# Rproject3_script1_multinomial_simulation.r
#
# Parametric Bootstrap simulation of sampling distributions for alternate estimators
# Multinomial Counts: Hardy Weinberg Equilibrium
# 1.1 Trinomial data----
# from Example 8.5.1.A, p. 273 of Rice.
#
# x=(X1,X2,X3) # counts of multinomial cells (1,2,3)
# Erythrocyte antigen blood types of n=1029 Hong Kong population in 1937.
x<-c(342,500,187)
# 1.2 Two estimators: Multinomial MLE and Binomial(X3) MLE ----
x.n=sum(x)
x.theta.mle=(2*x[3] + x[2])/(2*sum(x))
x.theta.binomialx3=sqrt(x[3]/sum(x))
print(x.theta.mle)
## [1] 0.4246842
print(x.theta.binomialx3)
## [1] 0.4262978
# 2.0 Simulate sampling distribution of estimators ----
# 1000 trials (the sampling distribution) of the two estimators
# For each trial, generate sample of size n=1027 from the multinomial distribution
# w.samplespace=c(1,2,3); the outcomes/cells of the multinomial
# prob=fcn.probs.hardyweinberg(x.theta.mle); the cell probilities
#
# Compute estimates of the Hardy-Weinberg theta parameter
# by Multinomial MLE and Binomial(X3) MLE
# 2.1 R functions for the simulation ----
# function computing cell probabilities given Hardy-Weinberg theta parameter
fcn.probs.hardyweinberg<-function(theta0){
probs=c((1-theta0)**2, 2*theta0*(1-theta0), theta0**2)
return(probs)
}
# function computing cell counts given w.sample, a sample of single-outcome multinomial
# random variables (comparable to Bernoulli outcomes underlying a binomial)
fcn.w.sample.counts<-function(w.sample, w.samplespace){
result=0*w.samplespace
for (j.outcome in c(1:length(w.samplespace))){
result[j.outcome]<-sum(w.sample==w.samplespace[j.outcome])
}
return(result)
}
# 2.2 Validate functions for single trial example ----
args(sample)
## function (x, size, replace = FALSE, prob = NULL)
## NULL
w.samplespace=c(1,2,3)
w.sample= sample(x=w.samplespace,size=x.n,replace=TRUE,
prob=fcn.probs.hardyweinberg(x.theta.mle))
w.sample.counts<-fcn.w.sample.counts(w.sample, w.samplespace)
par(mfcol=c(1,1))
plot(w.sample,main=paste("Single Multinomial Trial (n=", as.character(x.n),")",sep=""))
![](data:image/png;base64,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)
print(table(w.sample))
## w.sample
## 1 2 3
## 351 489 189
print(w.sample.counts)
## [1] 351 489 189
# 2.3 Conduct Simulation ----
n.simulations=20000
data.simulations<-matrix(NA,nrow=n.simulations, ncol=2)
dimnames(data.simulations)[[2]]<-c("MLE","Alternate")
for (j.simulation in c(1:n.simulations)){
j.w.sample= sample(x=w.samplespace,size=x.n,replace=TRUE,
prob=fcn.probs.hardyweinberg(x.theta.mle))
j.w.sample.counts<-fcn.w.sample.counts(j.w.sample, w.samplespace)
x.j=j.w.sample.counts
# print(x.j)
x.j.theta.mle=(2*x.j[3] + x.j[2])/(2*sum(x.j))
x.j.theta.binomialx3=sqrt(x.j[3]/sum(x.j))
data.simulations[j.simulation,1]=x.j.theta.mle
data.simulations[j.simulation,2]=x.j.theta.binomialx3
}
# 3. Simulation Results ----
# 3.1 Histogram of estimators sampling distributions -----
par(mfcol=c(2,1))
print(simulations.means<-apply(data.simulations,2,mean))
## MLE Alternate
## 0.4248393 0.4246122
print(simulation.stdevs<-sqrt(apply(data.simulations,2,var)))
## MLE Alternate
## 0.01083837 0.01402613
hist(data.simulations[,1], main="Multinomial MLE")
abline(v=simulations.means[1] +c(-1,0,1)*simulation.stdevs[1], col=c(3,3,3))
hist(data.simulations[,2], main="Binomial(X3) MLE")
abline(v=simulations.means[2] +c(-1,0,1)*simulation.stdevs[2], col=c(2,2,2))
![](data:image/png;base64,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)
# 3.2 Histograms of estimation errors for each estimator ----
data.simulations.error=data.simulations-x.theta.mle
par(mfcol=c(2,1))
hist(data.simulations.error[,1] , main="Error of Multinomial MLE")
print(simulations.error.means<-apply(data.simulations.error,2,mean))
## MLE Alternate
## 1.551749e-04 -7.192265e-05
print(simulations.error.stdevs<-sqrt(apply(data.simulations.error,2,var)))
## MLE Alternate
## 0.01083837 0.01402613
abline(v=simulations.error.means[1] +c(-1,0,1)*simulations.error.stdevs[1], col=c(3,3,3))
hist(data.simulations.error[,2], main="Error of Binomial(X3) MLE")
abline(v=simulations.error.means[2] +c(-1,0,1)*simulations.error.stdevs[2], col=c(2,2,2))
![](data:image/png;base64,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)
# 3.3 Boxplot comparing sampling distributions ----
par(mfcol=c(1,1))
boxplot(data.simulations,
main="Simulated Sampling Distribution\nHardy-Weinberg Parameter")
![](data:image/png;base64,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)
# 3.4 Scatterplot of joint distribution of estimates ----
plot(data.simulations[,1], data.simulations[,2],xlab="Multinomial MLE", ylab="Binomial(X3) MLE")
abline(v=simulations.means[1] +c(-1,0,1)*simulation.stdevs[1], col=c(3,3,3))
abline(h=simulations.means[2] +c(-1,0,1)*simulation.stdevs[2], col=c(2,2,2))
![](data:image/png;base64,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)
# 4. Bootstrap Confidence Interval ----
head(data.simulations.error)
## MLE Alternate
## [1,] -0.0004859086 -0.004124118
## [2,] 0.0126336249 0.022746688
## [3,] -0.0068027211 -0.008771333
## [4,] 0.0034013605 0.002751979
## [5,] 0.0048590865 -0.007604675
## [6,] 0.0072886297 0.013972683
quantile(data.simulations.error[,1],probs=c(.05,.95))
## 5% 95%
## -0.01797862 0.01797862
quantile(data.simulations.error[,2],probs=c(.05,.95))
## 5% 95%
## -0.02303547 0.02274669
x.theta.mle
## [1] 0.4246842
x.theta.binomialx3
## [1] 0.4262978
# 4.1 Approximate 90% confidence interval based on MLE ----
approx.CI.limits.90percent.mle=x.theta.mle +c(- quantile(data.simulations.error[,1], probs=.95),
- quantile(data.simulations.error[,1],probs=.05))
approx.CI.limits.90percent.mle
## 95% 5%
## 0.4067055 0.4426628
# 4.2 Approximate 90% confidence interval based on BINOMIALX3 ----
approx.CI.limits.90percent.binomialx3=x.theta.binomialx3 +c(- quantile(data.simulations.error[,2], probs=.95),
- quantile(data.simulations.error[,2],probs=.05))
approx.CI.limits.90percent.binomialx3
## 95% 5%
## 0.4035511 0.4493333