Coherence (statistics)
Encyclopedia
In probability theory
and statistics
, coherence can have two meanings.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, 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)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 on which he is wagering, even if his opponent makes...
. 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.
- In time series analysis, and particularly in spectral analysisSpectral analysisSpectral analysis or Spectrum analysis may refer to:* Spectrum analysis in chemistry and physics, a method of analyzing the chemical properties of matter from bands in their visible spectrum...
, 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. The concepts here are sometimes known as coherency and are essentially those set out for coherence (signal processing)Coherence (signal processing)-Background:The spectral coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function linear, it can be used to...
. However, note that the quantity coefficient of coherence may sometimes be called the squared coherence.