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Maximum likelihood
methods have a long history of use for point and interval estimation in
statistics. In contrast, likelihood principles have only more gradually
emerged as a foundation for an alternative to traditional hypothesis
testing via frequentist test statistics. The alternative framework
stresses the use of likelihood and information theory as the basis for
parameterizing and selecting among competing models, or in the simplest
case, among competing point estimates of a parameter of a model.
In contrast to
traditional approaches, in which the statistical models are often
constrained by the choice of a particular test statistic, a likelihood
framework stresses the specification of both the "scientific"
model that embodies the hypotheses and relationships to be tested, and
the appropriate "probability" model that characterizes the
statistical properties of the data and the error structure.
There are 4 general
steps involved in a likelihood analysis:
1. model specification, including both alternate scientific
models and appropriate error structures
2. maximum likelihood parameter
estimation, using optimization methods
3. model comparison, using information theory, and
4. model evaluation, using a variety of metrics of
precision, bias, and goodness of fit.
Recent References
- Bolker, B. M. 2008. Ecological Models and Data in
R. Princeton University
Press.
- Pawitan, Y. 2001. In All
Likelihood: Statistical Modelling and Inference Using Likelihood.
Clarendon Press, Oxford.
- Royall, R. 1997.
Statistical Evidence: A Likelihood Paradigm. Chapman and Hall/CRC,
Boca Raton
- Hilborn, R. and M.
Mangel. 1997. The Ecological Detective: Confronting Models with
Data. Princeton University Press
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