08-coverage-probability

[murraymegan]

Important Info: I will grade this before 12-6. Final Due Date will be 12-16 at 9am because of final grade deadlines.

[murraymegan]

FAIL

• Good setup! Code for first 4 steps is correct.
• Coverage probability should be less than 1.00 so there is an error in your code. First increase simulations to at least 1000. You do not have to show them all in the plot but this is important for the computation.
• In "sample_95_confidence" function you must first do: `samp= rnorm(201,0,1)

  get mle.mean and mle.sd`

• Then result[i] = median(rnorm(100, mle.mean, mle.sd))
• Please message me if you need further clarification!

[GGGGXY]

Hi Megan, i am so confused about this step "In "sample_95_confidence" function you must first do: samp= rnorm(201,0,1) #get mle.mean and mle.sd" I think i have already calculated the mean and standard deviation. Do you mean the step is as following: use new sample -> calculate mean and sd using MLE -> generate samples based on the information from previous step-> find median -> repeat previous two steps to get median distribution-> get the 95% CI of the distribution -> compare the 95% CI with the median of the new sample from step 1? Thanks!

[murraymegan]

sample_95_confidence <- function(){
  # 10000 samples
  sample <- rnorm(201,mean=0,sd=1)
# use mle to calculate the parameters based on the sample
ll_norm <- function(mean,sd){
  -sum(dnorm(sample,mean = mean,sd = sd,log=T))
}
z_norm <- mle(minuslogl=ll_norm, start=list(mean=1,sd=1),
                 method = "L-BFGS-B",
                 lower = c(0,0.01))
mean <- coef(z_norm)[1]
sd <- coef(z_norm)[2]
  result <- rep(NA, 10000)
  for (i in seq_along(result)){
    # each sample has 1000 values and find the median of each sample using quantile
    result[i] = quantile(rnorm(1000,mean = mean, sd = sd),0.5)
  }
  # find the minimum value among the 95% confidence interval
  x_0.025 = quantile(result,0.025)
  # fine the maximum value among the 95% confidence interval
  x_0.975 = quantile(result,0.975)
  return(c(x_0.025, x_0.975))
}

[murraymegan]

• You must regenerate "sample" in each outer loop. See code chunk^
• Does that help?
• Also you can message me on slack!

[soyeon-park1121]

FAIL

• I like your work!
• So you got "0.939" as your coverage probability. Can you explain what that means? You can explain what coverage probability is and what 0.939 means.

[soyeon-park1121]

PASS

Great job!