Search results
Results from the WOW.Com Content Network
In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called a Gaussian process . An important special case of a GRF is the Gaussian free field .
To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra.
A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
Gaussian processes can also be used in the context of mixture of experts models, for example. [28] [29] The underlying rationale of such a learning framework consists in the assumption that a given mapping cannot be well captured by a single Gaussian process model. Instead, the observation space is divided into subsets, each of which is ...
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ 2 = c 2. In this case, the Gaussian is of the form [1]
Regardless of whether the random variable is bounded above, below, or both, the truncation is a mean-preserving contraction combined with a mean-changing rigid shift, and hence the variance of the truncated distribution is less than the variance of the original normal distribution.
The generalized normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however ...