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I got a bit bored (sorry Mike), and wrote this. I didn’t take long (I tell you that not so much to cover my backside as to celebrate the majesty of R). First, I estimated probabilities of a day being rainy if the previous was dry, and of it being rainy if the previous day was rainy. I couldn’t be bothered with any thinking, so I used ABC, which basically is an incredibly simple and intuitive way of finding parameters than match data. I started with 16 rain days in July and 15 in August, in my home town of Winchester (which is also Swithun’s hood) from here, and that led to probabilities that I plugged into a simulator (it’s only AR1, but I’m no meteorologist). That ran 10,000 years of 40-day periods (there’s a sort of run-in of ten days to get to a stable distribution first; it’s basically a Markov chain), and not a single one had rain for 40 days.

It ain’t gon’ rain.

# Estmiate Winchester July/August rainy day transition probabilities
# We'll use Approximate Bayesian Computation
abciter<-1000
drytorain<-seq(from=0.15,to=0.35,by=0.01)
raintorain<-seq(from=0.5,to=0.7,by=0.01)
ldr<-length(drytorain)
lrr<-length(raintorain)
pb<-txtProgressBar(0,ldr*lrr*abciter,style=3)
loopcount<-1
prox<-matrix(NA,nrow=ldr,ncol=lrr)
for(i in 1:ldr) {
for(j in 1:lrr) {
trans<-c(drytorain[i],raintorain[j])
rainydays<-rep(NA,abciter)
for(k in 1:abciter) {
setTxtProgressBar(pb,loopcount)
runin<-rep(NA,10)
runin[1]<-rbinom(1,1,0.4)
for (m in 2:10) {
runin[m]<-rbinom(1,1,trans[runin[m-1]+1])
}
days<-rep(NA,40)
days[1]<-rbinom(1,1,trans[runin[10]+1])
for (m in 2:40) {
days[m]<-rbinom(1,1,trans[days[m-1]+1])
}
rainydays[k]<-sum(days)
loopcount<-loopcount+1
}
prox[i,j]<-sum(abs(rainydays-15.5)<1)/abciter
rainydays<-rep(NA,abciter)
}
}
close(pb)
image(prox)
# I'm going to go with P(rain | dry)=0.32, P(rain | rain)=0.51

# St Swithun's Day simulator
prain<-c(0.32,0.51),nrow=2)
iter<-10000
runs<-rep(NA,iter)

pb<-txtProgressBar(0,iter,style=3)
for (i in 1:iter) {
setTxtProgressBar(pb,i)
runin<-rep(NA,10)
runin[1]<-rbinom(1,1,0.4)
for (j in 2:10) {
runin[j]<-rbinom(1,1,trans[runin[j-1]+1])
}
days<-rep(NA,40)
days[1]<-rbinom(1,1,trans[runin[10]+1])
for (j in 2:40) {
days[j]<-rbinom(1,1,trans[days[j-1]+1])
}
runs[i]<-max(rle(days)\$lengths)
}
close(pb)
print(paste("There were ",sum(runs==40),
" instances of St Swithun's Day coming true, over ",
iter," simulated years.",sep=""))
hist(runs)</code>