IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i3p724-731.html

Implementing Bayesian predictive procedures: The K-prime and K-square distributions

Author

Listed:
  • Poitevineau, Jacques
  • Lecoutre, Bruno

Abstract

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple correlation coefficients. Their cumulative distribution functions can be expressed in terms of infinite series of multiples of incomplete beta function ratios, thus adequate for recursive calculations. Efficient algorithms are provided. To deal with special cases where possible underflows may prevent a recurrence to work properly, a simple solution is proposed which results in a procedure which is intermediate between two classes of algorithm. Some examples of applications are given.

Suggested Citation

  • Poitevineau, Jacques & Lecoutre, Bruno, 2010. "Implementing Bayesian predictive procedures: The K-prime and K-square distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 724-731, March.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:3:p:724-731
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00541-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Benton, Denise & Krishnamoorthy, K., 2003. "Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 249-267, June.
    2. Inoue, Lurdes Y.T. & Berry, Donald A. & Parmigiani, Giovanni, 2005. "Relationship Between Bayesian and Frequentist Sample Size Determination," The American Statistician, American Statistical Association, vol. 59, pages 79-87, February.
    3. Bruno Lecoutre & Jean‐Luc Guigues & Jacques Poitevineau, 1992. "Distribution of Quadratic Forms of Multivariate Generalized Student Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(3), pages 617-627, November.
    4. H. Frick, 1990. "A Remark on Algorithm as 226: Computing Non‐Central Beta Probabilities," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 311-312, June.
    5. David J. Spiegelhalter & Laurence S. Freedman & Mahesh K. B. Parmar, 1994. "Bayesian Approaches to Randomized Trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(3), pages 357-387, May.
    6. Lecoutre, Marie-Paule & Rouanet, Henry, 1993. "Predictive Judgments in Situations of Statistical Analysis," Organizational Behavior and Human Decision Processes, Elsevier, vol. 54(1), pages 45-56, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Steven E. Pav, 2015. "Inference on the Sharpe ratio via the upsilon distribution," Papers 1505.00829, arXiv.org, revised Aug 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ali Baharev & Hermann Schichl & Endre Rév, 2017. "Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy," Computational Statistics, Springer, vol. 32(2), pages 763-779, June.
    2. Martin E. Backhouse, 1998. "An investment appraisal approach to clinical trial design," Health Economics, John Wiley & Sons, Ltd., vol. 7(7), pages 605-619, November.
    3. James C. Felli & Gordon B. Hazen, 1998. "Sensitivity Analysis and the Expected Value of Perfect Information," Medical Decision Making, , vol. 18(1), pages 95-109, January.
    4. Alex N Nguyen Ba & Bob Strome & Jun Jie Hua & Jonathan Desmond & Isabelle Gagnon-Arsenault & Eric L Weiss & Christian R Landry & Alan M Moses, 2014. "Detecting Functional Divergence after Gene Duplication through Evolutionary Changes in Posttranslational Regulatory Sequences," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-15, December.
    5. Francesco De Pretis & Barbara Osimani, 2019. "New Insights in Computational Methods for Pharmacovigilance: E-Synthesis , a Bayesian Framework for Causal Assessment," IJERPH, MDPI, vol. 16(12), pages 1-19, June.
    6. Peter F. Thall & Richard M. Simon & Yu Shen, 2000. "Approximate Bayesian Evaluation of Multiple Treatment Effects," Biometrics, The International Biometric Society, vol. 56(1), pages 213-219, March.
    7. Charles F. Manski, 2018. "Reasonable patient care under uncertainty," Health Economics, John Wiley & Sons, Ltd., vol. 27(10), pages 1397-1421, October.
    8. David M. Rindskopf & William R. Shadish & M. H. Clark, 2018. "Using Bayesian Correspondence Criteria to Compare Results From a Randomized Experiment and a Quasi-Experiment Allowing Self-Selection," Evaluation Review, , vol. 42(2), pages 248-280, April.
    9. Nandini Dendukuri & Lawrence Joseph, 2001. "Bayesian Approaches to Modeling the Conditional Dependence Between Multiple Diagnostic Tests," Biometrics, The International Biometric Society, vol. 57(1), pages 158-167, March.
    10. Miguel A. Negrín & Francisco J. Vázquez-Polo & María Martel & Elías Moreno & Francisco J. Girón, 2010. "Bayesian Variable Selection in Cost-Effectiveness Analysis," IJERPH, MDPI, vol. 7(4), pages 1-20, April.
    11. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    12. Yang, Nian & Chen, Nan & Liu, Yanchu & Wan, Xiangwei, 2017. "Approximate arbitrage-free option pricing under the SABR model," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 198-214.
    13. Leonhard Held, 2020. "A new standard for the analysis and design of replication studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 431-448, February.
    14. Isakov, Leah & Lo, Andrew W. & Montazerhodjat, Vahid, 2019. "Is the FDA too conservative or too aggressive?: A Bayesian decision analysis of clinical trial design," Journal of Econometrics, Elsevier, vol. 211(1), pages 117-136.
    15. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    16. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    17. Paul Gustafson & Nhu D. Le & Refik Saskin, 2001. "Case–Control Analysis with Partial Knowledge of Exposure Misclassification Probabilities," Biometrics, The International Biometric Society, vol. 57(2), pages 598-609, June.
    18. Charles F. Manski, 2021. "Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald," Econometrica, Econometric Society, vol. 89(6), pages 2827-2853, November.
    19. Izabela Oliveira & Daniel Ferreira, 2013. "Computing the noncentral gamma distribution, its inverse and the noncentrality parameter," Computational Statistics, Springer, vol. 28(4), pages 1663-1680, August.
    20. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:3:p:724-731. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.