6. Parameter Inference

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch6

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Parameter Inference, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch6

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242

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Keywords:

  • Bayesian (B) inference;
  • maximum likelihood (ML) inference;
  • method of moments (MM);
  • method of percentiles (MP);
  • parameter inference

Summary

This chapter reviews the common methods of inference, namely the method of percentiles (MP), the method of moments (MM), maximum likelihood (ML) inference, and Bayesian (B) inference. It focuses on parameter inference, and point and interval estimation. The purpose of the chapter is to summarize the basic ideas behind each inferential method. Under quite general conditions, maximum likelihood estimators (MLEs) have a number of favorable properties. The chapter deals with those associated with i.i.d. variates, although generalizations of these properties hold for a likelihood function based on dependent variates in many settings. For Bayesian analysis of statistical problems, probability statements are considered a measure of belief. Bayesian statistics involves the formal updating of prior (pre-data) beliefs about parameter values in light of observed information (data) through a formal revision of probabilities undertaken using Bayes’ theorem.

Controlled Vocabulary Terms

moments