Skip to main content

Maximum Likelihood

  • Protocol
  • First Online:
Computational Toxicology

Part of the book series: Methods in Molecular Biology ((MIMB,volume 930))

Abstract

The maximum likelihood method is a popular statistical inferential procedure widely used in many areas to obtain the estimates of the unknown parameters of a population of interest. This chapter gives a brief description of the important concepts underlying the maximum likelihood method, the definition of the key components, the basic theory of the method, and the properties of the resulting estimates. Confidence interval and likelihood ratio test are also introduced. Finally, a few examples of applications are given to illustrate how to derive maximum likelihood estimates in practice. A list of references to relevant papers and software for a further understanding of the method and its implementation is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hald A (1999) On the history of maximum likelihood in relation to inverse probability and least squares. Statist Sci 14(2):214–222

    Article  Google Scholar 

  2. Aldrich J (1997) R.A. Fisher and the making of maximum likelihood 1912–1922. Statist Sci 12(3):162–176

    Article  Google Scholar 

  3. Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrox BN, Caski F (eds) Second international symposium on information theory. Akademiai Kiado, Budapest, pp 267–281

    Google Scholar 

  4. Schwarz G (1978) Estimating the dimension of a model. Ann Statist 6:461–464

    Article  Google Scholar 

  5. McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman and Hall, New York

    Google Scholar 

  6. Cox DR (1970) The analysis of binary data. Chapman and Hall, London

    Google Scholar 

  7. Cox DR (1972) Regression models and life tables. J Roy Statist Soc 34:187–220

    Google Scholar 

  8. Lindsey JK (2001) Nonlinear models in medical statistics. Oxford University Press, Oxford, UK

    Google Scholar 

  9. Wu L (2010) Mixed effects models for complex data. Chapman and Hall, London

    Google Scholar 

  10. Beal SL, Sheiner LB, Boeckmann AJ (eds) (1989–2009) NONMEM users guides. Icon development solutions. Ellicott City

    Google Scholar 

  11. Yang S, Roger J (2010) Evaluations of Bayesian and maximum likelihood methods in PK models with below-quantification-limit data. Pharm Stat 9(4):313–330

    Article  PubMed  Google Scholar 

  12. Fletcher R (1987) Practical methods of optimization, 2nd edn. Wiley, New York

    Google Scholar 

  13. Young GA, Smith RL (2005) Essentials of statistical inference, chapter 8. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  14. Bickel PJ, Doksum KA (1977) Mathematical statistics. Holden-day, Inc., Oakland, CA

    Google Scholar 

  15. Casella G, Berger RL (2002) Statistical inference, 2nd edn. Pacific Grove, Duxberry, CA

    Google Scholar 

  16. DeGroot MH, Schervish MJ (2002) Probability and statistics, 3rd edn. Addison-Wesley, Boston, MA

    Google Scholar 

  17. Spanos A (1999) Probability theory and statistical inference. Cambridge University Press, Cambridge, UK

    Google Scholar 

  18. Pawitan Y (2001) In all likelihood: statistical modelling and inference using likelihood. Cambridge University Press, Cambridge, UK

    Google Scholar 

  19. SAS Institute Inc. (2009) SAS manuals. http://support.sas.com/documentation/index.html

  20. STATA Data analysis and statistical software. http://www.stata.com/

  21. The R project for statistical computing. http://www.r-project.org/

  22. The Monolix software. http://www.monolix.org/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shuying Yang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media, LLC

About this protocol

Cite this protocol

Yang, S., De Angelis, D. (2013). Maximum Likelihood. In: Reisfeld, B., Mayeno, A. (eds) Computational Toxicology. Methods in Molecular Biology, vol 930. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-059-5_24

Download citation

  • DOI: https://doi.org/10.1007/978-1-62703-059-5_24

  • Published:

  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-62703-058-8

  • Online ISBN: 978-1-62703-059-5

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics