Mposterior (version 0.1.2)

findWeiszfeldMedian: Find M-posterior using samples from subset posteriors

Description

Find M-posterior given list of samples from subset posteriors using Weiszfeld algorithm of Minsker et al. (2014).

Usage

findWeiszfeldMedian(subsetAtomsList, sigma = 0.1, maxit = 100, tol = 1e-10)

Arguments

subsetAtomsList

list of samples from subset posteriors; each element of the list must be a matrix

sigma

parameter of RBF kernel with form exp(- sigma || x - y ||^2)

maxit

maximum number of iterations estimating M-posterior

tol

tolerance for declaring convergence of Weiszfeld algorithm

Value

list containing Weiszfeld wts of subset posteriors, M-posterior atoms, and the estimation set-up

Details

Samples from subset posteriors are represented as matrices, with the rows representing atoms and the columns indexing dimensions. Length of subsetAtomsList equals the number of subsets (and posteriors). M-posterior estimates the weights of its atoms given the atoms of subset posteriors using Weiszfeld algorithm as implemented in findWeiszfeldMedian; sigma controls the sensitivity of distance between subset posteriors.

References

Minsker, S., Srivastava, S., Lin, L., and Dunson, D.B. (2014). Robust and Scalable Bayes via a Median of Subset Posterior Measures. http://arxiv.org/abs/1403.2660

Examples

set.seed(12345)
## list that contains subset posterior samples from 2-dim Gaussian density
subAtomList <- vector("list", 5)
subAtomList[[1]] <- cbind(rnorm(100, mean = 1),  rnorm(100, mean = 1))
subAtomList[[2]] <- cbind(rnorm(100, mean = -1),  rnorm(100, mean= -1))
subAtomList[[3]] <- cbind(rnorm(100, mean = -1),  rnorm(100, mean = 1))
subAtomList[[4]] <- cbind(rnorm(100, mean = 1),  rnorm(100, mean = -1))
subAtomList[[5]] <- cbind(rnorm(100, mean = 2),  rnorm(100, mean = 2))
library(Mposterior)
medPosterior <- findWeiszfeldMedian(subAtomList, sigma = 0.1, maxit = 100, tol = 1e-10)
medPosterior
summary(medPosterior)
plot(medPosterior)