We generate 10000 Observations with mean 10 and multiplicative standard deviation of 1.5.
nObs <- 200; nRep <- 1000
#nObs <- 1000; nRep <- 100
xTrue <- rep(10, nObs)
sigmaStar <- rep(1.5, nObs) # multiplicative stddev of 1.2
theta <- getParmsLognormForExpval(xTrue, sigmaStar)
# generate observations with correlated errors
acf1 <- c(0.4,0.1)
corrM <- setMatrixOffDiagonals(
diag(nrow = nObs), value = acf1, isSymmetric = TRUE)
xObsN <- exp(mvtnorm::rmvnorm(
nRep, mean = theta[,1]
, sigma = diag(theta[,2]) %*% corrM %*% diag(theta[,2])))
ds <- tibble(i = 1:nObs, xTrue, xObs = xObsN[1,], xErr = xObs - xTrue)
summary(rowSums(xObsN))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1728 1941 2000 2000 2053 2353
#plot(density(rowSums(xObsN)))
(effAcf <- computeEffectiveAutoCorr(ds$xErr))
## [1] 1.0000000 0.2078811
(nEff <- computeEffectiveNumObs(ds$xErr))
## [1] 141.4744
Due to autocorrelation, the effective number of parameters is less than nObs = R nObs
.
coefSum <- estimateSumLognormal( theta[,1], theta[,2], effAcf = effAcf )
(sumExp <- getLognormMoments( coefSum[1], coefSum[2])[1,"mean"])
## mean
## 2000