msBP.compute.prob {msBP}

Compute binary tree of probabilities

Description

Compute the binary tree of probabilities using the multiscale stick-breaking process of Canale and Dunson (2016).

Usage

msBP.compute.prob(msBPtree, root = TRUE)

Arguments

msBPtree

An object of the class msBPTree

root

logical. if the root needs to be considered (default) or it should be cut (fixing S_{01} = 0)

Details

Compute a binary tree of weights. The general weights for node h of scale s, is

\pi_{s,h} = S_{s,h} \prod_{r<s} (1-S_{r,g_{shr}}) T_{shr}

where g_{shr} = \lceil h/2^{s-r} \rceil and T_{shr} = R_{r,g_{shr}} if (r+1,g_{shr+1}) is the right daughter of node (r,g_{shr}), or T_{shr} = 1-R_{r,g_{shr}} if (r+1,g_{shr+1}) is the left daughter of (r,g_{shr}). An object of the msBPTree class is basically a list containing two objects of the class binaryTree: the S tree (representing the stoping probabilities) and the R tree (representing the proceed-right probabilities).

Value

An object of the class msbpTree.

References

Canale, A. and Dunson, D. B. (2016), "Multiscale Bernstein polynomials for densities", Statistica Sinica, 26(3), 1175-1195.

Canale, A. (2017), "msBP: An R Package to Perform Bayesian Nonparametric Inference Using Multiscale Bernstein Polynomials Mixtures". Journal of Statistical Software, 78(6), 1-19.

See Also

msBP.rtree

Examples

S <-structure(list( T = list(1/8,c(1/3,1/3), c(1/4,1/4,1/4,1/4), 
	rep(1,8)), max.s=3), class  = "binaryTree")
R <-structure(list( T = list(1/2,c(1/2,1/2), c(1/4,1/2,1/2,1/2), 
	rep(1,8)), max.s=3), class  = "binaryTree")
RS <-structure(list(S = S, R = R), class  = "msbpTree")
probabilities <- msBP.compute.prob(RS)