Coherence (statistics)

In probability theory and statistics, coherence can have two meanings.

• When dealing with personal probability assessments, or supposed probabilities derived in nonstandard ways, it is a property of self-consistency across a whole set of such assessments. One way of expressing such self-consistency is in terms of responses to various betting propositions, as described in relation to coherence (philosophical gambling strategy).^[1] The coherency principle in Bayesian decision theory is the assumption that personal probabilities follow the ordinary rules for probability calculations (where the validity of these rules corresponds to the self-consistency just referred to) and thus that consistent decisions can be obtained from these probabilities.^[1]

• In time series analysis, and particularly in spectral analysis, it is used to describe the strength of association between two-series where the possible dependence between the two series is not limited to simultaneous values but may include leading, lagged and smoothed relationships.^[2] The concepts here are sometimes known as coherency^[1] and are essentially those set out for coherence (signal processing). However, note that the quantity coefficient of coherence may sometimes be called the squared coherence.^[2]

References

1. ^ ^{a b c} Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9.
2. ^ ^{a b} Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP. ISBN 0-521-81099-x.