MVN_BayesianIterator {MVNBayesian}

Parameter estimation using Bayesian iteration

Description

Function to execute parameter estimation for MVN distribution, under Bayesian analysis framework.

Usage

# Get parameters of Bayesian posteriori MVN:
MVN_BayesianIterator(data, pri_mean=colMeans(data), Gibbs_nums=5000,
pseudo_nums=dim(data)[1], threshold=1e-04, iteration=100, ...)

Arguments

data

A data.frame or matrix-like data: obervations should be arrayed in rows while variables should be arrayed in columns.

pri_mean

A numeric vector to assign priori mean for MVN. Default value applies colMeans() to data.

Gibbs_nums

A positive integer. The numbers of random vectors to be generated for each iteration step. Defult value is 5000.

pseudo_nums

A positive integer. The argument to determine numbers of generated vectors used for each iteration step. Default value keeps the same scale as input data. Notice that a too small value can result in singular matrix.

threshold

A numeric value to control stoping the iteration loop. Default value used 0.0001. While the Euclidean distance of mean vectors between pseudo-data (the last pseudo_nums items) and Bayesian posteriori is less than threshold, iteration stops.

iteration

A positive integer. Argument to assign the maximum steps for iteration. Default value is 100 after which the iteration loop will compulsively exit.

...

Other arguments to control the process in Gibbs sampling.

Details

Because that MVN distribution possess conjugated property in Bayesian analysis framework, the convergence of Bayesian iterator for MVN distribution can be ensured, accoumpanied with the shrink of 2nd-norm of Bayesian posteriori covariance matrix. But pay attention to the fact that pseudo-data leads to the randomness, the argument pseudo_nums should be set carefully.

Value

return a double level list containing Bayesian posteriori after iteration process:

mean

Bayesian posteriori mean vector

var

Bayesian posteriori covariance matrix

Note

If the parameter values are the only interested thing we concerned, this iterator makes sense. Since it can significantly help us decrease the scale of covariance matrix, to obtain a more reliable estimation for the parameters. However, in more cases, some correlationships of a certain group of pamameters are more valuable, which are usually clued by the covariance matrix.

See Also

MVN_BayesianPosteriori, MVN_GibbsSampler, MVN_FConditional, MatrixAlternative

Examples

library(mvtnorm)

# Bayesian posteriori before iteration using dataset1 as example,
# c(80, 16, 3) as priori mean:
# View 2-norm of covariance matrix of Bayesian posteriori:
BPos_init <- MVN_BayesianPosteriori(dataset1, c(80,16,3))
BPos_init
norm(as.matrix(BPos_init$var), type = "2")

# Bayesian posteriori after iteration using c(80,16,3) as priori
# Using 30 last samples generated by GibbsSampler for each step:
BPos_fina1 <- MVN_BayesianIterator(dataset1, c(80,16,3), 5000, 30)
BPos_fina1
norm(as.matrix(BPos_fina1$var), type = "2")

# Too small pseudo_nums setting can results in singular system, try:
MVN_BayesianIterator(dataset1, pseudo_nums=3)