get.var: Internal function. With stratified samples, calculate the...

In thq80/Owen_2000_Safe-and-Effective-IS: Optimal Mixture Weights in Multiple Importance Sampling

Description

Internal function. With stratified samples, calculate the variance of the estimate from importance sampling without control variates

Usage

get.var(Y, nvec)

Arguments

Y	vector of stratified samples of length n. i.e. Y_1 = Y[1:nvec[1]] are sampled from q_1, Y_i = Y[(nvec[i-1]+1):nvec[i]] are sample from q_i.
nvec	the vector of number of samples from each mixture component. It sums up to n.

Details

Suppose we sample Y from a mixture q_{α} = α_1*q_1 + ... + α_J*q_J. To estimate \mathrm{mean}(Y), fixing the number of samples from each mixture component and getting a stratified sample would reduce the variance of the estimate. The formula for \mathrm{Var}(\hat{μ}) with stratified samples is

\mathrm{Var}(\hat{μ}) = 1/n \times ∑_{j=1}^J α_j \mathrm{Var}(Y_j)

Value

the variance estimate of \hat{μ} = 1/n ∑_{i=1}^n Y[i]

thq80/Owen_2000_Safe-and-Effective-IS documentation built on May 10, 2019, 9:53 a.m.