approximateInverseWishart: approximateInverseWishart

In SampleSizeShop/invWishartSum: An approximation to the distribution of inverse Wishart sums

Description

Approximate the distribution of a sum of inverse Wishart matrices or a sum of quadratic forms in inverse Wishart matrices with a single inverse Wishart.

Usage

approximateInverseWishart(invWishartList, method = "trace",
  scaleMatrixList = NULL, cell = NULL)

Arguments

invWishartList	the list of inverse Wishart matrices in the sum
method	the moment-matching approach to use. Valid values are trace, log-determinant, and cell
scaleMatrixList	optional, list of scale matrices to form a sum of quadratic forms. There must be one scale matrix for each inverse Wishart in the invWishartList.
cell	optional, a vector containing the row and column of the cell used for variance matching when using method='cell'

Details

Three approximation methods are currently supported

1. trace: The default method which matches the expectation of the sum and the variance of the trace of the sum

2. logDeterminant: A method which matches the expectation of the sum and the expectation of the log determinant of the sum

3. cell: A method which matches the expectation of the sum and the variance of a specified cell of the sum

For quadratic forms, a list of scale matrices should be specified which will be pre- and post- multiplied onto each inverse Wishart. For example, for the inputs invWishartList = c(X1, X2) and scaleMatrixList = c(A,B), the function will calculate the approximate distribution of A'X1A + B'X2B

Value

the approximating inverse Wishart object

References

The trace method implements the approach of:
Kreidler, S. M., Muller, K. E., & Glueck, D. H. An Approximation to the Distribution of the Sum of Inverse Wishart Matrices, In review.

The logDeterminant method is based on the approach of:
Granstrom, K., & Orguner, U. (2012). On the reduction of Gaussian inverse Wishart mixtures. In 2012 15th International Conference on Information Fusion (FUSION) (pp. 2162-2169).

See Also

inverseWishart

SampleSizeShop/invWishartSum documentation built on Feb. 5, 2022, 5:04 a.m.