probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

and statistics, coherence can have several different meanings. Coherence in statistics is an indication of the quality of the information, either within a single data set, or between similar but not identical data sets. Fully coherent data are logically consistent and can be reliably combined for analysis.

In personal probability

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.

In gambling strategy

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) In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events ...

.Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. .

In Bayesian decision theory

The coherency principle in

Bayesian decision theory In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the pos ...

is the assumption that subjective probabilities follow the ordinary rules/axioms of 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.

In time series analysis

time series analysis In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. ...

, 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.Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP. {{ISBN, 0-521-81099-X. The concepts here are sometimes known as coherency and are essentially those set out for coherence as for signal processing. However, note that the quantity coefficient of coherence may sometimes be called the ''squared coherence''.

References

Probability assessment Bayesian statistics Frequency-domain analysis Statistical principles de:Kohärenz (Signalanalyse)