msBP (version 1.4-1)

msBP.compute.prob: 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)

Value

An object of the class msbpTree.

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).

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)