On Wed, 17 Dec 2008, Chris Oldmeadow wrote:
Hi all, I was hoping somebody may know of a function for simulating a large
binary sequence (length >10 million) using a (1st order) markov model with
known (2x2) transition matrix. It needs to be reasonably fast.
Chris,
The trick is to recognize that the length of each run is a sample from
the geometric distribution (with 1 added to it). rgeom() is vectorized,
so using it provides fast results.
Suppose that your transition matrix is
| | 0 | 1 |
|---+-------+-------|
| 0 | pi.11 | pi.12 |
| 1 | pi.21 | pi.22 |
|---+-------+-------|
where pi.11+p.12 == 1 and pi.21+pi.22 == 1
This function
foo <- function(n,pi.12,pi.21) inverse.rle( list(values=rep(0:1,n) ,
lengths=1+rgeom( 2*n, rep( c( pi.12, pi.21 ), n) )))
will generate a sequence of 0/1's according to that matrix with length
approximately n/pi.12+n/pi.21
On my macbook I get this timing:
system.time(res <- foo(1205000,.3,.2))
user system elapsed
1.088 0.204 1.291
prop.table(table(head(res,-1),tail(res,-1)),1) # check!
0 1
0 0.6999024 0.3000976
1 0.1997453 0.8002547
length(res) # long enough!
[1] 10048040
So, if this is fast enough, you just choose 'n' to be a bit larger
than desired length divided by (1/pi.12+1/pi.21) and then discard the
excess.
Chuck
I have tried
the following;
mc<-function(sq,P){
s<-c()
x<-row.names(P)
n<-length(sq)
p1<-sum(sq)/n
s[1] <- rbinom(1,1,p1);
for ( i in 2:n){
s[i] <- rbinom( 1, 1, P[s[i-1]+1] )
}
return(s)
}
P<-c(0.63,0.27)
x<-rbinom(500,1,0.5)
new<-mc(x,P)
thanks in advance!
Chris
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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