Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss
This paper uses p-tolerance with the lowest posterior
loss, quadratic loss function, average length criteria, average
coverage criteria, and worst outcome criterion for computing of
sample size to estimate proportion in Binomial probability function
with Beta prior distribution. The proposed methodology is examined,
and its effectiveness is shown.
[1] C. J. Adcock, "A Bayesian Approach to Calculating Sample Sizes", The
Statistician: Journal of the Institute of Statisticians, vol. 37, pp. 433-
439,1988.
[2] C. J. Adcock, "Sample Size Determination: A Review", The Statistician:
Journal of the Institute of Statisticians, vol. 46, pp. 261-283, 1997.
[3] J. M. Bernardo, "Intrinsic credible regions: an objective Bayesian
approach to interval estimation", Test, vol. 14, pp. 317- 384, 2005.
[4] M. M. Desu, And D. Raghavarao, "Sample Size Methodology", Boston:
Academic Press, 1990.
[5] P. M. Grundy, M. J. R. Healy and D. H Rees, "Economic choice of the
amount of experimentation", J. R. Statist. Soc. A, vol. 18, pp.32-48,
1956.
[6] L. Joseph, D. B. Wolfson, and R. D. Berger, "Sample Size Calculations
for Binomial Proportions Via Highest Posterior Density Intervals", The
Statistician: Journal of the Institute of Statisticians, vol. 44, pp. 143-154,
1995.
[7] L. Joseph, P. Belisle and P. Bélisle, "Bayesian Sample Size
Determination for Normal Means and Differences between Normal
Means", The Statistician: Journal of the Institute of Statisticians, vol. 46,
pp. 209-226, 1997a.
[8] D. V. Lindley, "The choice of Sample size", Statistician, vol. 46, pp.
129-138.
[9] C. E. M lan, L. Joseph and D. B. Wolfson, "Bayesian Sample Size
Determination for Binomial Proportions", Journal of the Bayesian
Analysis, vol. 2, pp.269-296, 2008.
[10] T. Pham-Gia and N. Turkkan, "Sample Size Determination in Bayesian
Analysis" (Disc: P399-404), The Statistician: Journal of the Institute of
Statisticians, vol. 41, pp.389-397, 1992.
[11] D. J. Spiegelhalter and L. S Freedman, "A predictive approach to
selecting the size of a clinical trial, based on subjective clinical opinion",
Statist. Med., vol. 5, pp.1-13, 1986.
[12] D. J. Spiegelhalter, L. S. Freedman and M. K. B. Parmar, "Bayesian
approaches to randomized trials (with discussion)", J. R. Statist. Soc. A,
vol. 157, pp. 357-416, 1994.
[1] C. J. Adcock, "A Bayesian Approach to Calculating Sample Sizes", The
Statistician: Journal of the Institute of Statisticians, vol. 37, pp. 433-
439,1988.
[2] C. J. Adcock, "Sample Size Determination: A Review", The Statistician:
Journal of the Institute of Statisticians, vol. 46, pp. 261-283, 1997.
[3] J. M. Bernardo, "Intrinsic credible regions: an objective Bayesian
approach to interval estimation", Test, vol. 14, pp. 317- 384, 2005.
[4] M. M. Desu, And D. Raghavarao, "Sample Size Methodology", Boston:
Academic Press, 1990.
[5] P. M. Grundy, M. J. R. Healy and D. H Rees, "Economic choice of the
amount of experimentation", J. R. Statist. Soc. A, vol. 18, pp.32-48,
1956.
[6] L. Joseph, D. B. Wolfson, and R. D. Berger, "Sample Size Calculations
for Binomial Proportions Via Highest Posterior Density Intervals", The
Statistician: Journal of the Institute of Statisticians, vol. 44, pp. 143-154,
1995.
[7] L. Joseph, P. Belisle and P. Bélisle, "Bayesian Sample Size
Determination for Normal Means and Differences between Normal
Means", The Statistician: Journal of the Institute of Statisticians, vol. 46,
pp. 209-226, 1997a.
[8] D. V. Lindley, "The choice of Sample size", Statistician, vol. 46, pp.
129-138.
[9] C. E. M lan, L. Joseph and D. B. Wolfson, "Bayesian Sample Size
Determination for Binomial Proportions", Journal of the Bayesian
Analysis, vol. 2, pp.269-296, 2008.
[10] T. Pham-Gia and N. Turkkan, "Sample Size Determination in Bayesian
Analysis" (Disc: P399-404), The Statistician: Journal of the Institute of
Statisticians, vol. 41, pp.389-397, 1992.
[11] D. J. Spiegelhalter and L. S Freedman, "A predictive approach to
selecting the size of a clinical trial, based on subjective clinical opinion",
Statist. Med., vol. 5, pp.1-13, 1986.
[12] D. J. Spiegelhalter, L. S. Freedman and M. K. B. Parmar, "Bayesian
approaches to randomized trials (with discussion)", J. R. Statist. Soc. A,
vol. 157, pp. 357-416, 1994.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57185", author = "H. Bevrani and N. Najafi", title = "Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss", abstract = "This paper uses p-tolerance with the lowest posterior
loss, quadratic loss function, average length criteria, average
coverage criteria, and worst outcome criterion for computing of
sample size to estimate proportion in Binomial probability function
with Beta prior distribution. The proposed methodology is examined,
and its effectiveness is shown.", keywords = "Bayesian inference, Beta-binomial Distribution, LPLcriteria, quadratic loss function.", volume = "4", number = "5", pages = "544-4", }