Likelihood

Lindsey, J K

doi:10.1093/oso/9780198523598.003.0003

Chapter

3 Likelihood

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https://doi.org/10.1093/oso/9780198523598.003.0003

Pages

69–140

Published:

May 1996

Abstract

In the preceding two chapters, we have looked at various aspects of probability theory and of statistical model building. In that context, we assume that we have a reasonable model, and explore what predictions can be made about the possible events which might occur. This model formulation is the first step in solving a problem, as well as an an ultimate goal of any model construction process. However, in order to develop such models, we must also be able to integrate information from the real world: which models describe well what we have observed and what can we learn from them. Thus, statistical inference is classically concerned with the reverse process as compared to Chapter 2 and Appendix B: instead of assuming a model and predicting events, we know that certain events have occurred and attempt to discover what can be said about the probabilistic process which might have produced them. As we proceed to study ways of making such inferences, we shall also introduce, as examples, some of the more common statistical models which are based on this probability theory, and, in particular, on the families that we studied in Chapter 2. Measure theory is important in the development of statistical models, as we can see from Appendix B and Section 2.8. Nevertheless, it will play little role in our presentation of statistical inference, because the observable values of all random variables are discrete (see, however, Chapter 8).

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3 Likelihood

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