How is the inverse Wishart distribution used in statistics?
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution. .
What kind of matrix is the Wishart distribution?
The Wishart distribution W(§;d;n) is a probability distribution of random nonnegative-deflnite d £ d matrices that is used to model random covariance matrices. The parameter n is the number of de- grees of freedom, and § is a nonnegative-deflnite symmetric d £ d matrix that is called the scale matrix. By deflnition.
When to use the inverse Wishart conjugate prior?
The Inverse-Wishart Conjugate Prior. An important use of the Wishart distribution is as a conjugate prior for multivariate normal sampling. This leads to a d-dimensional analog of the inverse-gamma-normal conjugate prior for normal sampling in one dimension.
When is the inverse Wishart distribution conjugate to the multivariate Gaussian?
If the observations are independent p-variate Gaussian variables drawn from a distribution, then the conditional distribution has a distribution, where . Because the prior and posterior distributions are the same family, we say the inverse Wishart distribution is conjugate to the multivariate Gaussian.
What do you need to know about mcmcglmm?
MCMC is a bit more complicated to explain. Most simply put, it’s an algorithm which can draw random samples from a posterior distribution so that we can explore its characteristics. If you would like to understand a bit more about how Markov chain Monte Carlo algorithms work, check out these links, and this one.
Do you need to know Bayesian statistics to use mcmcglmm?
If some or all of those things make no sense to you, don’t worry – you can still use MCMCglmm without understanding all of this. Bayesian statistics sounds scary, but actually it’s more intuitive to understand (in my opinion) than frequentist statistics.