Description Usage Arguments Details Value Author(s) Examples

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

1 2 3 4 5 6 7 8 | ```
# 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
``` |

`data` |
Design matrix: data.frame or matrix-like data, |

`pri_mean` |
priori mean: necessary vector which should be of the identical dimensions of data ( |

`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. |

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.

return a list of:

`mean` |
mean vector of Bayesian posterior |

`var` |
covariance of Bayesian posterior |

ZHANG Chen

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# 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]))
``` |

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