Lovegrove Mathematicals

"Dedicated to making Likelinesses the entity of prime interest"

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The entity commonly called 'the best estimate of a probability' can be defined without using the concept of probability.

If we do this then we need another name for 'The best-estimate of a
probability' since there is no
probability for it to be the best-estimate of: on this site, we shall call it a *Likeliness*.

Removing probability from our concept of Likeliness means that we have also removed the idea of Likeliness as an approximation to probability, and so have removed large swathes of theory associated with approximations, such as tolerances, convergence, goodness-of-fit etc. This leaves a cleaner and more abstract theory which is of great intrinsic interest and use in its own right.

Likelinesses are a generalisation of probability. The Venn diagram showing the relationship between the two is as in A, not B.

Likelinesses:-

- form an alternative measure of chance to frequentist probability, but reduce to frequentist probability when this is known;
- are not defined in terms of a limiting process and so do not depend upon having a 'large sample';
- give a consistent 'theory of small samples'. If we imagine the range of sample sizes ranging from 0 to ∞ there is an initial gap which frequentist probabilities cannot handle: likelinesses fill that gap;
- are at home with non-parametric concepts such as 'ranked distributions', 'unimodal distributions', 'sequential systems' etc.

This site is about the theory, and practical calculation, of likelinesses.