Segment 15 Sanmit Narvekar
1. In slide 4, we used "posterior predictive p-value" to get the respective p-values 1.0e-13, .01, .12, and .0013. What if we had mistakenly just used the maximum likelihood estimate r=0.003, instead of integrating over r? What p-values would we have obtained?
Here is the code for calculating the pvalues using the MLE estimate for r (the procedure is similar to that on slide 3):
r = 0.003; % T11 t11 = sum(binopdf(5:37, 9*37,r)) % T2 t2 = sum(binopdf(23:37,10*37, r)) % T13 -- Remember we only have 12 of the 37 values t13 = sum(binopdf(4:12, 10*12, r)) % T5 t5 = sum(binopdf(3:37, 10*37, r))
The calculated pvalues are:
t11 = 0.0036 % 0.01 using posterior predictive t2 = 7.8210e-23 % 1e10^-13 using posterior predictive t13 = 5.0435e-04 % 0.0013 using posterior predictive t5 = 0.1013 % 0.12 using posterior predictive
To Think About
1. Can you think of a unified way to handle the Towne family problem (estimating r and deciding which family members are likely "non-paternal") without trimming the data? We'll show one such method in a later segment, but there is likely more than one possible good answer.
Perhaps you could weigh outlier data less while forming your estimate of R.