How to count number of fish in an odd shaped pond? The Capture-Mark-Recapture technique of estimation Let’s say that we first captured 80, marked them and released them back. (m=80) A few days later, catch 60 (n=60) [sample set] 13 of them are from m. (k=13) N-hat : 80 = 60:13 Okay, very clever. But how good is this estimate? Bootstrapping can g…

fish_resampling.R

BigN<- NULL # BigN is the DISTRIBUTION of N.hats
m <- 80 # initial number of fish that we caught and marked and released
n <- 60 # the fish that were caught again. Our "sample”
for(i in 1:5000) {
  s <- sample.int(n, replace=T) #resampling from our second captured set
  k <- sum(s<14) # how many of them were the marked ones
  N.hat  <- (m * n)/k 
  BigN <- c(N.hat, BigN)  
}
# Let's inspect what we got 
library(ggplot2)
ggplot() + geom_histogram(aes(BigN), binwidth=25)
#Explore
mean(BigN)
summary(BigN)
sd(BigN)
t.test(BigN) # Confidence Interval for the Mean
wilcox.test(BigN, conf.int=TRUE) #confidence Interval for the Median
median(BigN) #Note that it is different from the Wilcox (pseudo-Mean)