Segment 15 Sanmit Narvekar

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Segment 15

To Calculate

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.