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**GAUSSIAN PROCESS**

In probability theory and statistics, a Gaussian process is a stochastic process whose realizations consist of random values associated with every point in a range of times (or of space) such that each such random variable has a normal distribution. Moreover, every finite collection of those random variables has a multivariate normal distribution. Gaussian processes are important in statistical modeling because of properties inherited from the normal distribution.

For example, if a random process is modeled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include: the average value of the process over a range of times; the error in estimating the average using sample values at a small set of times.

A process is Gaussian if and only if for every finite set of indices t_{1}, ..., t_{k} in the index set T

is a vector-valued Gaussian random variable. Using characteristic functions of random variables, the Gaussian property can be formulated as follows:{ X_{t} ; t âˆˆ T } is Gaussian if and only if, for every finite set of indices t_{1}, ..., t_{k} , there are reals Ïƒl j with Ïƒ_{ii} > 0 and reals Î¼_{j} such that

The numbers Ïƒ_{lj} and Î¼_{j} can be shown to be the covariances and means of the variables in the process.

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26 videos|29 docs|8 tests

### Gaussian Processes

- Video | 12:06 min
### Noise And Shot Noise

- Doc | 2 pages
### Noise & its Sources

- Video | 13:53 min
### Noise

- Video | 12:09 min
### Thermal Noise

- Doc | 7 pages
### White Noise

- Doc | 8 pages

- Random Variable
- Video | 06:31 min
- Random Variables and Random Process
- Doc | 10 pages