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

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Description

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

Usage

1
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]