You know (Maxwell’s devil told you) that the value of bilirubin in the blood of a healthy person is a Gaussian random variable with mean 0 and variance 02; a person with pancreas tumor has the value of bilirubin in the blood which is again Gaussian with mean 1 and variance 12. You decide that the bilirubin test is positive if the measured bilirubin value is above threshold
.
Write the formulas of your test speci city and sensitivity. Let us say that the incidence of pancreas tumor in the population is p. Write the formulas for the probabilities P (DyjTp) that a person really is a ected by pancreas tumor given that the test is positive and P (DnjTn) that a person really is healthy given that the test is negative.
Write a Matlab script that plots:
test sensitivity and speci city as functions of the threshold T
P (DyjTp) as function of T and p (a surface, you can use mesh or meshc)
P (DnjTn) as function of T and p (a surface, you can use mesh or meshc)
the superimposed contour plots of P (DyjTp) and P (DnjTn) at probability values 0:5; 0:9; 0:99; 0:999; 0:9999
Use initially
0=10, 02=4 1=15, 12=8
then, once you can plot the results for this case, change these values and comment the results.
