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What (who) is multivariate - definition

multivariate

WIKIMEDIA DISAMBIGUATION PAGE

Multivariate (disambiguation); Trivariate

[?m?lt?'v?:r??t]

¦ adjective Statistics involving two or more variable quantities.

Multivariate statistics

SIMULTANEOUS OBSERVATION AND ANALYSIS OF MORE THAN ONE OUTCOME VARIABLE

Multivariable analysis; Multivariate analysis; Multivariate Analysis; Multivariate analyses; Multivariate data analysis; Statistics/Multivariate; Multivariate methods; Multivariate data; Multivariate datasets

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

https://en.wikipedia.org/wiki/Multivariate_statistics

Multivariate normal distribution

$Left: Classification of seven multivariate normal classes. Coloured ellipses are 1 sd error ellipses. Black marks the boundaries between the classification regions. <math>p_e</math> is the probability of total classification error. Right: the error matrix. <math>p_{ij}</math> is the probability of classifying a sample from normal <math>i</math> as <math>j</math>. These are computed by the numerical method of ray-tracing <ref name="Das" /> ([https://www.mathworks.com/matlabcentral/fileexchange/84973-integrate-and-classify-normal-distributions Matlab code]).$
$Top: the probability of a bivariate normal in the domain <math>x\sin y-y\cos x>1</math> (blue regions). Middle: the probability of a trivariate normal in a toroidal domain. Bottom: converging Monte-Carlo integral of the probability of a 4-variate normal in the 4d regular polyhedral domain defined by <math>\sum_{i=1}^4 \vert x_i \vert < 1</math>. These are all computed by the numerical method of ray-tracing. <ref name="Das"></ref>$
$'''a:''' Probability density of a function <math>\cos x^2</math> of a single normal variable <math>x</math> with <math>\mu=-2</math> and <math>\sigma=3</math>. '''b:''' Probability density of a function <math>x^y</math> of a normal vector <math>(x, y)</math>, with mean <math>\boldsymbol{\mu}=(1, 2)</math>, and covariance <math>\mathbf{\Sigma} = \begin{bmatrix} .01 & .016 \\ .016 & .04 \end{bmatrix}</math>. '''c:''' Heat map of the joint probability density of two functions of a normal vector <math>(x, y)</math>, with mean <math>\boldsymbol{\mu}=(-2, 5)</math>, and covariance <math>\mathbf{\Sigma} = \begin{bmatrix} 10 & -7 \\ -7 & 10 \end{bmatrix}</math>. '''d:''' Probability density of a function <math>\sum_{i=1}^4 \vert x_i \vert</math> of 4 iid standard normal variables. These are computed by the numerical method of ray-tracing. <ref name="Das" />$

GENERALIZATION OF THE ONE-DIMENSIONAL NORMAL DISTRIBUTION TO HIGHER DIMENSIONS

Multivariate gaussian distribution; Multivariate Gaussian distribution; Multivariate normal; Multivariate Gaussian; Bivariate Gaussian distribution; MVN; Bivariate normal distribution; Joint normality; Jointly normal; Jointly Gaussian; Jointly gaussian; Multivariate Gaussian random variable; Multinormal distribution; Jointly normally distributed; Bivariate normal; Gaussian discriminant analysis; Normal random vector; Multinormal; Multivariate normal random variable; Mardia's test; BHEP test; Gaussian random vector; Joint normal distribution; Multidimensional normal distribution; Friedman Rafsky Test; Multivariate Gaussian vector

\, \exp ( -\frac{1}{2}(\mathbf{x} - \boldsymbol\mu)^} \boldsymbol\Sigma^{-1}(\mathbf{x} - \boldsymbol\mu) ),exists only when Σ is positive-definite

https://en.wikipedia.org/wiki/Multivariate_normal_distribution

Wikipedia

Multivariate

Multivariate may refer to:

https://en.wikipedia.org/wiki/Multivariate

Examples of use of multivariate

1. Howells is probably best known for his work on human skull variation and the analytical use of multivariate statistical techniques.

2. When they applied univariate and multivariate analysis to the data, they found that age and parity were not associated with malaria.