Wishart distribution
E728886
The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Wishart matrices | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
matrix-variate distribution
ⓘ
probability distribution ⓘ |
| appearsAs | likelihood of covariance matrix under multivariate normal sampling ⓘ |
| category | exponential family distribution ⓘ |
| conjugatePriorFor |
covariance matrix of multivariate normal distribution
ⓘ
precision matrix of multivariate normal distribution ⓘ |
| definedOn | space of symmetric positive-definite matrices ⓘ |
| degreesOfFreedomSymbol | n ⓘ |
| dimensionSymbol | p ⓘ |
| fullRankIf | n ≥ p ⓘ |
| generalizes | chi-squared distribution ⓘ |
| hasProperty |
degrees of freedom must exceed dimension minus one for finite mean
ⓘ
scale matrix must be positive-definite ⓘ support is convex cone ⓘ |
| hasRandomMatrixForm | X'X where X has independent multivariate normal rows ⓘ |
| introducedBy | John Wishart NERFINISHED ⓘ |
| introducedInYear | 1928 ⓘ |
| isSpecialCaseOf | matrix gamma distribution ⓘ |
| logLikelihoodUsedIn | maximum likelihood estimation of covariance matrices ⓘ |
| mean | nS ⓘ |
| meanExistsIf | n > p - 1 ⓘ |
| namedAfter | John Wishart NERFINISHED ⓘ |
| notation |
W_p(
u,
Sigma)
ⓘ
W_p(n, S) ⓘ |
| parameter |
degrees of freedom
ⓘ
dimension ⓘ scale matrix ⓘ |
| reductionToChiSquared | p = 1 ⓘ |
| relatedDistribution |
gamma distribution
ⓘ
inverse Wishart distribution ⓘ matrix normal distribution ⓘ multivariate normal distribution ⓘ |
| scaleMatrixSymbol | S ⓘ |
| support | symmetric positive-definite matrices ⓘ |
| usedAs | sampling distribution of sample covariance matrix ⓘ |
| usedIn |
Bayesian statistics
NERFINISHED
ⓘ
Gaussian graphical models NERFINISHED ⓘ covariance matrix estimation ⓘ econometrics ⓘ factor analysis ⓘ genetics ⓘ machine learning ⓘ multivariate analysis of variance ⓘ multivariate statistics ⓘ principal component analysis ⓘ random matrix theory ⓘ signal processing ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wishart matrices
subject surface form:
David Wishart