Journal articles: 'Bayesian Sample size'

1

Nassar, M. M., S. M. Khamis, and S. S. Radwan. "On Bayesian sample size determination." Journal of Applied Statistics 38, no. 5 (May 2011): 1045–54. http://dx.doi.org/10.1080/02664761003758992.

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2

Pham-Gia, T., and N. Turkkan. "Sample Size Determination in Bayesian Analysis." Statistician 41, no. 4 (1992): 389. http://dx.doi.org/10.2307/2349003.

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3

Sobel, Marc, and Ibrahim Turkoz. "Bayesian blinded sample size re-estimation." Communications in Statistics - Theory and Methods 47, no. 24 (December 8, 2017): 5916–33. http://dx.doi.org/10.1080/03610926.2017.1404097.

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4

Wang, Ming-Dauh. "Sample Size Reestimation by Bayesian Prediction." Biometrical Journal 49, no. 3 (June 2007): 365–77. http://dx.doi.org/10.1002/bimj.200310273.

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Wang, Ming-Dauh. "Sample Size Reestimation by Bayesian Prediction." Biometrical Journal 49, no. 3 (June 2007): NA. http://dx.doi.org/10.1002/bimj.200510273.

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6

JOSEPH, LAWRENCE, ROXANE DU BERGER, and PATRICK BÉLISLE. "BAYESIAN AND MIXED BAYESIAN/LIKELIHOOD CRITERIA FOR SAMPLE SIZE DETERMINATION." Statistics in Medicine 16, no. 7 (April 15, 1997): 769–81. http://dx.doi.org/10.1002/(sici)1097-0258(19970415)16:7<769::aid-sim495>3.0.co;2-v.

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7

De Santis, Fulvio. "Sample Size Determination for Robust Bayesian Analysis." Journal of the American Statistical Association 101, no. 473 (March 2006): 278–91. http://dx.doi.org/10.1198/016214505000000510.

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8

Weiss, Robert. "Bayesian sample size calculations for hypothesis testing." Journal of the Royal Statistical Society: Series D (The Statistician) 46, no. 2 (July 1997): 185–91. http://dx.doi.org/10.1111/1467-9884.00075.

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9

Katsis, Athanassios, and Blaza Toman. "Bayesian sample size calculations for binomial experiments." Journal of Statistical Planning and Inference 81, no. 2 (November 1999): 349–62. http://dx.doi.org/10.1016/s0378-3758(99)00019-1.

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10

Clarke, B., and Ao Yuan. "Closed form expressions for Bayesian sample size." Annals of Statistics 34, no. 3 (June 2006): 1293–330. http://dx.doi.org/10.1214/009053606000000308.

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11

M'Lan, Cyr E., Lawrence Joseph, and David B. Wolfson. "Bayesian sample size determination for binomial proportions." Bayesian Analysis 3, no. 2 (June 2008): 269–96. http://dx.doi.org/10.1214/08-ba310.

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12

Zhang, Xiao, Gary Cutter, and Thomas Belin. "Bayesian sample size determination under hypothesis tests." Contemporary Clinical Trials 32, no. 3 (May 2011): 393–98. http://dx.doi.org/10.1016/j.cct.2010.12.012.

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13

Joseph, Lawrence, David B. Wolfson, and Roxane du Berger. "Some Comments on Bayesian Sample Size Determination." Statistician 44, no. 2 (1995): 167. http://dx.doi.org/10.2307/2348442.

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14

Nassar, M. M., S. M. Khamis, and S. S. Radwan. "Geometric sample size determination in Bayesian analysis." Journal of Applied Statistics 37, no. 4 (March 3, 2010): 567–75. http://dx.doi.org/10.1080/02664760902803248.

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15

Pham-Gia, T. "On Bayesian analysis, Bayesian decision theory and the sample size problem." Journal of the Royal Statistical Society: Series D (The Statistician) 46, no. 2 (July 1997): 139–44. http://dx.doi.org/10.1111/1467-9884.00069.

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16

Sanz-Alonso, Daniel, and Zijian Wang. "Bayesian Update with Importance Sampling: Required Sample Size." Entropy 23, no. 1 (December 26, 2020): 22. http://dx.doi.org/10.3390/e23010022.

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Importance sampling is used to approximate Bayes’ rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for importance sampling in terms of the χ2-divergence between target and proposal. We illustrate through examples the roles that dimension, noise-level and other model parameters play in approximating the Bayesian update with importance sampling. Our examples also facilitate a new direct comparison of standard and optimal proposals for particle filtering.

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17

ChiChang Chang, and KuoHsiung Liao. "Bayesian Sample-size Determination for Medical Decision Making." International Journal of Advancements in Computing Technology 5, no. 8 (April 30, 2013): 1190–97. http://dx.doi.org/10.4156/ijact.vol5.issue8.132.

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18

De Santis, Fulvio. "Using historical data for Bayesian sample size determination." Journal of the Royal Statistical Society: Series A (Statistics in Society) 170, no. 1 (January 2007): 95–113. http://dx.doi.org/10.1111/j.1467-985x.2006.00438.x.

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19

Sadia, Farhana, and Syed S. Hossain. "Contrast of Bayesian and Classical Sample Size Determination." Journal of Modern Applied Statistical Methods 13, no. 2 (November 1, 2014): 420–31. http://dx.doi.org/10.22237/jmasm/1414815720.

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20

Brakenhoff, TB, KCB Roes, and S. Nikolakopoulos. "Bayesian sample size re-estimation using power priors." Statistical Methods in Medical Research 28, no. 6 (May 2, 2018): 1664–75. http://dx.doi.org/10.1177/0962280218772315.

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The sample size of a randomized controlled trial is typically chosen in order for frequentist operational characteristics to be retained. For normally distributed outcomes, an assumption for the variance needs to be made which is usually based on limited prior information. Especially in the case of small populations, the prior information might consist of only one small pilot study. A Bayesian approach formalizes the aggregation of prior information on the variance with newly collected data. The uncertainty surrounding prior estimates can be appropriately modelled by means of prior distributions. Furthermore, within the Bayesian paradigm, quantities such as the probability of a conclusive trial are directly calculated. However, if the postulated prior is not in accordance with the true variance, such calculations are not trustworthy. In this work we adapt previously suggested methodology to facilitate sample size re-estimation. In addition, we suggest the employment of power priors in order for operational characteristics to be controlled.

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21

M'Lan, Cyr Emile, Lawrence Joseph, and David B. Wolfson. "Bayesian Sample Size Determination for Case-Control Studies." Journal of the American Statistical Association 101, no. 474 (June 1, 2006): 760–72. http://dx.doi.org/10.1198/016214505000001023.

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22

Inoue, Lurdes Y. T., Donald A. Berry, and Giovanni Parmigiani. "Relationship Between Bayesian and Frequentist Sample Size Determination." American Statistician 59, no. 1 (February 2005): 79–87. http://dx.doi.org/10.1198/000313005x21069.

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23

Pham-Gia, T. "Sample Size Determination in Bayesian Statistics-A Commentary." Statistician 44, no. 2 (1995): 163. http://dx.doi.org/10.2307/2348441.

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24

Brutti, Pierpaolo, Fulvio De Santis, and Stefania Gubbiotti. "Robust Bayesian sample size determination in clinical trials." Statistics in Medicine 27, no. 13 (2008): 2290–306. http://dx.doi.org/10.1002/sim.3175.

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25

Wang, Yu, Zheng Guan, and Tengyuan Zhao. "Sample size determination in geotechnical site investigation considering spatial variation and correlation." Canadian Geotechnical Journal 56, no. 7 (July 2019): 992–1002. http://dx.doi.org/10.1139/cgj-2018-0474.

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Site investigation is a fundamental element in geotechnical engineering practice, but only a small portion of geomaterials is sampled and tested during site investigation. This leads to a question of sample size determination: how many samples are needed to achieve a target level of accuracy for the results inferred from the samples? Sample size determination is a well-known topic in statistics and has many applications in a wide variety of areas. However, conventional statistical methods, which mainly deal with independent data, only have limited applications in geotechnical site investigation because geotechnical data are not independent, but spatially varying and correlated. Existing design codes around the world (e.g., Eurocode 7) only provide conceptual principles on sample size determination. No scientific or quantitative method is available for sample size determination in site investigation considering spatial variation and correlation of geotechnical properties. This study performs an extensive parametric study and develops a statistical chart for sample size determination with consideration of spatial variation and correlation using Bayesian compressive sensing or sampling. Real cone penetration test data and real laboratory test data are used to illustrate application of the proposed statistical chart, and the method is shown to perform well.

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26

Kuen Cheung, Ying. "Sample size formulae for the Bayesian continual reassessment method." Clinical Trials: Journal of the Society for Clinical Trials 10, no. 6 (August 21, 2013): 852–61. http://dx.doi.org/10.1177/1740774513497294.

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27

DasGupta, Anirban, and Brani Vidakovic. "Sample size problems in ANOVA Bayesian point of view." Journal of Statistical Planning and Inference 65, no. 2 (December 1997): 335–47. http://dx.doi.org/10.1016/s0378-3758(97)00056-6.

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28

Joseph, Lawrence, and Patrick Bélisle. "Bayesian consensus‐based sample size criteria for binomial proportions." Statistics in Medicine 38, no. 23 (July 11, 2019): 4566–73. http://dx.doi.org/10.1002/sim.8316.

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29

Hand, Austin L., James D. Stamey, and Dean M. Young. "Bayesian sample-size determination for two independent Poisson rates." Computer Methods and Programs in Biomedicine 104, no. 2 (November 2011): 271–77. http://dx.doi.org/10.1016/j.cmpb.2010.10.010.

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30

Lan, KK Gordan, and Janet T. Wittes. "Some thoughts on sample size: A Bayesian-frequentist hybrid approach." Clinical Trials 9, no. 5 (August 3, 2012): 561–69. http://dx.doi.org/10.1177/1740774512453784.

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Background Traditional calculations of sample size do not formally incorporate uncertainty about the likely effect size. Use of a normal prior to express that uncertainty, as recently recommended, can lead to power that does not approach 1 as the sample size approaches infinity. Purpose To provide approaches for calculating sample size and power that formally incorporate uncertainty about effect size. The relevant formulas should ensure that power approaches one as sample size increases indefinitely and should be easy to calculate. Methods We examine normal, truncated normal, and gamma priors for effect size computationally and demonstrate analytically an approach to approximating the power for a truncated normal prior. We also propose a simple compromise method that requires a moderately larger sample size than the one derived from the fixed effect method. Results Use of a realistic prior distribution instead of a fixed treatment effect is likely to increase the sample size required for a Phase 3 trial. The standard fixed effect method for moving from estimates of effect size obtained in a Phase 2 trial to the sample size of a Phase 3 trial ignores the variability inherent in the estimate from Phase 2. Truncated normal priors appear to require unrealistically large sample sizes while gamma priors appear to place too much probability on large effect sizes and therefore produce unrealistically high power. Limitations The article deals with a few examples and a limited range of parameters. It does not deal explicitly with binary or time-to-failure data. Conclusions Use of the standard fixed approach to sample size calculation often yields a sample size leading to lower power than desired. Other natural parametric priors lead either to unacceptably large sample sizes or to unrealistically high power. We recommend an approach that is a compromise between assuming a fixed effect size and assigning a normal prior to the effect size.

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31

Cressie, Noel, and Jonathan Biele. "A Sample-Size-Optimal Bayesian Procedure for Sequential Pharmaceutical Trials." Biometrics 50, no. 3 (September 1994): 700. http://dx.doi.org/10.2307/2532784.

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32

Islam, A. F. M. Saiful, and Lawrence I. Pettit. "Bayesian sample size determination for the bounded linex loss function." Journal of Statistical Computation and Simulation 84, no. 8 (January 7, 2013): 1644–53. http://dx.doi.org/10.1080/00949655.2012.757766.

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33

Sahu, S. K., and T. M. F. Smith. "A Bayesian method of sample size determination with practical applications." Journal of the Royal Statistical Society: Series A (Statistics in Society) 169, no. 2 (March 2006): 235–53. http://dx.doi.org/10.1111/j.1467-985x.2006.00408.x.

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34

Pezeshk, Hamid, Nader Nematollahi, Vahed Maroufy, and John Gittins. "The choice of sample size: a mixed Bayesian / frequentist approach." Statistical Methods in Medical Research 18, no. 2 (April 29, 2008): 183–94. http://dx.doi.org/10.1177/0962280208089298.

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35

Islam, A. F. M. Saiful, and L. I. Pettit. "Bayesian Sample Size Determination Using Linex Loss and Linear Cost." Communications in Statistics - Theory and Methods 41, no. 2 (January 15, 2012): 223–40. http://dx.doi.org/10.1080/03610926.2010.521279.

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36

Jones, P. W., and S. A. Madhi. "Bayesian minimum sample size designs for the bernoulli selection problem." Sequential Analysis 7, no. 1 (January 1988): 1–10. http://dx.doi.org/10.1080/07474948808836139.

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37

De Santis, Fulvio. "Statistical evidence and sample size determination for Bayesian hypothesis testing." Journal of Statistical Planning and Inference 124, no. 1 (August 2004): 121–44. http://dx.doi.org/10.1016/s0378-3758(03)00198-8.

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38

Brutti, Pierpaolo, Fulvio De Santis, and Stefania Gubbiotti. "Bayesian-frequentist sample size determination: a game of two priors." METRON 72, no. 2 (May 13, 2014): 133–51. http://dx.doi.org/10.1007/s40300-014-0043-2.

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39

Cao, Jing, J. Jack Lee, and Susan Alber. "Comparison of Bayesian sample size criteria: ACC, ALC, and WOC." Journal of Statistical Planning and Inference 139, no. 12 (December 2009): 4111–22. http://dx.doi.org/10.1016/j.jspi.2009.05.041.

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40

Wang, Hansheng, Shein-Chung Chow, and Murphy Chen. "A Bayesian Approach on Sample Size Calculation for Comparing Means." Journal of Biopharmaceutical Statistics 15, no. 5 (September 1, 2005): 799–807. http://dx.doi.org/10.1081/bip-200067789.

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41

Stamey, James, and Richard Gerlach. "Bayesian sample size determination for case-control studies with misclassification." Computational Statistics & Data Analysis 51, no. 6 (March 2007): 2982–92. http://dx.doi.org/10.1016/j.csda.2006.01.014.

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42

Whitehead, John, Elsa Valdés-Márquez, Patrick Johnson, and Gordon Graham. "Bayesian sample size for exploratory clinical trials incorporating historical data." Statistics in Medicine 27, no. 13 (2008): 2307–27. http://dx.doi.org/10.1002/sim.3140.

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43

Hoofs, Huub, Rens van de Schoot, Nicole W. H. Jansen, and IJmert Kant. "Evaluating Model Fit in Bayesian Confirmatory Factor Analysis With Large Samples: Simulation Study Introducing the BRMSEA." Educational and Psychological Measurement 78, no. 4 (May 23, 2017): 537–68. http://dx.doi.org/10.1177/0013164417709314.

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Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, maximum likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian CFA is limited. We propose, therefore, a Bayesian variant of the root mean square error of approximation (RMSEA), the BRMSEA. A simulation study was performed with variations in model misspecification, factor loading magnitude, number of indicators, number of factors, and sample size. This showed that the 90% posterior probability interval of the BRMSEA is valid for evaluating model fit in large samples ( N≥ 1,000), using cutoff values for the lower (<.05) and upper limit (<.08) as guideline. An empirical illustration further shows the advantage of the BRMSEA in large sample Bayesian CFA models. In conclusion, it can be stated that the BRMSEA is well suited to evaluate model fit in large sample Bayesian CFA models by taking sample size and model complexity into account.

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44

Xie, Xuan, Hui Feng, and Bo Hu. "Bandwidth Detection of Graph Signals with a Small Sample Size." Sensors 21, no. 1 (December 28, 2020): 146. http://dx.doi.org/10.3390/s21010146.

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Bandwidth is the crucial knowledge to sampling, reconstruction or estimation of the graph signal (GS). However, it is typically unknown in practice. In this paper, we focus on detecting the bandwidth of bandlimited GS with a small sample size, where the number of spectral components of GS to be tested may greatly exceed the sample size. To control the significance of the result, the detection procedure is implemented by multi-stage testing. In each stage, a Bayesian score test, which introduces a prior to the spectral components, is adopted to face the high dimensional challenge. By setting different priors in each stage, we make the test more powerful against alternatives that have similar bandwidth to the null hypothesis. We prove that the Bayesian score test is locally most powerful in expectation against the alternatives following the given prior. Finally, numerical analysis shows that our method has a good performance in bandwidth detection and is robust to the noise.

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45

Al-Labadi, Luai, Yifan Cheng, Forough Fazeli-Asl, Kyuson Lim, and Yanqing Weng. "A Bayesian One-Sample Test for Proportion." Stats 5, no. 4 (December 1, 2022): 1242–53. http://dx.doi.org/10.3390/stats5040075.

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This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let x=(x1,…,xn) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ0, the goal is to test the null hypothesis H0:θ=θ0 against all possible alternatives. The proposed approach is based on using the well-known formula of the Kullback–Leibler divergence between two binomial distributions chosen in a certain way. Then, the difference of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Some theoretical properties of the method are developed. Examples and simulation results are included.

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46

Singh, Saroja Kumar, Sarat Kumar Acharya, Frederico R. B. Cruz, and Roberto C. Quinino. "Bayesian sample size determination in a single-server deterministic queueing system." Mathematics and Computers in Simulation 187 (September 2021): 17–29. http://dx.doi.org/10.1016/j.matcom.2021.02.010.

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47

Martin, Jörg, and Clemens Elster. "GUI for Bayesian sample size planning in type A uncertainty evaluation." Measurement Science and Technology 32, no. 7 (April 30, 2021): 075005. http://dx.doi.org/10.1088/1361-6501/abe2bd.

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48

Sakamaki, Kentaro, Michio Kanekiyo, Shoichi Ohwada, Kentaro Matsuura, Tomoyuki Kakizume, Fumihiro Takahashi, Akira Takazawa, Shunsuke Hagihara, and Satoshi Morita. "Bayesian decision theory for clinical trials: Utility and sample size determination." Japanese Journal of Biometrics 41, no. 1 (2020): 55–91. http://dx.doi.org/10.5691/jjb.41.55.

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49

Beavers, Daniel P., and James D. Stamey. "Bayesian sample size determination for cost-effectiveness studies with censored data." PLOS ONE 13, no. 1 (January 5, 2018): e0190422. http://dx.doi.org/10.1371/journal.pone.0190422.

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50

Wang, Yuedong. "Sample size calculations for smoothing splines based on Bayesian confidence intervals." Statistics & Probability Letters 38, no. 2 (June 1998): 161–66. http://dx.doi.org/10.1016/s0167-7152(97)00168-5.

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Journal articles on the topic 'Bayesian Sample size'

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