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In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization...

prices Multivariate normal distribution (aka multivariate Gaussian distribution), for vectors of correlated outcomes that are individually Gaussian-distributed...

collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those...

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ⁡ ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}...

called normal or Gaussian laws, so a certain ambiguity in names exists. The multivariate normal distribution describes the Gaussian law in the k-dimensional...

(f(x1), ..., f(xN)) will always be distributed as a multivariate Gaussian. Brownian sheet Gaussian free field Peacock, John (1999). Cosmological Physics...

i ) ) ∈ R q {\textstyle \mu ^{(g(i))}\in \mathbb {R} ^{q}} with multivariate Gaussian noise: y i = μ ( g ( i ) ) + ε i ε i ∼ i.i.d. N q ( 0 , Σ )  for ...

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e.,...

ratio statistic for testing equality of covariance matrices of multivariate Gaussian models". Biometrika. 71 (3): 555–559. doi:10.1093/biomet/71.3.555...

decoder through a probabilistic latent space (for example, as a multivariate Gaussian distribution) that corresponds to the parameters of a variational...

assignments to clusters, instead of deterministic assignments, and multivariate Gaussian distributions instead of means. k-means++ chooses initial centers...

{\displaystyle {\mathcal {N}}()} is the Gaussian distribution, in this case specifically the multivariate Gaussian distribution. The interpretation of the...

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each...

Thomas (November 2014). "A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions". Far East Journal of Theoretical...

, X 2 , … , X n {\displaystyle X_{1},X_{2},\ldots ,X_{n}} from multivariate Gaussian distribution X ∼ N ( 0 , Σ ) {\displaystyle X\sim N(0,\Sigma )}...

computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs...

squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable...

n-dimensional vector x[xT = (x1, x2, ..., xn)] are taken from a multivariate Gaussian distribution, N(m, M), having mean m and moment matrix M. The samples...

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...

f(x_{1}),\ldots ,f(x_{n})} are jointly distributed according to a multivariate Gaussian with mean m = [ m ( x 1 ) , … , m ( x n ) ] ⊺ {\displaystyle m=[m(x_{1})...