Änderungszeitpunkts

Änderungszeitpunkts, also known as change points or change detection, refers to the identification of points in time where a statistical property of a sequence of observations changes. This concept is widely used in various fields such as signal processing, finance, and quality control. The primary goal of change point detection is to determine whether a change has occurred and, if so, to estimate the time at which the change took place.

There are several methods for detecting change points, each with its own assumptions and applications. Some common approaches include:

1. Cumulative Sum (CUSUM) method: This method is used to detect changes in the mean of a sequence. It accumulates the differences between observed values and a target value, and a change is detected when this sum exceeds a certain threshold.

2. Sequential Probability Ratio Test (SPRT): This method is based on hypothesis testing and is used to detect changes in the mean or variance of a sequence. It compares the likelihood of the observed data under two hypotheses: one with a change and one without.

3. Bayesian methods: These methods use Bayesian inference to model the uncertainty in the change point. They often involve specifying prior distributions for the change point and updating these distributions as new data becomes available.

4. Non-parametric methods: These methods do not assume a specific distribution for the data and can be used when the underlying distribution is unknown or complex. Examples include the Kolmogorov-Smirnov test and the Mann-Whitney U test.

Change point detection is a challenging problem, especially when dealing with noisy data or when the change is gradual rather than abrupt. However, it is a powerful tool for understanding the dynamics of complex systems and for making informed decisions based on changes in data.