# MVN_FConditional: Calculate full conditional normal ditribution of MVN In CubicZebra/MVNBayesian: Bayesian Analysis Framework for MVN (Mixture) Distribution

## Description

Function to export parameters of full conditional normal distribution in basis of given MVN distribution, the undecided dimension, as well as all values in the rest dimensions.

## Usage

 ```1 2 3 4 5``` ```# Bayesian posteriori as input data: # data <- MVN_BayesianPosteriori(dataset1, c(80,16,3)) # inquire parameters of full-conditional distribution based on Bayesian posteriori: MVN_FConditional(data, variable, z) ```

## Arguments

 `data` A double level list containing all parameters of MVN distribution: mean vector (`data\$mean`) and covariance matrix (`data\$var`). `variable` A integer to specify the undecided dimension. `z` A nd-vector to assign conditions (n = dimensions of given MVN distribution). It should be noted that the value in dimension specified by `variable` doesn't participate in the calculation.

## Details

It can be proved that any full conditional distribution from a given MVN will degenerate to an 1d-normal distribution.

## Value

return a double level list containing the following parameters of full conditional normal distributions of given MVN in specified dimension:

 `mean` a numberic mean of a normal distribution `var` a numberic variance of a normal distribution

`MVN_BayesianPosteriori`, `MatrixAlternative`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```head(dataset1) BPos <- MVN_BayesianPosteriori(dataset1, c(80,16,3)) BPos # Bayesian Posteriori result <- MVN_FConditional(BPos, variable = 1, z=c(75, 13, 4)) result\$mean class(result\$mean) result\$var class(result\$var) # compare the following results: MVN_FConditional(BPos, variable = 2, z=c(75, 13, 4)) MVN_FConditional(BPos, variable = 2, z=c(75, 88, 4)) MVN_FConditional(BPos, variable = 1, z=c(75, 88, 4)) ```