Transcript Monte Carlo methods - Applied Biomathematics Inc

Answer to #1
How could you sample deviates from a normal and a
lognormal distribution that have opposite dependence?
Use inverse transform sampling with the uniform deviate for
the lognormal deviate equal to one minus the uniform deviate
for the normal. In R, this can be done with the following script:
p <- runif(200)
x <- qnorm(p, mean=0, sd=1)
y <- qlnorm(1 - p, meanlog=1, sdlog=1)
30
plot(x,y)
In Excel, similar calculations can be
20
done with this construction:
y
A=RAND()
10
B=NORMINV(A,0,1)
C=LOGINV(1-A,1,1)
0
-2 -1 0 1
x
2
Answer to #2
Why is the concentration generally modeled as a point value in
PRA’s? Under what conditions should a distribution be used?
It’s usually modeled as a point value because receptors (e.g.,
individual mink, or duck hunters) experience many independent
exposures (fish/invertebrate prey, or meals of duck tissue). In
effect, the receptor integrates these many independent
exposures over time and so his or her exposure is the average
of the concentration distribution. When the number of
exposures (meals) is few, then there is less contraction to the
mean. In general, the standard deviation of the distribution of
means from independent samples taken from a distribution with
standard deviation s is s/N where N is the number of samples
being averaged.
Answer to #3
What are the implications of using a uniform distribution to
model an interval range?
If the interval range is representing incertitude, then the
incertitude is treated as though it is variability. This would
confound the two forms of uncertainty, the result would likely
be an underestimate of the uncertainty in the quantitative
output.