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

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]


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