In statistical analysis, change detection tries to identify changes in the probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

 of a stochastic process

Stochastic process

In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...

 or time series

Time series

In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

. In general the problem concerns both detecting whether or not a change has occurred, or whether several changes might have occurred, and identifying the times of any such changes.

Specific applications may be concerned with changes in the mean

Mean

In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

, variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

, correlation

Correlation

In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

, or spectral density

Spectral density

In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...

 of the process. More generally change detection also includes the detection of anomalous behavior: anomaly detection

Anomaly detection

Anomaly detection, also referred to as outlier detection refers to detecting patterns in a given data set that do not conform to an established normal behavior....

.

Online change detection

Using the sequential analysis

Sequential analysis

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results...

 ("online") approach, any change test must make a trade-off between these common metrics:

• False alarm rate
• Misdetection rate
• Detection delay

Bayes change detection

In a Bayes change-detection problem, a prior distribution is available for the change time.

Minimax change detection

In minimax change detection, the objective is to minimize the expected detection delay for some worst-case change-time distribution, subject to a cost or constraint on false alarms.

A key technique for minimax change detection is the CUSUM

CUSUM

In statistical quality control, the CUSUM is a sequential analysis technique due to E. S. Page of the University of Cambridge. It is typically used for monitoring change detection...

 procedure.

Offline change detection

Offline algorithms may employ clustering based on maximum likelihood estimation.

Applications of change detection

Change detection tests are often used in manufacturing (quality control

Quality control

Quality control, or QC for short, is a process by which entities review the quality of all factors involved in production. This approach places an emphasis on three aspects:...

), intrusion detection

Intrusion detection

In Information Security, intrusion detection is the act of detecting actions that attempt to compromise the confidentiality, integrity or availability of a resource. When Intrusion detection takes a preventive measure without direct human intervention, then it becomes an Intrusion-prevention...

, spam filtering, website tracking

Website tracking

Website tracking refers to the act of archiving existing websites and tracking changes to the website over time. There are many applications to website tracking which can be applied to many different business. The different applications are listed in depth below:- Website monitoring :Website...

, and medical diagnostics.

Linguistic change detection

Linguistic change detection refers to the ability to detect word-level changes across multiple presentations of the same sentence. Researchers have found that the amount of semantic

Semantics

Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 overlap (i.e., relatedness) between the changed word and the new word influence the ease with which such a detection is made (Sturt, Sanford, Stewart, & Dawydiak, 2004).
Additional research has found that focussing one's attention to the word what will be changed during the initial reading of the original sentence can improve detection. This was shown usng italicized

Italic type

In typography, italic type is a cursive typeface based on a stylized form of calligraphic handwriting. Owing to the influence from calligraphy, such typefaces often slant slightly to the right. Different glyph shapes from roman type are also usually used—another influence from calligraphy...

 text to focus attention, whereby the word that will be changing is italicized in the original sentence (Sanford, Sanford, Molle, & Emmott, 2006), as well as using clefting constructions such as "It was the tree that needed water." (Kennette, Wurm, & Van Havermaet, 2010). These change-detection phenomenon appear to be robust, even occurring cross-linguistically when bilinguals read the original sentence in their native language

First language

A first language is the language a person has learned from birth or within the critical period, or that a person speaks the best and so is often the basis for sociolinguistic identity...

 and the changed sentence in their second language

Second language

A second language or L2 is any language learned after the first language or mother tongue. Some languages, often called auxiliary languages, are used primarily as second languages or lingua francas ....

 (Kennette, Wurm & Van Havermaet, 2010).

See also

• Structural break
  Structural break
  A structural break is a concept in econometrics. A structural break appears when we see an unexpected shift in a time series. This can lead to huge forecasting errors and unreliability of the model in general...
  
   -- Change in model structure
• Change detection (GIS)
  Change detection (GIS)
  Change detection for GIS is a process that measures how the attributes of a particular area have changed between two or more time periods. Change detection often involves comparing aerial photographs or satellite imagery of the area taken at different times...
  
  
• Detection theory
  Detection theory
  Detection theory, or signal detection theory, is a means to quantify the ability to discern between information-bearing energy patterns and random energy patterns that distract from the information Detection theory, or signal detection theory, is a means to quantify the ability to discern between...
  
  
• Hypothesis testing
• Recall rate
• Receiver operating characteristic
  Receiver operating characteristic
  In signal detection theory, a receiver operating characteristic , or simply ROC curve, is a graphical plot of the sensitivity, or true positive rate, vs. false positive rate , for a binary classifier system as its discrimination threshold is varied...