sir {BaM} R Documentation

## sir

### Description

Implementation of Rubin's SIR, see pages 338-341 (2nd Edition)

### Usage

sir(data.mat,theta.vector,theta.mat,M,m,tol=1e-06,ll.func,df=0)


### Arguments

 data.mat A matrix with two columns of normally distributed data theta.vector The initial coefficient estimates theta.mat The initial vc matrix M The number of draws m The desired number of accepted values tol The rounding/truncing tolerance ll.func loglike function for empirical posterior df The df for using the t distribution as the approx distribution

Jeff Gill

### Examples

## Not run:
sir <- function(data.mat,theta.vector,theta.mat,M,m,tol=1e-06,ll.func,df=0) {
importance.ratio <- rep(NA,M)
rand.draw <- rmultinorm(M,theta.vector,theta.mat,tol = 1e-04)
if (df > 0)
rand.draw <- rand.draw/(sqrt(rchisq(M,df)/df))
empirical.draw.vector <- apply(rand.draw,1,ll.func,data.mat)
if (sum(is.na(empirical.draw.vector)) == 0) {
print("SIR: finished generating from posterior density function")
print(summary(empirical.draw.vector))
}
else {
print(paste("SIR: found",sum(is.na(empirical.draw.vector)),
"NA(s) in generating from posterior density function, quiting"))
return()
}
if (df == 0) {
normal.draw.vector <- apply(rand.draw,1,normal.posterior.ll,data.mat)
}
else {
theta.mat <- ((df-2)/(df))*theta.mat
normal.draw.vector <- apply(rand.draw,1,t.posterior.ll,data.mat,df)
}
if (sum(is.na(normal.draw.vector)) == 0) {
print("SIR: finished generating from approximation distribution")
print(summary(normal.draw.vector))
}
else {
print(paste("SIR: found",sum(is.na(normal.draw.vector)),
"NA(s) in generating from approximation distribution, quiting"))
return()
}
importance.ratio <- exp(empirical.draw.vector - normal.draw.vector)
importance.ratio[is.finite=F] <- 0
importance.ratio <- importance.ratio/max(importance.ratio)
if (sum(is.na(importance.ratio)) == 0) {
print("SIR: finished calculating importance weights")
print(summary(importance.ratio))
}
else {
print(paste("SIR: found",sum(is.na(importance.ratio)),
"NA(s) in calculating importance weights, quiting"))
return()
}
accepted.mat <- rand.draw[1:2,]
while(nrow(accepted.mat) < m+2) {
rand.unif <- runif(length(importance.ratio))
accepted.loc <- seq(along=importance.ratio)[(rand.unif-tol) <= importance.ratio]
rejected.loc <- seq(along=importance.ratio)[(rand.unif-tol) > importance.ratio]
accepted.mat <- rbind(accepted.mat,rand.draw[accepted.loc,])
rand.draw <- rand.draw[rejected.loc,]
importance.ratio <- importance.ratio[rejected.loc]
print(paste("SIR: cycle complete,",(nrow(accepted.mat)-2),"now accepted"))
}
accepted.mat[3:nrow(accepted.mat),]
}
# The following are log likelihood functions that can be plugged into the sir function above.

logit.posterior.ll <- function(theta.vector,X) {
Y <- X[,1]
X[,1] <- rep(1,nrow(X))
sum( -log(1+exp(-X
-log(1+exp(X)))))
}

normal.posterior.ll <- function(coef.vector,X) {
dimnames(coef.vector) <- NULL
Y <- X[,1]
X[,1] <- rep(1,nrow(X))
e <- Y - X
sigma <- var(e)
return(-nrow(X)*(1/2)*log(2*pi)
-nrow(X)*(1/2)*log(sigma)
-(1/(2*sigma))*(t(Y-X)*(Y-X)))
}

t.posterior.ll <- function(coef.vector,X,df) {
Y <- X[,1]
X[,1] <- rep(1,nrow(X))
e <- Y - X
sigma <- var(e)*(df-2)/(df)
d <- length(coef.vector)
return(log(gamma((df+d)/2)) - log(gamma(df/2))
- (d/2)*log(df)
-(d/2)*log(pi) - 0.5*(log(sigma))
-((df+d)/2*sigma)*log(1+(1/df)*
(t(Y-X*(Y-X)))))
}

probit.posterior.ll <- function (theta.vector,X,tol = 1e-05) {
Y <- X[,1]
X[,1] <- rep(1,nrow(X))
Xb <- X
h <- pnorm(Xb)
h[h<tol] <- tol
g <- 1-pnorm(Xb)
g[g<tol] <- tol
sum( log(h)*Y + log(g)*(1-Y) )
}

## End(Not run)



[Package BaM version 1.0.3 Index]