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# Gaussian Process Electronics and Communication Engineering (ECE) Notes | EduRev

## Communication Theory

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## Electronics and Communication Engineering (ECE) : Gaussian Process Electronics and Communication Engineering (ECE) Notes | EduRev

The document Gaussian Process Electronics and Communication Engineering (ECE) Notes | EduRev is a part of the Electronics and Communication Engineering (ECE) Course Communication Theory.
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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 t1, ..., tk 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:{ Xt ; t âˆˆ T } is Gaussian if and only if, for every finite set of indices t1, ..., tk , there are reals Ïƒl j with Ïƒii > 0 and reals Î¼j such that

The numbers Ïƒlj and Î¼j can be shown to be the covariances and means of the variables in the process.

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