MVN_BayesianPosterior: MVN_BayesianPosterior

In CubicZebra/MVNBayesian: Bayesian Analysis Framework for MVN (Mixture) Distribution

Description

Given a design matrix (data) and priori information, export the mean vector and covariance matrix of Bayesian posterior multivariate normal distribution.

Usage

# Given the data as design matrix, priori mean vector and priori covariance
# matrix, this function will export a list which contains mean ($mean) and
# covariance ($var) of Bayesian posterior multivariate normal distribution.

MVN_BayesianPosterior(data, pri_mean, pri_var)

# defualt pri_mean uses colMenas()
# defualt pri_var uses unit matrix

Arguments

data	Design matrix: data.frame or matrix-like data, dim(data)[1] should be the number of observations and dim(data)[2] should be the number of variables or parameters.
pri_mean	priori mean: necessary vector which should be of the identical dimensions of data (length(pri_mean) == dim(data)[2]). Users can set according to their own prior knowledge.
pri_var	prior covariance matrix: a real symmetric matrix by definition; the default value is an unit matrix with the same dimension of priori mean vector.

Details

Although this function is very simple, the observation data should be diagnosed firstly. it is strongly recommanded that researchers and developers should have some prior knowledge of ill-conditioned system before using this function. Simply, ill-conditioned system, or singular matrix, is caused by a) insufficient data or b) almostly linear dependency of two certain parameters, which two can result in a too small eigenvalue then cause a ill-conditioned (singular) system. Therefore users should make sure the data contains enough observations and the degree of freedom is strictly equal to the number of parameters.

Value

return a list of:

mean	mean vector of Bayesian posterior
var	covariance of Bayesian posterior

Author(s)

ZHANG Chen

Examples

# Demo using dataset1:
head(dataset1)
BPos <- MVN_BayesianPosterior(dataset1, c(80,16,3))
BPos$mean
BPos$var

# Singular system caused by insufficient data
eigen(var(dataset1[1:3,]))$values
rcond(var(dataset1[1:3,]))
eigen(var(dataset1[1:6,]))$values
rcond(var(dataset1[1:6,]))

# Singular system caused by improper degree of freedom
K <- cbind(dataset1, dataset1[,3]*(-2)+3)
eigen(var(K[,2:4]))$values
rcond(var(K[,2:4]))

CubicZebra/MVNBayesian documentation built on May 17, 2019, 2:14 a.m.