ASSUMPTION..........7
     2.3STRATEGIES..........9
     3KNOWN TRIAL LENGTH 12
     3.1INTRODUCTION..........12
     3.2GENERAL RESULTS..........13
     3.3THE INFLUENCE OF THE VARIANCE FACTOR..........24
     3.4CONTINUITY OF UTILITY FUNCTION..........37
     4CONCLUSION AND COMMENTS 41
     Bibliography 43		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002003013en_US
dc.subject (關鍵詞) Two-armed bandit問題zh_TW
dc.subject (關鍵詞) 治療法zh_TW
dc.subject (關鍵詞) 策略zh_TW
dc.subject (關鍵詞) 效用函數zh_TW
dc.subject (關鍵詞) 變異因子zh_TW
dc.title (題名) The Influence of Variance in Two-Armed Bandit Problemszh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Apostal, T. M. (1975) Mathematical analysis. Addison- Wesley.
     [2] Berry, D. A. and Fristedt, B. (1985) Bandit problems - Sequential allocation of experiments, Ch.apm.an and Hall.
     [3] Berry, D. A. and Pearson, L. (1984) Optimal design for two-stage clinical trials with dichotomous responses. Unit. of Minnesota Tech.. Rep.
     [4] Canner, P. L. (1970). Selecting one of the two treatments when the responses are dichotomous, J.A.S.A. , 65, 293-306.
     [5] Chernoff, H. and Ray, S. N. (1965). A bayes sequential sampling inspection plan. Ann. Math.. Statist. 36, 1387-1407.
     [6] Clayton, M. K. and ` Witmer, J. A. (1988) Two-stage bandit , Annals of Stat. Vo1.16 , No.2, 887-894.
     [7] Colton, T. (1963) A model for selecting one of two medical treatment. J.A.S.A. , 58, 388-400.
     [8] Cornfield, J., Halperin, M. , and Greenhouse, S.W. (1969). An adaptive procedure for sequential clinical trials. 1. A.S.A, 64, 759- 770.
     [9] Eick, S. G. (1988) The two-armed bandit with delayed responses, Annals of Stat, Vol.l6, No.2: 254-264.
     [10] Eick, S. G. (1988) Gittins procedures for bandits with delayed responses: J.R.S.S. , Soc. B , 50, No.1, 125-132 .
     [11] Petkau, A. J. (1978) Sequential medical trials for comparing an experimental with a standard treatment. 1. Am.er. Statist. Assoc, 73, 328-338.
     [12] Witmer, J. A. (1983) Bayesian multistage decision problems, Ph. D. Thesis.
     [13] Witmer , J. A. (1986) Bayesian multistage decision problems, Annals of Stat., Vol. 14, No. 1. 283-297.		zh_TW